$P_{v}$ [2]. We call a point where this happens a _gulls-point_ of $M$

The goose (resp. butterfly) singularities of $P_{v}$ appear at special points
on the parabolic (resp. flecnodal) curve. We call a point on $M$ where these
singularities occur a _goose-point_ (resp. _butterfly-point_) on $M$.

The above robust features are defined in terms of the principal curvatures
$\kappa_{1}$ and $\kappa_{2}$. We can suppose $\kappa_{1}<\kappa_{2}$ (away
from umbilic curves) and give different colors to the robust features
associated to each principal curvature. For instance, we can have a blue ridge
(associated to $\kappa_{1}$) and a red ridge (associated to $\kappa_{2}$).

###  6.2 The geometry of $k$-folding map-germs

We obtain here the robust features determined by the singularities of
$k$-folding map-germs, for $k\geq 3$. We start with the case where $p$ is not
an umbilic point and treat the $k=3$ case separately.

###### Theorem 6.1

Let $M$ be a generic surface in $\mathbb{R}^{3}$, $p$ a non umbilical point on
$M$ and $\pi$ a plane through $p$ and orthogonal to $v$. The map-germ
$F_{3}^{\pi}$ at $p$ is an immersion if, and only if, $v$ is not tangent to
$M$ at $p$. It has an $S_{1}$-singularity if, and only if, $v\in T_{p}M$ but
is neither a principal nor an asymptotic direction. We have the following when
$v$ is a principal or an asymptotic direction at $p$.

  1. (1)

If $v$ is a principal direction at $p$, then the possible singularities of
$F_{3}^{\pi}$ at $p$ and their geometric characterisations are as follows:

$S_{3}$: |  $p$ is not on the sub-parabolic curve associated to $v$.
---|---
$S_{5}$: |  $p$ is a generic point on the sub-parabolic curve associated to $v$.
$S_{7}$: |  $p$ is an $S_{3}$-point on the sub-parabolic curve associated to $v$.

  2. (2)

Suppose that $v$ is an asymptotic and that $p$ is a hyperbolic point. Then
$F_{3}^{\pi}$ has a singularity at $p$ of type $H_{k},k=2,3,4$. The
$H_{3}$-singularities occur on a regular curve on $M$. We call its closure the
$H_{3}$-curve. The $H_{4}$-singularities occur at isolated points on this
curve.

  3. (3)

If $p$ is a parabolic point and $v$ is the unique asymptotic direction at $p$
which is also a principal direction, then the possible topological classes of
$F_{3}^{\pi}$ at $p$ and their geometric characterisations are as follows:

$X_{4}$: |  $p$ is a generic point on the parabolic curve.
---|---
${\bf U}^{3}_{4}$: |  $p$ is an $A_{2}^{*}$-point (see [11, 12]); it is on the closure of the $H_{3}$-curve.
${\bf X}^{3}_{4}$: |  $p$ is on the sub-parabolic curve associated to $v$; the principal map with value $v$ at $p$ has a beaks singularity at $p$ ([9]).
${\bf W}^{3,1}_{4}$: |  $p$ is on the sub-parabolic curve associated to the other principal direction $v^{\perp}$; it is on the closure of the $H_{3}$-curve; the frame map has a cross-cap singularity at $p$ ([9]).

  * Proof

The proof follows by considering the defining equations and the open
conditions of the strata of $3$-folding map-germs in Theorem 4.4 and the
geometric interpretation of the algebraic conditions in Table 1 given in
Tables 8 and 9. $\Box$

###### Proposition 6.2

The $H_{3}$-curve of a generic surface is a regular curve and meets the
parabolic curve tangentially at $A_{2}^{*}$ and ${\bf W}^{3,1}_{4}$-points.

  * Proof

The regularity of the $H_{3}$-curve follows by a transversality argument. We
compute the 1-jets of the parabolic and $H_{3}$-curves and find that they are
tangential at their points of intersection. This is expected as the
$H_{3}$-singularities of $F_{3}^{\pi}$ occur when $v$ is an asymptotic
direction, so the $H_{3}$-curve lies in the closure of the hyperbolic region
of the surface. $\Box$

We turn now to the case $k\geq 4$, still assuming $p$ not to be an umbilical
point. We recall that some topological classes in Tables 2, 4, 6 come with
divisibility conditions on $k$. For example, the ${\bf N}^{k}_{3}$ class
requires $2\mid k$ (see Remarks 6.4).

###### Theorem 6.3

Let $k\geq 4$ and let $M$ be a generic surface in $\mathbb{R}^{3}$, $p$ a non
umbilical point on $M$ and $\pi$ a plane through $p$ and orthogonal to $v$.
The map-germ $F_{k}^{\pi}$ at $p$ is an immersion if, and only if, $v$ is not
tangent to $M$ at $p$. It has a singularity which is topologically equivalent
to $M^{k}_{1}$ if, and only if, $v\in T_{p}M$ but is neither a principal nor
an asymptotic direction at $p$. We have the following when $v$ is a principal
or an asymptotic direction at $p$.

  1. (1)

If $v$ is a principal direction at $p$, then $F_{k}^{\pi}$ belongs to a
stratum in Table 2. The possible topological classes of $F_{k}^{\pi}$ and
their geometric interpretations are as follows:

${\bf M}^{k}_{2}$: |  $p$ is not on the sub-parabolic curve associated to $v$.
---|---
${\bf M}^{k}_{3}$: |  $p$ is a generic point on the sub-parabolic curve associated to $v$.
${\bf M}^{k}_{4}$: |  $p$ is an $S_{3}$-point on the sub-parabolic curve associated to $v$.
${\bf N}^{k}_{3}$: |  $p$ is a generic point on the ridge curve associated to $v$.
${\bf N}^{k}_{4}$: |  $p$ is a $B_{3}$-point on the ridge curve associated to $v$.
${\bf O}^{k}_{4}$: |  $p$ is a $C_{3}$-point (intersection point of the ridge and sub-parobolic curves associated to $v$).

  2. (2)

If $p$ is a hyperbolic point and $v$ is an asymptotic direction at $p$, then
$F_{k}^{\pi}$ belongs to a stratum in Table 4. The possible topological
classes of $F_{k}^{\pi}$ and their geometric interpretations are as follows:

${\bf P}^{k}_{2}$: |  $p$ is not on the flecnodal curve associated to $v$, and is not on the $H_{3}$-curve associated to $v$ when $3\mid k$.
---|---
${\bf P}^{k}_{3}$: |  $p$ is a generic point on the $H_{3}$-curve associated to $v$.
${\bf P}^{k}_{4}$: |  $p$ is an $H_{4}$-point on the $H_{3}$-curve associated to $v$.
${\bf Q}^{k}_{3}$: |  $p$ is a generic point on the flecnodal curve associated to $v$.
${\bf Q}^{k}_{4}$: |  $p$ is a point of intersection of the flecnodal and $H_{3}$-curves associated to $v$.
$\widetilde{\bf Q}^{k}_{4}$: |  $p$ is a special point on the flecnodal curve associated to $v$.
${\bf R}^{k}_{4}$: |  $p$ is a butterfly-point on the flecnodal curve associated to $v$.

  3. (3)

If $p$ is a parabolic point and $v$ is an asymptotic (and a principal)
direction at $p$, then $F_{k}^{\pi}$ belongs to a stratum in Table 6. The
possible topological classes of $F_{k}^{\pi}$ and their geometric
interpretations are as follows:

${\bf U}^{k}_{3}$: |  $p$ is a generic point on the parabolic curve.
---|---
${\bf U}^{k}_{4}$: |  $p$ is an $A^{*}_{2}$-point.
${\bf V}^{k,j,j^{\prime}}_{4}$: |  $p$ is a special point on the parabolic curve.
${\bf W}^{k,j}_{4}$: |  $p$ is a special point on the parabolic curve.
${\bf W}^{3q,q}_{4}$: |  $p$ is on the sub-parabolic curve associated to $v^{\perp}$; it is on the closure of the $H_{3}$-curve associated to $v$; the frame map has a cross-cap singularity at $p$ ([9]).
${\bf X}^{k}_{4}$: |  $p$ is on the intersection of the parabolic and sub-parabolic curves associated to $v$; the principal map with value $v$ at $p$ has a beaks singularity at $p$ ([9]).
${\bf Y}^{k}_{4}$: |  $p$ is a cusp of Gauss point and a gulls-point.

  * Proof

With the setting as in the proof of Theorem 6.1, the results follow by
interpreting the conditions in Tables 2, 4 and 6 using Tables 8 and 9. $\Box$

###### Remarks 6.4

1\. The singularities in Branches 1 and 2 are associated to principal
directions, those in Branch 3 to asymptotic directions at hyperbolic points
and those in Branch 4 to asymptotic directions at parabolic points.

2\. Theorems 6.1 and 6.3 show clearly that $k$-folding maps capture the robust
features obtained by $2$-folding maps and by the contact of the surface with
lines, planes and spheres, giving thus new geometric characterisations of
these features and a unified approach to study them. We also obtain a new
1-dimensional robust feature (the $H_{3}$-curve) and several $0$-dimensional
ones: the $H_{4}$, ${\bf Q}^{k}_{4}$, $\widetilde{\bf Q}^{k}_{4}$, ${\bf
V}^{k,j,j^{\prime}}_{4}$ and ${\bf W}^{k,j}_{4}$ points.

3\. The $H_{3}$-curve is captured by $k$-folding maps when $k$ is divisible by
$3$. The sub-parabolic and flecnodal curves are captured by $k$-folding maps
for any $k$ while the ridge curve is captured by $k$-folding maps when $k$ is
even. Regarding the ridge, it is the locus of points where the surface has
more infinitesimal symmetry with respect to planes ([10]). The map-germs
$(x,y)\mapsto(x,y^{2p},f(x,y))$ identify the pair of points $(x,y)$ and
$(x,-y),$ which explains why all the $F_{2p}$ folding maps capture the ridge
curve.

4\. The condition $\Delta_{j}^{k}=0$ can be satisfied for any $k,j$ when the
coefficients $a_{sl}$ are real, so ${\bf W}^{k,j}_{4}$-points can occur on
surfaces in $\mathbb{R}^{3}$ for all $k,j$. For the ${\bf
V}^{k,j,j^{\prime}}_{4}$ topological class, it follows from Proposition 4.21
that only ${\bf V}^{k,j,k-j}_{4}$, ${\bf V}^{k,j,2j}_{4}$ and ${\bf
V}^{k,k-j,2j}_{4}$-points can occur on surfaces in $\mathbb{R}^{3}$.

5\. Theorem 6.1 gives a new geometric interpretation for the
$A^{*}_{2}$-points in [11, 12].

6\. Observe that the open conditions (those involving expressions $\neq 0$)
for the singularities of the $k$-folding map in Tables 1, 2, 4, 6 and their
associated ones in Tables 8 and 9 are not always identical. For the
$0$-dimensional robust features, the open conditions in both tables are
satisfied on a generic surface. For the $1$-dimensional robust features, this
means that some special points in one setting are not special in the other.
For example, the $3$-folding map does not distinguish between a $C_{3}$-point
and a generic point on the sub-parabolic curve.

We consider now the situation at umbilic points. For a generic surface $M$,
these occur at isolated points in its elliptic region, and every direction in
the tangent plane of $M$ at such points can be considered a principal
direction. We take $M$ locally in Monge form $z=f(z,y)$, consider the origin
to be an umbilic point and write
$f(x,y)=\frac{\kappa}{2}(x^{2}+y^{2})+C(x,y)+O_{4}(x,y)$ where $C$ is a
homogeneous cubic form in $x,y$. We can take $C(x,y)$ to be the real part of
$z^{2}+\beta z^{2}\overline{z}$, with $z=x+iy$ and $\beta=s+it$ (see for
example [10]). Then, $C=(1+s)x^{3}-tx^{2}y+(s-3)xy^{2}x-ty^{3}.$

###### Theorem 6.5

Let $k\geq 3$ and let $M$ be a generic smooth surface in $\mathbb{R}^{3}$, $p$
an umbilic point on $M$ and $\pi$ a plane through $p$ and orthogonal to $v\in
T_{p}M$.

  1. 1.

If $2\nmid k$, then for almost all directions $v$ in $T_{p}M$ the singularity
of $F_{k}^{\pi}$ at $p$ is of type $S_{3}$ when $k=3$ and of type ${\bf
M}^{k}_{2}$ when $k\geq 4$. There are three directions (resp. one direction)
where the singularity is of type $S_{5}$ when $k=3$ and of type ${\bf
M}^{k}_{3}$ when $k\geq 4$ if $\beta$ is inside (resp. outside) the outer
hypocycloid $\beta=-3(2e^{2i\theta}+e^{-4i\theta})$ in Figure 4.

  2. 2.

If $2\mid k$, then for almost all directions $v$ in $T_{p}M$ the singularity
of $F_{k}^{\pi}$ at $p$ is of type ${\bf M}^{k}_{2}$. There are three
directions (resp. one direction) where the singularity is of type ${\bf
M}^{k}_{3}$ if $\beta$ is inside (resp. outside) the hypocycloid
$\beta=-3(2e^{2i\theta}+e^{-4i\theta})$. There are also three directions
(resp. one direction) where the singularity is of type ${\bf N}^{k}_{3}$ when
$\beta$ is inside (resp. outside) the inner hypocycloid
$\beta=2e^{2i\theta}+e^{-4i\theta}$ in Figure 4.

Figure 4: Partition of the space of cubic forms.

  * Proof

We take $v=(\cos(\theta),\sin(\theta),0)$, $\theta\in[0,2\pi]$ and consider
the rotation

$R=\left(\begin{array}[]{ccc}\sin(\theta)&\cos(\theta)&0\\\
-\cos(\theta)&\sin(\theta)&0\\\ 0&0&1\end{array}\right),$

which takes the direction $(0,1,0)$ to $v$. Then,

$F_{k}^{\pi}\circ
R^{-1}(x,y)=(x\sin(\theta)-y\cos(\theta),(x\cos(\theta)+y\sin(\theta))^{k},f(x,y)).$

Changes of coordinates in the source give

$F_{k}^{\pi}\circ
R^{-1}(X,Y)=(X,Y^{k},f(X\sin(\theta)+Y\cos(\theta),-X\cos(\theta)+Y\sin(\theta))).$

We denote by $\bar{a}_{lj}$ the coefficient of $X^{l-j}Y^{j}$ in the Taylor
expansion of $f(X\sin(\theta)+Y\cos(\theta),-X\cos(\theta)+Y\sin(\theta))$.
The proof follows then considering the conditions for the singularities of
$F_{k}^{\pi}$ in Tables 1 and 2.

(1) We have

$\bar{a}_{31}=(s-3)\cos(\theta)^{3}-t\cos(\theta)^{2}\sin(\theta)+(9+s)\sin(\theta)^{2}\cos(\theta)-t\sin(\theta)^{3}.$

When $2\nmid k$ and $\bar{a}_{31}\neq 0$, the singularity of $F_{k}^{\pi}$ at
the origin is of type $S_{3}$ when $k=3$ or of type $M^{k}_{2}$ when $k\geq
4$.

The coefficient $\bar{a}_{31}$ is a cubic form in $\cos(\theta)$ and
$\sin(\theta)$. Its discriminant is the hypocycloid
$\beta=-3(2e^{2i\theta}+e^{-4i\theta})$. The cubic has three roots for $\beta$
inside the hypocycloid and one root when it is outside. For $v$ corresponding
to one of these roots, the singularity of $F_{k}^{\pi}$ is of type $S_{5}$
when $k=3$ and of type ${\bf M}^{k}_{3}$ when $k\geq 4$, provided
$\bar{a}_{41}\neq 0$. The condition $\bar{a}_{41}\neq 0$ is satisfied at
umbilic points on generic surfaces.

(2) We have

$\bar{a}_{33}=(1+s)\cos(\theta)^{3}-t\cos(\theta)^{2}\sin(\theta)+(s-3)\cos(\theta)\sin(\theta)^{2}-t\sin(\theta)^{3}.$

When $2\mid k$ (so $k\geq 4$) and $\bar{a}_{33}\neq 0$, the singularity of
$F_{k}^{\pi}$ at the origin is of type ${\bf M}^{k}_{2}$. We also get the
${\bf M}^{k}_{3}$ singularities as in (1) when $\bar{a}_{31}=0$.

The coefficient $\bar{a}_{33}$ is also a cubic form in $\cos(\theta)$ and
$\sin(\theta)$. Its discriminant is the hypocycloid
$\beta=2e^{2i\theta}+e^{-4i\theta}$. The cubic has three roots for $\beta$
inside the hypocycloid and one root when it is outside. For $v$ corresponding
to one of these roots, the singularity of $F_{k}^{\pi}$ is of type ${\bf
N}^{k}_{3}$ if $\bar{a}_{31}\neq 0$.

We have $\bar{a}_{33}=\bar{a}_{31}=0$ if, and only if, $\beta$ is on one of
the tangent lines $t(3s^{2}-t^{2})=0$ to the hypocycloids at their cusp
points, see Figure 4. (On these lines, the singularity is of type ${\bf
O}^{k}_{4}$ or more degenerate. This singularity does not occur at umbilic
points on a generic surface.) $\Box$

###### Remark 6.6

1\. Theorem 6.5 is merely another interpretation of the results in [10, 32]
when using the geometric characterisations of the singularities of $k$-folding
maps in Theorems 6.1 and 6.3. We know from [6, 10, 32] that there are one or
three ridge curves and one or three sub-parabolic curves at umbilic points on
a generic surface. These curves meet transversally and change colour at the
umbilic point.

2\. Figure 4 is first obtain in [10] when considering 2-folding maps. In that
case both hypocycloids are present, whereas when $k\geq 3$ only one of them is
present when $k$ is odd (both are present when $k$ is even). Also in [10] is
considered the circle $|\beta|=3$ which corresponds to the Monge-Taylor map
failing to be transverse to the umbilics stratum. The circle $|\beta|=1$ is
also exceptional and corresponds to two ridges through the umbilic being
tangential, see [8]. As these conditions are geometric, the circles
$|\beta|=1$ and $|\beta|=3$ can also be considered exceptional for $k$-folding
maps and are added to Figure 4.

3\. Umbilic points on a generic surface occur at elliptic points, that is why
we do not get flecnodal curves or $H_{3}$-curves through such points.

  * Acknowledgments.

GPS was partially supported by the Basque Government through the BERC
2018-2021 program and Gobierno Vasco Grant IT1094-16, by the Spanish Ministry
of Science, Innovation and Universities: BCAM Severo Ochoa accreditation
SEV-2017-0718, by the ERCEA Consolidator Grant 615655 NMST, and by Programa de
Becas Posdoctorales en la UNAM, DGAPA, Instituto de Matemáticas, UNAM.

FT was partially supported by the FAPESP Thematic project grant 2019/07316-0
and the CNPq research grant 303772/2018-2.

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GPS: Departament de Matemàtiques - Universitat de València, Calle Dr. Moliner
50, 46100, Burjassot (València), Spain.
E-mail<EMAIL_ADDRESS>

FT: Instituto de Ciências Matemáticas e de Computação - USP, Avenida
Trabalhador são-carlense, 400 - Centro, CEP: 13566-590 - São Carlos - SP,
Brazil.
E-mail<EMAIL_ADDRESS>


# Levelling Up Learning: Exploring the Impact of Gamification in Flipped
Classrooms

Eilidh Jack
School of Mathematics and Statistics
University of Glasgow
Glasgow, G12 8QQ
<EMAIL_ADDRESS>
Craig Alexander
School of Mathematics and Statistics
University of Glasgow
Glasgow, G12 8QQ
<EMAIL_ADDRESS>
Elinor Jones
Department of Statistical Science
University College London
London, WC1E 7HB
<EMAIL_ADDRESS>

###### Abstract

In recent years, the integration of gamification into educational settings has
garnered significant attention as a means to enhance student engagement and
learning outcomes. By leveraging gamified elements such as points and
leaderboards, educators aim to promote active participation, motivation, and
deeper understanding among students. This study investigates the effects of
gamification on student engagement in a flipped classroom environment. The
findings suggest that gamification strategies, when effectively implemented,
can have a positive impact on student motivation and engagement. This paper
concludes with recommendations for educators, potential challenges such as
superficial engagement and demotivation, and future directions for research to
address these challenges and further explore the potential of gamification in
fostering student success.

_K_ eywords Gamification; Flipped learning; Student engagement; Active
learning.

##  1 Introduction

Over recent years, the rapid advancement in teaching technology has led to an
increased interest in the adoption of active learning approaches. Active
learning shifts instruction to a learner-centred approach and incorporates a
wide range of instructional strategies which may include student interaction,
collaboration, problem solving, or reflection time, among many others
([Hartikainen et al., 2019]). Specifically in higher education, institutions
are evolving their teaching away from a focus on the teacher, to a more
distributed learning approach where students can study at a time and pace that
suits them. Many have developed their own Learning and Teaching Strategy
placing emphasis on such approaches, such as at the lead authors’ institution,
The University of Glasgow111https://www.gla.ac.uk/media/Media_842671_smxx.pdf.

A common approach which allows for the implementation of active learning is
through flipped learning. Flipping the classroom is enabled through
information and content instruction taking place outside of the classroom with
in-class time instead being used for consolidation of learning, for example
through interacting with their peers, solving problems and applying conceptual
knowledge ([Cronhjort et al., 2017]). The flipped classroom thus facilitates
active learning by requiring students to engage with the pre-class content,
which in turn frees up class time for interactive activities that would not
otherwise be possible ([Wood, 2023]).

There is growing evidence that a flipped learning approach can – when
carefully implemented – benefit students. The meta analyses by [Lo et al.,
2017] and [Bredow et al., 2021] point to increased learning in the
mathematical sciences when a flipped model is used in place of traditional
lectures. There is also evidence that this mode of learning boosts student
enjoyment, for example in terms of perceived understanding (e.g. [Touchton,
2015]). More generally, flipped learning can be an effective strategy for
dealing with large lecture courses where student engagement and interaction
would otherwise be infrequent ([Marcey, 2014]).

Despite the positive evidence in favour of a flipped classroom, the benefits
can only be realised when students are motivated to complete out-of-class
activities ([Huang and Hew, 2018]). Since the change in teaching style places
responsibility on the students to take ownership of their learning, this can
lead to issues with student engagement with pre-lecture activities including
possible resistance from students ([Stone, 2012]).

A sub-optimal strategy to ensure that students keep on track is to use some of
the in-class time to summarise the material which students should have studied
in advance ([Wilson, 2013]). This reduces time available for consolidating
understanding and runs the risk of a vicious cycle where students learn to
rely on these summaries rather than complete the work before the session.
Alternatively, adaptations can be made to a course curriculum to encourage
engagement, for example using frequent summative and formative assessment
after lessons ([Owens et al., 2020]).

A further option, which does not require changes to course curriculum, is to
embed a ‘gamification’ strategy on the virtual learning environment that hosts
the learning material ([Ekici, 2021]). Gamification aims to utilise elements
of classic game design into a non-game context ([Deterding et al., 2011]) and
awards points for participation in certain activities. In a virtual learning
environment, course leaders can specify additional constraints on rewards such
as timeliness of engagement and/or minimum level of interaction with - or
achievement on - an activity. Strategies that reward active participation with
the pre-lecture work have been shown to enhance student motivation to
participate in the learning process and complete tasks prior to lecture
sessions in flipped learning classrooms ([Lo and Hew, 2017], [Buckley and
Doyle, 2016], [Dahlstrøm, 2012]).

The purpose of this study is to investigate the effects of introducing a
gamification element to flipped learning materials in a mathematical sciences
course. The study will focus on levels of engagement with such materials
before and after the gamification intervention is introduced. Section 2
describes the nature of the courses under consideration, while section 3
outlines the motivation for implementing a gamification strategy in these
courses and how this was achieved. In section 4, we report on the remarkable
increase in student engagement with pre-lecture materials after a game-based
approach was employed. We conclude in section 5 with a discussion of the
potential of gamification along with its potential drawbacks.

##  2 Course information

At the University of Glasgow, the School of Mathematics and Statistics offer
courses in introductory Statistics to undergraduate students across the
University. These level 1 courses are typically taken in year 1 or 2 (pre-
honours) of a student’s university career, which typically lasts 4 years. In
year 1, single honours students will take courses in three subjects, one of
which will be the subject they have chosen to specialise in. Any of these
three courses can be considered in year 2, and students have the option to
switch their chosen degree programme to any of these subjects conditional on
meeting the requirements for progression. The purpose of the level 1
statistics courses is predominately to prepare students who are interested in
studying statistics at higher levels and, given that most students will have
little experience of statistics when they arrive at university, introduce
students to the subject with the hope that students will choose to continue
studying statistics in future years. There are two level 1 courses taught over
two semesters (semester 1: Sep-Dec and semester 2: Jan-Mar) with final exams
taking place at the end of each semester. Given the growing awareness of the
importance of statistics across many disciplines, the courses have become
increasingly popular over the past few years with 200+ students enrolled.

To align with the University of Glasgow Learning and Teaching strategy, the
courses were re-designed for 2020-21 with the aim of evolving the approach to
learning and teaching towards student-centered, active learning. The approach
taken for these courses was to introduce a flipped learning model, with a
variety of online learning materials for students to complete before live
teaching sessions. In-person sessions were then used to consolidate learning
through a variety of interactive activities for students to complete
individually or in small groups. For the purpose of this study we will call
these online learning materials, ‘pre-lecture activities’.

###  2.1 Data

The data for this study are taken from Moodle activity logs. These can be used
to view all student interactions with Moodle, including engagement with the
activities of interest for the courses under consideration here. Data such as
these are becoming increasingly available and the use of data in the support
of student learning is commonly referred to as learning analytics ([Leitner et
al., 2017]). At this institution, staff may undertake learning analytics
activities which enable interventions to assist students through the analysis
of their own data. However, when such projects are intended for external
dissemination they also require ethical approval. This study falls into the
latter category and ethical approval was sought and granted in advance of this
study taking place (application number 300220006). The research ethics
associated with this study required students to consent to their data being
used as part of this project. Consent was requested during live teaching
sessions and was granted for $n=100$ (out of a total of 257) students in
2022-23 and $n=77$ (out of a total of 280) students in 2023-24. Unfortunately
we were unable to obtain retrospective ethical approval to access data from
2020-21 (when flipped learning was introduced) and 2021-22 due to the opt-in
nature of the study. We can therefore only provide results and comparisons for
engagement using the 2022-23 and 2023-24 cohorts.

Students attended three in-person sessions a week, and before each of these
were asked to complete the following pre-lecture activities:

  * •

Textbook readings \- students were asked to read a section of the course
textbook in advance of the associated in-person session. The purpose of the
readings was to introduce students to the course material. Completion of these
can only be tracked through students manually marking completion via activity
tracking on Moodle.

  * •

Formative reading quizzes \- students were asked to complete a short quiz
associated with after reading the corresponding textbook section. The purpose
of the quizzes was for students to consolidate their learning and test their
understanding of the course material in advance of the corresponding in-person
session. Information on attempts for all quizzes is automatically stored in
Moodle. It is therefore possible to determine which students have completed a
quiz, when they started/finished the quiz, and their performance on the quiz.
We can therefore track engagement in the quizzes and compare this with
different cohorts as well as monitoring performance to inform the active
learning sessions. These will be referred to as pre-lecture quizzes.

##  3 Motivation and intervention

The pre-lecture activities were made available to students via the University
of Glasgow’s virtual learning environment Moodle 222https://moodle.org/. As
such, it is straightforward for course instructors to check if students are
engaging with these activities and crucially, given the flipped learning
approach, whether they are engaging with them in advance of the in-person
sessions.

As discussed in Section 2.1, the University of Glasgow Learning Analytics
Policy allows staff to undertake learning analytics activities which enable
interventions to assist students learning. From the year in which the flipped
learning approach was introduced (2020-21) staff on the course were therefore
monitoring engagement in pre-lecture activities through activity logs on
Moodle.

For the purpose of this study, only engagement with the formative reading
quizzes (pre-lecture quizzes) is measured, where activity completion can be
indicated by certain conditions being met (e.g. whether a student has received
a grade for a quiz), rather than students being able to manually mark
completion (e.g. for link to reading from course textbook). This means that we
cannot measure and compare engagement across all pre-lecture activities and we
may be misrepresenting true engagement as some students may choose to read the
textbook but not complete the reading quiz (or vice versa). However, this
should give a more reliable estimate of meaningful engagement in activities
since students have to engage somewhat with the activity (e.g. start and
submit the quiz) rather than being able to manually mark that the activity is
complete by checking a button. This does not fully guard against non-
meaningful engagement (e.g. a student could begin the quiz, complete no
questions, submit, and still be counted as having completed this activity) but
performance in these activities (e.g. questions attempted and marks achieved)
was also checked to understand the extent of meaningful engagement.

Despite students indicating that they enjoyed the flipped learning approach
through course evaluation forms, when looking at the data it was clear that
engagement in the pre-lecture quizzes was extremely low. For example, the
average completion of pre-lecture quizzes in advance of the active learning
session taking place was 6.88% in semester 1 of 2022-23. This was of concern
to course instructors given the in-class sessions involved spending less time
presenting material and more time engaging in active learning activities as
per the goal of flipped learning. This pattern was persistent over a number of
years. Given that the introduction of the new courses coincided with the
Covid-19 pandemic, it was also difficult to disentangle the lack of engagement
with the flipped learning material, and the general lack of engagement HE
institutions saw over the course of the pandemic ([Wester et al., 2021]).

The academic year of 2022-23 saw a return to campus for the majority of
teaching but the issue of low engagement in pre-lecture activities persisted.
This is demonstrated in Figure 1 (a) which shows the cumulative mean
percentage of students engaging in the pre-lecture quizzes for each week
across an 11 week period in semester 1 of 2022-23. Each coloured line
represents the cumulative average percentage of students who have engaged in
the collection of quizzes associated with one week of teaching over the course
of the semester (an average is shown here since each week may have a number of
quizzes for students to complete). Of most interest is the level of engagement
in the pre-lecture quizzes for the week in which the material is covered in
class, which is represented by the first point for each weekly line in Figure
1 (a). These figures are also presented in column 1 of Table 1. This figure
starts off low (around 27%) for week 1 and continues to drop for each week of
material, before reaching a point around week 7 where less than 5% of students
have engaged with the pre-lecture quizzes on the week in which the material is
covered in class. Another interesting feature of Figure 1 (a) is the pattern
of engagement for each collection of weekly quizzes over the semester.
Although the engagement in the weekly material does increase slightly over the
semester, at most only about half of the students in the class have ever
engaged with the material at all on average for week 1, and after week 8 this
drops to less than 25%. Interestingly, for all weeks an increase in average
engagement can be seen between weeks 10 and 11 and we believe this to be
related to exam preparation as the exam takes place immediately after the
course finishes. These features are clearly of huge concern to the course
instructors as they indicate that not only are students not engaging with the
pre-lecture quizzes ‘on time’ to benefit from a flipped approach, the majority
of students aren’t engaging with the materials at all across the entire
duration of the course.

Figure 1: Cumulative mean percentage of students engaging in weekly pre-
lecture quizzes across each semester of interest. Figure (a) shows data for
semester 1 in academic year 2022-23 before the Level Up! intervention was
implemented. Figure (b) shows data for semester 2 in academic year 2022-23
after the Level Up! intervention was implemented. Figure (c) shows data for
semester 1 in academic year 2023-24 after the Level Up! intervention was
implemented.

In an attempt to tackle this low engagement the decision was made to add an
element of gamification to the course which would encourage students to engage
in the pre-lecture activities. This was implemented through the the Level Up!
Moodle plug-in333https://moodle.org/plugins/block_xp which was introduced to
the course in semester 2 of 2022-23. Level Up! allows students to gain points
by participating in the course via Moodle. Points were awarded for the
completion for a variety of course activities including the pre-lecture
activities, tutorial questions, lab materials, and assessed quizzes and points
were awarded based on completion only, i.e. the points system was endeavour-
based and not merit-based. In an attempt to explicitly tackle engagement in
the pre-lecture activities, full points were only awarded if the activity was
completed before the associated lecture/tutorial/lab with half-points being
awarded thereafter. Figure 2 shows how this plug-in is integrated within the
course Moodle page with the left-hand image showing the Level Up! block that
students can see on the main course page and the right-hand image showing the
leaderboard view which shows students where they rank individually on an
anonymous leaderboard throughout the semester. There is also an option to view
where the students’ tutorial group rank in a team leaderboard.

Figure 2: The left-hand image shows the Level Up! block that students can see
on the Moodle course page. The right-hand image shows the leaderboard view
that students can see within the Level Up! block.

Level Up! was initially introduced in an attempt to increase engagement in
pre-lecture activities in semester 2 of the 2022-23 academic year and, after
initial success, introduced from semester 1 of the 2023-24 academic year. This
allows us to make a number of comparisons which form our questions of
interest:

  1. 1.

How do engagement levels in pre-lecture quizzes compare after the
implementation of Level Up! between the same students across two courses.

  2. 2.

How do engagement levels in pre-lecture quizzes compare after the
implementation of Level Up! within the same course across two academic years.

##  4 Findings

Below we will present findings which relate to the questions of interest
listed in Section 3.

###  4.1 Comparison within year (same students, different courses)

We consider engagement levels for the same group of students across two
semesters: in semester 1 Level Up! was not used, but in semester 2 it was
fully implemented. Figure 1 (b) shows the cumulative mean percentage of
students engaging in the pre-lecture quizzes each week across a 9 week period
in semester 2 of 2022-23. Of the 100 students who provided consent in semester
1 of 2022-23, 83 continued to study statistics in semester 2. Therefore, the
data displayed in this figure relate to a subset of the same students in
Figure 1 (a) that provided consent to take part in this study across an entire
academic year. It is immediately clear that overall the levels of engagement
in semester 2 of 2022-23 (after Level Up! was implemented) are higher when
comparing to semester 1 (before Level Up! was implemented) as shown in Figure
1 (a). Similar to Figure 1 (a), a drop-off in completion of pre-lecture
quizzes for each week is still observed, however the baseline level of
engagement for each week remains substantially higher, with the lowest mean
engagement for a collection of weekly pre-lecture quizzes in the week the
material is covered in-class being 25% in Week 9. This is around the same
level as for Week 1 in Figure 1 (a), which showed the highest levels of
engagement across the semester. This suggests that Level Up! has had a
positive impact on engagement in pre-lecture quizzes across this student
cohort. Another key feature of this figure is the clear drop-off in engagement
after Week 1, which can be seen by the red line (associated with Week 1
materials) sitting considerably higher and separate to the lines representing
the other weeks. This indicates that the effect of Level Up! on engagement
drops more substantially from week 1 to week 2 compared to any other pairs of
weeks and could be attributed to the initial excitement of the gamification
and competition wearing off after week 1. Despite this, it can still be
concluded that over the course of the semester the levels of engagement in the
pre-lecture quizzes were higher than for semester 1. The average percentage of
students engaging in the pre-lecture quizzes during the corresponding teaching
week is also shown in Table 1. These figures correspond to the first point in
each weekly line in Figures 1 (a) and 1 (b).

|  | Mean % of students completing pre-lecture
---
materials during teaching week
Teaching Week |  | Semester 1 2022-23
---
(n=100)
| Semester 2 2022-23
---
(n=83)
| Semester 1 2023-24
---
(n=77)
Week 1 | 26.7% | 59.0% | 81.8%
Week 2 | 18.0% | 36.1% | 78.4%
Week 3 | 12.0% | 31.3% | 80.5%
Week 4 | 10.5% | 34.9% | 64.0%
Week 5 | 9.0% | 32.5% | 61.0%
Week 6 | 7.0% | 30.7% | 59.7%
Week 7 | 4.3% | 27.7% | 62.3%
Week 8 | 6.5% | 26.5% | 57.8%
Week 9 | 4.0% | N/A | 52.6%
Week 10 | 8.0% | N/A | 42.9%
Level Up! Implemented | No | Yes | Yes
Table 1: Mean percentage of students engaging pre-lecture materials during
teaching week across each semester.

In order to confirm the increase in engagement that can be seen in semester 2
(Figure 1 (b)) compared to semester 1 (Figure 1 (a)), a 95% confidence
interval was computed which compares the difference in average proportion of
pre-lecture quizzes completed in the week the material is covered in class for
semester 1 and 2 for each student who participated in the study. The 95%
confidence interval for the mean difference in engagement between semester 1
and semester 2 is $(-0.29-0.15)$ suggesting that the implementation of Level
Up! significantly improved the proportion of pre-lecture quizzes completed by
the students.

Figure 3: Percentage of pre-lecture quizzes completed for the 83 students who
were enrolled in both courses during 2022-23 in semester 1 (no Level Up!) and
semester 2 (Level Up! implemented).

We were also interested in whether all students were more engaged (in general)
in semester 2, or if the gamification aspect was drawing out students who were
not engaged in semester 1 who then go on to become very engaged in semester 2.
Figure 3 shows the average engagement levels of the 83 students who were
enrolled in both courses in 2022-23 across both semesters, with each pair of
points and connecting line representing one student. This figure shows some
interesting features. Firstly, as we would expect, the engagement levels tend
to increase for most students across both semesters, however there are some
instances where engagement levels decrease. For students who had comparatively
high levels of engagement in semester 1, we tend to see a reasonable increase
in semester 2 indicating that students who were already more engaged than
their peers are likely to engage further after the implementation of Level
Up!. We also see a number of very sharp increases from semester 1 to semester
2 for students who were not very engaged (or not engaged at all) in semester
1, who then show some of the highest engagement levels in semester 2. For
these students it seems that the gamification element drastically improved
their motivation and engagement levels and is evidence that including a
gamification element to a course may encourage engagement from students who
would otherwise not engage.

Despite these positive results, there may be other factors which could affect
the engagement levels across these semesters. Engagement levels may be
impacted by the materials which are covered in each course, as these will will
differ from one semester to the next, and to compound matters, the teaching
team differed between semesters. However, in general, course evaluations show
that students are very positive about the teaching across both semesters and
rate the teaching team very highly in both courses.

It is not possible to investigate the effect of Level Up! on end-of-semester
exam performance within the 2022-23 cohort since each course covers different
material. However, we can assess meaningful engagement with the formative
reading quizzes by monitoring grades for these quizzes. The average percentage
grade for formative reading quizzes in semester 1 of 2022-23 was 68% compared
to 69% for semester 2 of 2022-23. These percentages only include students who
completed the quizzes and so we would not necessarily expect to see an
increase in percentage grade after the implementation of Level Up! but it is
reassuring to see that the average percentage grade is similar to the previous
semester indicating that, in general, students are engaging with these quizzes
in a meaningful way rather than just completing them to gain points and ‘game’
the leaderboard.

###  4.2 Comparison between years (different students, same course)

The second question of requires us to compare engagement levels for different
groups of students for the same course (i.e. same semester) across two
academic years. In 2022-23, Level Up! was not implemented and in 2023-24 it
was. There were some small changes made to the course materials between these
years, however the course aims, intended learning outcomes and structure
remained the same. Figure 1 (c) shows the cumulative mean percentage of
students engaging in the pre-lecture quizzes each week across a 11 weeks in
semester 1 of the 2023-24 academic year. The data displayed in this figure
relate to different students than in Figure 1 (a) but for the same course.
When comparing to Figure 1 (a) it is again very clear to see that overall
engagement levels in the pre-lecture materials were substantially higher after
Level Up! was implemented.

In week 1, around 82% of students had completed the pre-lecture quizzes,
compared to only around 27% for the same material in 2022-23. Although we
still see a drop-off in engagement through the semester, the engagement levels
in each week always remain substantially higher than observed the previous
year. We also see a larger drop in engagement between weeks 3 and 4, although
interestingly this comes later when compared to semester 2 of 2022-23 (Figure
1 (b)) where a large drop-off occurred after week 1. Overall, engagement
levels are higher for semester 1 of 2023-24 compared to semester 2 of 2022-23,
even though both courses implemented Level Up!. This may be explained by the
observation that students are generally more engaged at the beginning of an
academic year, particularly for a Level 1 course where most students are
studying at University for the first time. The average percentage of students
engaging in the pre-lecture quizzes during the corresponding teaching week is
also shown in Table 1. These figures correspond to the first point in each
weekly line in Figures 1 (a) and 1 (c).

In order to confirm the increase in engagement that can be seen in semester 1
of 2023-24 (Figure 1 (c)) compared to semester 1 of 2022-23 (Figure 1 (a)), a
95% confidence interval was computed which compares the average proportion of
pre-lecture quizzes completed by each student in the week the material is
covered in class for each year. The 95% confidence interval for the mean
difference in engagement between 2022-23 and 2023-24 is $(-0.53-0.37)$
suggesting that the implementation of Level Up! significantly improved the
proportion of pre-lecture quizzes completed by the students.

It was also of interest to compare achievement in this course across both
cohorts to understand if the increased engagement led to better understanding
of the material amongst the students. At course level, we believe the
increased engagement has contributed to an increase in performance with 82% of
students receiving a grade of A, B or C in the semester 1 course of 2023-24
compared to 60% in 2022-23. We can also assess meaningful engagement with the
formative reading quizzes by monitoring grades for these quizzes. The average
percentage grade in formative reading quizzes semester 1 of 2023-24 was 64%
compared to 68% for semester 1 of 2022-23. Again, these percentages only
include students who completed the quizzes and so we would not necessarily
expect to see an increase in percentage grade after the implementation of
Level Up! but it is reassuring to see that the average percentage grade is
similar to the previous year indicating that, in general, students are
engaging with these quizzes in a meaningful way rather than just completing
them to gain points.

As in Section 4.1, it should be noted that there may be other factors which
could affect the engagement levels and performance across these cohorts.
Clearly the set of students in each cohort was different and so some of the
changes we identified could be attributed to a cohort effect. There was also a
change in the teaching team, with a change in one (of two) course lecturers.
However, in general, course evaluations from each year show that students were
very positive about the teaching team across both years. The changes
identified in performance will also be impacted by a different exam paper,
however the material covered and difficulty level of the paper was kept as
consistent as possible between the two years.

##  5 Discussion

The purpose of this study was to investigate the effects of a gamification
element in a mathematical sciences course taught in flipped format. The study
compared levels of engagement with pre-lecture quizzes before and after the
gamification intervention was introduced. Comparisons were made across
semesters (different courses, same students) and across academic years (same
course, different students). Our study found that in both cases the level of
engagement (measured by average percentage of students completing pre-lecture
quizzes prior to the associated in-person sessions) was significantly higher
when compared to a course where Level Up! was not implemented. Although
engagement levels did drop over the course of each semester, they remained
substantially higher for each week when compared to the previous semester or
year. These results provide convincing evidence that introducing a
gamification element to a course taught in flipped format increases students
motivation and engagement to complete work outside of scheduled class time.

When comparing engagement levels within students between two semesters, we
found a general increase in engagement across both semesters but more
interestingly found that some students with very low engagement levels in
semester 1 went on the have some of the highest engagement levels in semester
2. For these students it seems that the gamification element drastically
improved their motivation and engagement levels and is evidence that including
a gamification element to a course may encourage engagement from students who
would otherwise not engage.

Our results also found that this increase in engagement could lead to an
increase in performance with 82% of students receiving a grade of A, B or C in
the semester 1 course of 2023-24 compared to 60% in 2022-23. Although we
cannot say for sure what led to this increase in achievement and there are
many factors which could influence this (such as cohort effect, different exam
paper, etc.), an increase in engagement throughout a semester is compatible
with an increase in performance since students are more likely to be
distributing their learning over the course of a semester. This is especially
beneficial for mathematical sciences courses where learning is often thought
of as linear with each topic building on the previous one and poor
understanding of early material can have a detrimental effect later in the
course [Ireland and Mouthaan, 2020].

This study focuses on Year 1 undergraduate students who typically fall into a
post-secondary education age range. The transition to university for students
can be overwhelming, with changes in teaching delivery, workload and cognitive
demands ([Blair, 2017]). Our results show that gamification can improve the
learning experience, which may help with this transition, in line with
observations by [Zaric et al., 2017]. This being said, [Kim and Castelli,
2021] looked at the effects of gamification across three age cohorts and found
that university level participants found the least significant results in
terms of positive interaction when compared to secondary school and adult
learners, indicating that younger and older learners may have more interest in
gamified factors. Currently, gamification is only present within the Year 1
modules of the undergraduate programme, and is not implemented within other
modules on the programme. There is scope to explore the effects of
gamification on a more mature cohort to observe if we see similar patterns of
engagement.

This study has considered student engagement levels in terms of completing
pre-lecture quizzes, though it is important to note that we see meaningful
engagement instead of cases where students are simply trying to ‘game’ the
leaderboard. Our results are based solely on participation on formative
reading quizzes where participation is identified through criteria being met,
as this material was found to show that genuine participation took place.
There are other activities in the course, such as textbook readings, which
simply require a manual completion indicator and could be exposed to non-
meaningful engagement. We feel that a reasonable performance on the quizzes
indicates engagement with the other activities available (or indeed, of
students independently finding their own resources for study).

The results presented here are for a self-selected subset of students.
However, course instructors were able to view results for the entire cohort of
students to inform their future decision making on the learning and teaching
approach for this course and others. The results presented here were found to
be similar to the results for the entire cohort and the general conclusions
made would not change if data on the entire cohort of students were
considered.

Although studies in gamification have reflected positive outcomes in terms of
increased motivation and engagement in tasks, this teaching strategy has
potential downsides. Effects such as increased competition between students
([Hakulinen et al., 2013]) and task evaluation difficulties, where certain
tasks may not be suitable for a game based element or may have ways of being
marked as complete without proper engagement in the learning materials
([Domínguez et al., 2013]) may become issues. The design of game based
elements within a course must also be considered with a balance of reward and
level of work and engagement required. Tasks which are overly complex can lead
to a lack of engagement from learners ([Dong et al., 2012]). There is also
potential for demotivation through the full gamification process, particulaly
if students find themselves placed low on the points leaderboard. The
competency levels of students may lead to negative consequences, including
frustration and loss of self confidence ([Alomari et al., 2019]). A study by
[Ding et al., 2018] showed that some students in a gamified learning activity
may require more time to obtain the necessary understanding to progress
through learning process.

Engagement in gamification not only requires active participation from
students, but time and attention from staff to implement the system
effectively. From our experience using Level Up!, it takes time to set up the
system. Several considerations have to be made at the set-up stage, including
the allocation of experience points to certain tasks, and allocating points in
such a way as to reflect the level of engagement required from the student.
Levels were attainable for students which were split by weekly tasks, which
requires manual intervention to tally the available points over a given week.
For example, students could receive half points for completing certain tasks
after a deadline which requires manual intervention from the course lecturer
to reset the points awarded to a different total after each deadline. Though
our study explored gamification using Level Up!, there are a host of other
plug-ins which can be adapted in virtual learning environments such as
Quizventure444https://github.com/xow/moodle-mod_quizgame and Block
Game555https://moodle.org/plugins/block_game. [Heilbrunn et al., 2017] provide
a detailed review of tools for gamification analytics.

Finally, we highlight the importance of using learning analytics, where
possible, to access data from students on a course when measuring the success
of a new teaching method or intervention. If the instructors of the two
courses under consideration here had relied on feedback from students to
inform teaching strategy - which was consistently positive even before the
implementation of Level Up! - the true extent of the lack of engagement in the
pre-lecture materials may never have been identified.

##  6 Conclusion

The results we present here are in line with previous research (for example
[Lo and Hew, 2017], [Buckley and Doyle, 2016], [Dahlstrøm, 2012]) and show a
stark increase in student engagement with pre-lecture activities on a course
taught in flipped mode. As the pre-lecture activities of interest were quiz-
based - with points awarded for attempting the quizzes on time rather than
quiz score - we were able to investigate whether the increased engagement was
meaningful or the result of students ‘gaming’ the leaderboard. In our study,
there was no evidence of the latter.

It is thought that the two statistics courses considered here are the only
time the students came across the Level Up! plugin or other form of
gamification. It is therefore not known whether the increased engagement is
due to the novelty of a leaderboard and whether gamification would be as
successful if implemented widely across multiple courses.

The significant increase in student engagement after the adoption of a
gamification strategy is certainly worthy of further research. Though the
results from the gamification intervention were very positive, student
engagement is still far from perfect. Diversity in teaching and learning
approaches is surely the key to engaging students across their courses, with
gamification a valuable strategy in a teacher’s toolbox.

##  7 References

## References

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# Estimating electricity saving-potential in small offices using adaptive
thermal comfort

Yujiao Chen  Rongxin Yin<EMAIL_ADDRESS>Sidewalk Labs, New York, NY, USA
Lawrence Berkeley National Laboratory, Berkeley, CA, USA

###### Abstract

Small office buildings below 10,000 square feet account for approximately 75%
of the total number of office buildings in the United States. Unlike large
office buildings, small office buildings usually use packaged HVAC systems for
environmental control and are not equipped with building management systems.
The lack of smart control in small office buildings leaves low-hanging fruit
unpicked in terms of energy efficiency. The commonly seen missed opportunities
include the fixed cooling setpoint schedule that ignores people’s comfort
needs and actual occupancy patterns, and the wasted energy from equipment and
appliances while not being used by occupants.

The smart control informed by IoT sensors and enabled by remotely controlled
devices can optimize the building operation to minimize unnecessary energy
consumption and improve indoor thermal comfort. This paper quantifies the
potential for electricity savings in small office buildings from smart
thermostat control and occupancy-informed smart plug control. This is done by
simulating the effect of adaptive setpoint temperature, occupancy-based HVAC
control, and night-purge free cooling on small office buildings across all
major climate zones in the United States. Adopting these smart control
measures can achieve 8.9% to 20.4% of savings in total electricity consumption
of small office buildings, or equivalent to annual reductions between 12.2
$kWh/m^{2}$ and 30.4 $kWh/m^{2}$ in electricity usage intensity. Among all
climate zones, the hot and dry climates benefit the most from proposed smart
controls and achieve the highest percentages of electricity savings.

###### keywords:

energy efficiency , adaptive thermal comfort , IoT sensing and control ,
occupancy-based HVAC and plug load control , smart thermostat control

††journal: ASHRAE Journal

##  1 Introduction

In the United States, more than 73% of electricity is consumed by buildings
[1]. Electricity used for space cooling in buildings reached 392 billion kWh
in 2020, which accounted for approximately 10% of overall electricity
consumption [2]. Among all building types, electricity used for space cooling
in commercial buildings accounted for 4% of overall electricity consumption in
the U.S. Small office buildings, with a floor area of less than 10,000 square
feet, account for approximately 75% of the total number of office buildings
[2]. Reducing the energy required for space cooling not only makes a great
impact on total energy consumption but also significantly alleviates the
stress on electricity generation and the power grid, which consequently leads
to more economical operation and lower carbon intensity.

For small office buildings, the most widely used space cooling system is
packaged air-conditioning equipment, which serves more than half of the total
square footage of commercial buildings in the United States [3]. Packaged air-
conditioning equipment usually has discrete on-off control for single-stage or
two-stage cooling, operating on a fixed schedule of desired indoor air
temperature (setpoints) by day and time. A more sophisticated approach to
control, using commercial off-the-shelf devices and cloud-based optimization
techniques can substantially improve energy efficiency and occupant
satisfaction.

This paper focuses on three opportunities for improving energy use in small
office buildings:

###  1.1 Overcooling in office buildings

It is not uncommon for people in the United States to experience excessively
cooled office buildings on a hot summer day. Often, people need to put on an
additional layer of clothes if sitting at their desk for extended periods.
This is especially common for women, as described in [4] and [5]. These
studies find that females prefer higher room temperatures than males, based on
large scale field surveys and actual metabolic rate through biophysical
analysis. The empirical rules to set cooling temperature follow a model
developed in the 1960s that derived from male test subjects only [6], which
causes the intrinsic mismatch in providing comfort to all occupants. In
addition to discomfort, according to [7], the overcooling in the United States
resulted in an annual energy waste of 103,929 GWh, a carbon footprint of
57,125 kt $CO_{2}$e, and a financial loss of 10 billion dollars.

The technical barrier to the flexible cooling setpoint that reflects the true
occupants’ preference usually lays on the lack of feedback channel and access
to the setpoint control. Namely, occupants don’t have a convenient way to
effectively express their thermal feedback, and there is no mechanism to
collect occupants’ feedback and take appropriate actions to address it. This
issue has started to improve with the implementation of consumer-grade IoT
sensors and integrated smart control. Some smart building solutions, such as
Mesa [8], provide comfort buttons and a user app in their offering that allows
each occupant’s thermal preference to be heard by the smart control engine,
and subsequently adjusts the setpoint to improve overall occupants’
satisfaction towards their thermal environment.

###  1.2 Occupancy-decoupled operation

Programmable thermostats are the most prevailing devices to control HVAC
operation in small and medium-sized offices. Those devices adjust the
temperature according to a series of settings to be triggered by the time of
the day and day of the week. For example, the thermostat can be programmed to
set the temperature at 22°C during business hours and switch to a setback of
28°C at night and on weekends. However, the programmable thermostat itself
does not save energy; its energy-efficiency performance can only be as good as
how users operate it. Issues come up in practice as the previous survey
results revealed that 40% of users do not operate their programmable
thermostats as expected by the manufacturers [9]. Assumptions about business
hours may fail to reflect the true occupancy - for example, the AC turns off
at 6 pm sharp while people are still working in the office, or the AC operates
on Saturday when the office is unoccupied. Whoever sets the programs of
thermostat in small and medium-sized office also needs a better solution -
more than often, it is either the case that the thermostat is physically
locked into a plastic box to prevent unauthorized interference, or multiple
people interacting with the thermostat and their conflicts inadvertently cause
the increase of energy use [10].

The motion-sensor embedded or coupled thermostat, on the other hand, captures
the true occupancy patterns instead of solely relying on user settings. This
mechanism allows temperature control to be more accurate and dynamic, thus
improving the energy efficiency of HVAC operations.

The occupancy-centric operation also saves energy on plug loads and lighting.
It has been supported by multiple studies that plug loads account for about
30% of electricity consumption in U.S. commercial buildings [11, 12, 13].
Unlike lighting that has widely adopted occupancy sensors for automatic
control, equipment and appliances in general solely rely on manual control and
consume energy even when not being used. This standby power consumption is
called phantom load or vampire load. The smart plugs and power strips that
allow remote control consequently save a substantial amount of energy when
coupled with occupancy signals.

###  1.3 Unused free cooling resources

Most climate zones in the United States offer the opportunity to utilize
natural ventilation as free cooling for various lengths of time [14]. The
fresh outdoor air at the pleasant temperature and humidity level not only
improves indoor air quality by flushing out the pollutant in the stale air,
but also saves significant amounts of cooling and fan energy [15]. The most
convenient implementation of natural ventilation is the night purge, which is
to leave the windows and louvers open during the night if the weather is
suitable. This passive ventilation is most effective in the climate with
substantial diurnal temperature swings and in buildings with a significant
amount of thermal mass (e.g. concrete, brick, phase-change material) [16].

With the increasing adoption of window actuators, IoT sensors, and integrated
intelligent control, more natural ventilation opportunities can be unlocked to
reduce the load and carbon footprint of building operations.

To address these missed opportunities and harvest the low-hanging fruit, this
paper is intended to quantify the cooling energy savings potential in small
and medium-sized office buildings across all major climate zones in the United
States. By adopting adaptive cooling setpoints, occupant-centric thermostat
control, and night purge as free cooling, the total cooling energy savings in
kilowatt-hours are estimated for typical small and medium-sized office
buildings.

##  2 Methodology

###  2.1 Overall Framework

For each prototype building model at each climate, we will evaluate the
energy-saving potentials with individual or combined measures. As illustrated
in Figure 1, we use the DOE prototype small office model as the baseline and
create the proposed model with individual and combined energy efficiency
measures in EnergyPlus [17]. It is worth noting that the energy efficiency
measures proposed in this study can be deployed through a set of ”plug and
play” IoT sensing and control technologies. Therefore, we need to keep the
same HVAC system design capacity between the baseline and proposed models.

Figure 1: Proposed Modeling Framework

###  2.2 Prototype Building Model

The models of small office buildings to quantify cooling energy savings are
based on the U.S. Department of Energy commercial benchmark models developed
by DOE national labs [18]. These benchmark models serve as a consistent
baseline to compare the efficiency and effectiveness of different improvements
on building systems and operations. Table 1 presents the general model input
for a small office that complies with ASHRAE 90.1-2004 and 62.1-1999
standards.

Table 1: Small Office Prototype Model Summary Building Type |  Small Office
---|---
Compliance |  ASHRAE Standards 90.1-2004 and 62.1-1999
Description |  Single-story five-zone office building
Total Floor Area |  511 m2 (5,500 ft2)
HVAC - Cooling |  Packaged Single Zone Air Conditioner (PSZ-AC)
Economizer |  No
Internal Gains - Lighting |  1 W/ft2
Internal Gains - Plug Loads |  1 W/ft2
Internal Gains - People |  5 W/ 1,000 ft2
Envelope |  Envelope thermal properties vary with climate according to ASHRAE Standard 90.1-2004.

###  2.3 Climate zone

The climate zone designation is based on the climate zone map used by the
International Energy Conservation Code (IECC) and the American Society of
Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE). This climate
zone map was developed by Pacific Northwest National Laboratory, dividing the
United States into eight main climate zones based on the temperature, using
cooling degree days and heating degree days. Ordered by descending average
temperature, these zones are Zone 1 (Very Hot), Zone 2 (Hot), Zone 3 (Warm),
Zone 4 (Mixed), Zone 5 (Cool), Zone 6 (Cold), and Zone 7 (Very Cold), and Zone
8 (subarctic). Each zone is further divided into three subcategories by
moisture regimes, as A (Humid), B (Dry), and C (Marine) [19].

The land and population under each climate zone vary dramatically in the
United States. For example, Zone 8 Subarctic climate is only found in Alaska.
The number of small and medium-sized office buildings under each climate zone,
summarized by researchers at Pacific Northwest National Laboratory and
National Renewable Energy Laboratory [19] is listed in Table 2.

Table 2: Number of Buildings by Type and Climate Zone in the United States Climate Zone |  Represent City | # Small Office
---|---|---
1A (Hot-Humid) |  Miami, Florida |  28,000
2A (Hot-Humid) |  Houston, Texas |  354,930
2B (Hot-Dry) |  Phoenix, Arizona |  96,470
3A (Hot-Humid and Mixed-Humid) |  Atlanta, Georgia |  321,170
3B (Hot-Dry) |  Las Vegas, Nevada |  158,390
3C (Marine) |  San Francisco, California |  25,930
4A (Mixed-Humid) |  New York, New York |  312,150
4B (Mixed-Dry) |  Albuquerque, New Mexico |  15,790
4C (Marine) |  Seattle, Washington |  40,880
5A (Cold) |  Chicago, Illinois |  306,880
5B (Cold) |  Boulder, Colorado |  107,340
6A (Cold) |  Minneapolis, Minnesota |  80,460
6B (Cold) |  Helena, Montana |  10,080
7 (Very Cold) |  Duluth, Minnesota |  10,790

###  2.4 Adaptive Thermal Comfort Model

The adaptive thermal comfort model was developed through a data-driven
approach from the ASHRAE Global Thermal Comfort Database [20]. The adaptive
comfort model relates the zone operative temperature setpoint to the recent
history of outdoor air temperatures. The adaptive comfort models only apply to
cooling mode and generate a single setpoint value for each day. During
summertime in hot climates, the zone thermostat setting can be higher than the
traditional thermostat setting based on the adaptive thermal comfort model,
which results in energy savings of HVAC systems.

For the adaptive comfort model selected in this paper, the thermostat setpoint
temperature schedule for space cooling will be overwritten with the calculated
operative temperature based on the selected acceptability limits of the
comfort model defined in ASHRAE 55-2020 [6], as shown in Figure 2

Figure 2: ASHRAE 55 Adaptive Comfort Model

. The adaptive comfort model takes into account the variation of comfort
preference along with the seasonality and has a wider comfort range. The
ASHRAE adaptive comfort model is only applicable when the running average
outdoor air temperature for the past 30 days is between 10.0 and 33.5°C.

##  3 Results

###  3.1 Adaptive Thermal Comfort Model

In this study, we first compare the temperature range between the ASHRAE 55
standard and adaptive comfort model as follows.

  1. 1.

”Adaptive-ASH55-Central” (Adaptive-55) is the central line of the
acceptability limits of the ASHRAE Standard 55-2020 adaptive comfort model
that will be used to generate the zone operative temperature setpoint. It is
derived from the prevailing mean outdoor temperature and is calculated as
shown below Central line = 0.31 prevailing mean outdoor temperature + 17.8°C
The Adaptive-55 is strictly bounded between 20.9°C and 28.2°C.

  2. 2.

”Adaptive-ASH55-90percent-Upper” (Adaptive-90) is the upper line of the 90%
acceptability limits of the ASHRAE Standard 55-2020 adaptive comfort model. It
is calculated as the equation shown below 90% upper line = 0.31 prevailing
mean outdoor temperature + 20.3°C The Adaptive-90 is strictly bounded between
23.4°C and 30.6°C. This upper line is only used in this section to demonstrate
additional cooling energy savings compared to the Adaptive-55. In all other
sections, only the Adaptive-55 is used to quantify the energy savings.

  3. 3.

The adaptive comfort models only apply to cooling mode and generate a single
setpoint value for each day. During summertime in hot climates, the zone
thermostat setting can be higher than the traditional thermostat setting based
on the adaptive thermal comfort model, which results in energy savings of HVAC
systems.

The cooling setpoints in climate zone 4A, based on both Adaptive-55 and
Adaptive-90, are shown in Figure 3. The X-axis is the maximum daily outdoor
air temperature, and the Y-axis is the mean cooling setpoint temperature. The
baseline static cooling setpoint at 22.2°C is plotted as a dashed line. In
climate 4A, the adaptive cooling setpoint based on Adaptive-55 is never above
25.8°C and the adaptive cooling setpoint based on Adaptive-90 is never above
28.3°C.

Figure 3: Comparison of Thermostat Cooling Setpoints between the Static and
Adaptive Comfort Models

The daily cooling setpoints in climate zone 4A based on Adaptive-55 are shown
in Figure 4. The cooling setpoint changes in the same direction of prevailing
outdoor temperature, which starts to rise from late May, peaks in August, and
falls back to the baseline setback temperature in November. On weekends and
holidays, the system cooling setpoint is the same as the setback temperature
at 29°C.

Figure 4: Annual Cooling Setpoints

Raising cooling setpoints by a mere few degrees from the baseline leads to
significant energy savings. As shown in Figure 5, the cooling setpoints based
on Adaptive-55, ranging from 22.2°C to 25.8°C, achieve approximately 20% of
total cooling energy savings; the cooling setpoints based on Adaptive-90,
ranging from 22.2°C to 28.3°C, achieve an even higher 38% of total cooling
energy savings. This cooling energy savings include both compressor energy
savings and fan energy savings.

Figure 5: Comparison of HVAC Savings (%) between ASHRAE55-CentralLine and
90PercentUpperLine under different daily weather conditions (left) and total
savings in climate 4A (right)

###  3.2 Occupancy-based HVAC and Plug Load Control

The occupancy input is based on the realistic schedule for office space
developed at Lawrence Berkeley National Laboratory (LBNL) by incorporating
real data collection and stochastic modeling methods [21]. It is also the
result of the International Energy Agency Energy in Buildings and Communities
Programme (IEA-EBC) Annex 66 - Definition and Simulation of Occupant Behavior
in Buildings [22]. The realistic occupancy level at 10-minute intervals is
generated by LBNL’s occupant behavior web application [23] considering the
diversity and stochastics of occupant activities. The occupancy level is shown
in Figure 6. Unlike the traditional assumption of static occupancy e.g. 8 am -
5 pm, the stochastic occupancy takes into account the variations in real
offices setting, providing a high-resolution occupancy level at sub-hourly
intervals. As shown in Figure 6, the occupancy level in the early morning,
around noon, and in the evening has larger variations due to day-to-day and
person-to-person differences.

Figure 6: Dynamic Occupant Behaviours (e.g., Open Office) and Plug Load on
Weekdays

The accurate occupancy sensing enabled by IoT sensors not only saves HVAC
system energy consumption but also helps to save electricity on lighting and
plug load. The smart plug control automatically turns off non-critical
equipment and appliances (such as monitors, televisions, coffee makers, water
heaters, etc.) if occupancy is not detected for an extended period. The
occupancy-centric control alone achieves 7.7% of total electricity consumption
savings in small offices located in Climate 4A, by reducing 6.7% HVAC
consumption and 28.2% plug loads. The electricity intensity is thus reduced
from 132.4 $kWh/m^{2}$ to 122.2 $kWh/m^{2}$, achieving substantial savings of
10.2 $kWh/m^{2}$.

Figure 7: Comparison of Electricity Consumption Intensity between Static and
Dynamic Occupancy-based Control for Small Offices in Climate 4A

###  3.3 Passive Cooling Strategies (Night Purge)

We implement a strategy for precooling a building at night using outdoor air.
This strategy can consist of running the system fans with the outdoor air
dampers open when outdoor conditions are favorable for a precooling strategy.
The zone terminal unit air dampers may also be held at their fully open
position to minimize fan energy consumption while precooling.

Figure 8 shows the daily energy saving from the HVAC by different daily mean
OAT ranges for a small office building in the climate zone 4A. It can be seen
that the night purge strategy has played a role in reducing HVAC energy
consumption when the climate is suitable. When the daily mean OAT exceeds
about 25 ºC, night ventilation may not be able to effectively reduce the HVAC
operating time during the day, thus wasting the energy of the fan at night.

Figure 8: Daily Energy Saving from HVAC by Different Daily Mean OAT Ranges
(left) and Cooling Electricity Consumption intensity in Cooling Season (right)

During the cooling season, the night purge alone saves 3.0% of HVAC energy
consumption in small offices located in Climate 4A, as shown in Figure 8. The
energy intensity is reduced by approximately 0.7 $kWh/m^{2}$, which includes
0.7 $kWh/m^{2}$ of cooling energy savings and 0.05 $kWh/m^{2}$ of fan energy
increase.

Night purge is most effective in the buildings with high thermal mass and
climates that diurnal temperature swing is significant or summer is mild [24].
In the cases when buildings have exposed concrete slabs, the night purge will
cool down the slab temperature, which will help reduce the daytime HVAC energy
consumption thanks to lowered radiant temperature and operative temperature.
When night purge is applied along with phase changing material and adaptive
thermal comfort setpoint, it will create a synergistic effect and unlock more
energy savings [16]. The cooling demand on the HVAC system is greatly reduced
as the phase-changing material that is cooled by the cool night air, slowly
absorbs heat throughout the day and keeps indoor air temperature close to the
adaptive thermal comfort temperature.

###  3.4 Combined Measures

Combining the three optimization strategies above, buildings can achieve the
highest energy savings. As shown in Figure 9, the standard small office in
climate zone 4A reduces annual electricity consumption by 12.4%, implementing
adaptive setpoint, occupancy-centric control, and night purge natural
ventilation. Among these individual measures, occupancy-centric control is the
most effective strategy and leads to a 7.7% reduction in total electricity
consumption, as the savings come from the HVAC system, plug load, and
lighting. The adaptive setpoint achieves a 4.6% reduction in annual
electricity savings, all of which stems from reduced cooling energy of the
HVAC system. The night purge ventilation is the least effective measure and
saves 0.4% of total electricity consumption, which is also solely from reduced
cooling energy consumption. The interactive effect of these three measures is
insignificant as the sum of individual savings (12.7%) is very close to the
combined savings (12.4%).

Figure 9: Potential Annual Electricity Savings for Individual and Combined
Measures in Small Office

###  3.5 Comparison between Different Climates

Figure 10 shows the annual electricity savings comparison of EE measures
between different climates. It can be clearly seen that the effect of the
dynamic occupancy behavior model is consistent in all climate conditions,
saving about 7.4-9.5% per year. In contrast, the adaptive comfort model is
primarily influenced by the climate, as shown in Figure 10 (a). In terms of
reducing cooling power consumption, the effect of the adaptive comfort model
decreases from 12% to 1.5% as the climate changes from hot to cold. On the
other hand, the humidity also has a large impact on the effect of the adaptive
comfort model. Under the same climatic conditions, a drier climate can achieve
much higher savings compared to a humid climate.

Among the three measures, the effect of the ”night purge” strategy is fairly
limited, saving only about 0.1% to 1% per year. As shown in Figure 10 (c), the
most effective climate zone for night purge is 3C (ocean), which is warm
during the day and cool at night. Previous studies have shown that in dry
climates with warm days and cool nights, this measure is usually worth
considering.

Figure 10: Comparison of Energy Efficiency Measures between Different Climates

From hot to cold climates, the annual electricity savings percentage by
adopting adaptive thermal comfort decreases as the cooling energy is
responsible for smaller proportions of total electricity consumption in cooler
climates. Climates that belong to different humidity subcategories also show
different levels of cooling energy savings. As shown in Figure 11, dry
climate, or subcategory B, benefits most from the adaptive cooling setpoints.
Humid climate, or subcategory A, sees a lower saving percentage as the HVAC
system consumes energy to meet the latent cooling load for moisture removal.
Marine climate, or subcategory C, shows the least saving percentage because of
its mild summer that results in a smaller percentage of cooling energy of the
total electricity consumption.

Figure 11: Cooling Energy Savings by Climates

Figure 12 presents the annual electricity savings achieved by combining three
EE measures across all climate zones in the United States. In the hot and dry
climate zone ”2B”, the highest saving is about 20%. In contrast, the lowest
saving observed in the cold climate zone “6A” is only 8.9%, and most of the
electricity savings come from smart plug load control.

Figure 12: Potential Annual Electricity Savings for Combined Measures in Small
Office among Difference Climates

Table 3 summarizes the annual electricity savings at the entire building level
and HVAC end-use level in different climate regions in the United States. The
deployment of combined energy efficiency measures can save 12.2 $kWh/m^{2}$ to
30.4 $kWh/m^{2}$ per year. Most of the savings come from HVAC end-use, which
is about 6.5 $kWh/m^{2}$ to 22.6 $kWh/m^{2}$. Compared to the baseline,
combined energy efficiency measures can achieve electricity savings of 9% to
20% for the entire building, and 23% to 39% for HVAC end-use.

Table 3: Annual Electricity Saving of Combined Energy Efficiency Measures for Small Offices in Different Climates Climate Zone | Annual Savings ($kWh/m^{2}$) | Annual Savings (%)
---|---|---
Total Electricity | HVAC | Total Electricity | HVAC
1A | 29.5 | 21.4 | 19% | 33%
2A | 26.6 | 18.6 | 18% | 32%
2B | 30.4 | 22.6 | 20% | 39%
3A | 22.3 | 15.0 | 16% | 36%
3B | 25.1 | 17.6 | 18% | 37%
3C | 18.3 | 10.5 | 15% | 30%
4A | 16.4 | 10.0 | 12% | 30%
4B | 21.1 | 13.9 | 16% | 35%
4C | 12.4 | 6.6 | 10% | 25%
5A | 14.3 | 7.7 | 11% | 29%
5B | 16.9 | 10.2 | 13% | 30%
6A | 12.2 | 6.5 | 9% | 23%
6B | 13.4 | 7.2 | 10% | 26%

##  4 Conclusion

The U.S. commercial buildings have substantial energy-saving potential if the
building control could address varying occupancy, occupant’s thermal
preference, and utilizing free cooling. This study quantifies the energy
savings in small office buildings across all major U.S. climate zones, based
on the commercial prototype building models developed by the U.S. Department
of energy. The energy-saving effectiveness of each individual measure and all
measures combined are presented.

The adaptive cooling setpoints are applied to avoid over-cooling in commercial
buildings, taking into consideration people’s adaptive behavior and clothing
adjustment against general weather conditions. This measure is extremely
effective in reducing cooling energy consumption, especially in climate 2B, in
which the adaptive cooling setpoint alone saves 12% electricity consumption of
the small office building, compared to the baseline static cooling setpoint at
22.2°C.

The occupancy-centric control, enabled by IoT sensors that detect occupancy
and motion, is applied to both the HVAC system and smart plugs control. The
corresponding savings of the HVAC system energy consumption is around 6.7% and
savings of plug load is about 28.2%. This measure alone saves approximately
7.7% of total electricity consumption across all climate zones.

The night purge ventilation utilizes free cooling and improves indoor air
quality. This measure alone reduces up to 3.0% of the cooling energy
consumption of the HVAC system for small offices in climate 4A. Specifically,
it is most effective in marine climates such as 3C (San Francisco) and 4C
(Seattle), and can achieve approximately 5.6% of cooling electricity
consumption. It is equivalent to about 0.9% of the total electricity
consumption of the building.

Significant total electricity savings ranging from 8.9% to 20.4% can be
achieved by combining all three measures, which are equivalent to 12.2
$kWh/m^{2}$ to 30.4 $kWh/m^{2}$ annual reductions in electricity usage
intensity. The electricity-saving percentages show a decreasing trend from hot
to cold climate. For climate zones with similar numbers of cooling degree days
and heating degree days, the dry subzones achieve the highest energy savings.

Enabled by building IoT sensors, smart hardware, and automated building
subsystems, more energy-saving opportunities can be unlocked by smart control
to improve the energy efficiency of commercial buildings. This study
quantifies the electricity savings from adaptive setpoint, occupant-centric
control, and night purge ventilation in small office buildings across all U.S.
climate zones. The next step is to carry out experiments of such ”plug and
play” IoT sensing and control devices (for example, smart thermostats with
occupancy sensors, smart plugs, window actuators) in small offices and
quantify the energy-saving and demand reduction potential.

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