=Paper= {{Paper |id=Vol-3120/paper4 |storemode=property |title=Design of a User-Interpretable Math Quiz Recommender System for Japanese High School Students |pdfUrl=https://ceur-ws.org/Vol-3120/paper4.pdf |volume=Vol-3120 |authors=Yiling Dai,Brendan Flanagan,Kyosuke Takami,Hiroaki Ogata }} ==Design of a User-Interpretable Math Quiz Recommender System for Japanese High School Students== https://ceur-ws.org/Vol-3120/paper4.pdf

Design of a User-Interpretable Math Quiz Recommender System
for Japanese High School Students
Yiling Dai1, Brendan Flanagan 1, Kyosuke Takami1, and Hiroaki Ogata 1
1
Academic Center for Computing and Media Studies, Kyoto University, Japan

Abstract
In the context of K-12 math education, identifying the quizzes of the appropriate difficulty is
essential to improve the students’ understanding of math concepts. In this work, we propose a
quiz recommender system which not only considers the difficulty of the quiz but also the
expected learning outcome of solving that quiz. To increase the students’ motivation of
accepting the recommendations, our system provides interpretable information, i.e., the
difficulty and expected learning gain of a recommendation, to the students. We conducted a
pilot to implement this recommender system in a Japanese high school classroom. Overall, the
log data showed a low rate of usage. We summarized challenges in implementing the
recommender system in our specific setting, which help direct the future development of the
system and its evaluation at a larger scale.

Keywords 1
Adaptive learning, K-12 math education, Quiz recommendation, User-interpretable

1. Introduction
In the context of K-12 math education, identifying the quizzes of the appropriate difficulty is
essential to improve the students’ understanding of math concepts. Previous knowledge tracing works
have focused on estimating the knowledge states of the students and predicting students’ performance
of the learning materials [2, 5, 7, 8, 11]. This is based on an assumption that learning happens when
students attempt tasks in the zone of proximal development [13], i.e., the tasks they cannot achieve by
themselves but can achieve with assistance. However, these works did not consider how knowledge
states are improved and what improvement brought by the “proximal” learning materials should be
prioritized. In this work, we propose a quiz recommender system which not only considers the difficulty
of the quiz but also the expected learning outcome of solving that quiz. Among various learning
outcomes, we focus on the average improvement of the understanding of related math concepts. By
doing so, a quiz that helps the student to practice weaker concepts will be prioritized in the
recommendation.
Recent adaptive learning systems have attempted to recommend learning materials based on
complex methods such as deep learning methods [6] and reinforcement learning methods [12].
However, the mechanism and output of these methods are difficult to interpret, which may lead to the
decrease of students’ beliefs that they are able to do the task and their perceived values of completing
the task, which further decreases their motivation to participate [14]. Being intuitive and simple, our
recommender system is able to provide interpretable information, i.e., the difficulty and expected
learning gain of a recommendation, to the students.
Some works proposed educational recommender systems with explanations for different subjects,
different types of learning tasks, and different levels of education [1, 9]. Consequently, such
recommender systems are context-specific and difficult to be applied in our case. We conducted a pilot
to implement our proposed recommender system in a Japanese high school classroom. By analyzing
the log and questionnaire data, we identified some challenges which help direct the future development
of the system and its evaluation at a larger scale.

Proceedings of the 4th Workshop on Predicting Performance Based on the Analysis of Reading Behavior, March 21-22, 2022
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CEUR Workshop Proceedings (CEUR-WS.org)
2. System overview

(a) Recommender system and other modules. (b) Interface of BookRoll.
Figure 1: An overview of the learning system.

As Figure 1a shows, our recommender system is built on an integrated learning system where an e-
book reading module called BookRoll [3] works to register and present the quizzes, and a learning
record store (LRS) module stores the students’ answers of the quizzes. The interface of viewing and
answering the quizzes is shown in Figure 1b. In this work, we only record whether the student correctly
answered the quiz for each attempt. In the recommendation module, we first extract the necessary
concepts for the registered quizzes. Then, we estimate the students’ mastery levels on the concepts
based on their answers on the quizzes, which is further utilized to recommend quizzes that complement
and extend their knowledge. In the following section, we describe the mechanism of the recommender
system in detail.

3. Proposed recommender system
3.1. Problem definition
Suppose we have a student 𝑠 and |𝑄| quizzes. We model the student’s attempts on the quizzes
as 𝑠𝑡 = {(𝑞1 , 𝑟1 ), . . . , (𝑞𝑡 , 𝑟𝑡 )}, where 𝑟𝑡 is the student’s response to 𝑞𝑡 at step 𝑡 . 𝑟 equals 1 if the
answer is correct and 0 otherwise. Our goal is to select and rank a subset of the quizzes that improve
the student’s knowledge acquisition. We denote it as 𝑅𝑒𝑐𝑜𝑚𝑚𝑒𝑛𝑑(𝑄|𝑠𝑡 ) = (𝑞1 , 𝑞2 , . . . , 𝑞𝑛 ), where n
is a predefined number of quizzes to recommend. In the following sections, we describe the procedures
in detail with a running example showed in Table 1.

3.2. Procedure
3.2.1. Extracting underlying concepts.
Table 1.
Examples of quizzes.
Quiz Content
𝑞1 Proof of the following equality of triangles (𝑏 − 𝑐)𝑠𝑖𝑛𝐴 + (𝑐 − 𝑏)𝑠𝑖𝑛𝐵 + (𝑎 −
𝑏)𝑠𝑖𝑛𝐶 = 0.
𝑞2 What is the shape of the triangle if the equality 𝑎𝑠𝑖𝑛𝐴 = 𝑏𝑠𝑖𝑛𝐵 holds?
𝑞3 Given △ 𝐴𝐵𝐶 and the radius of its circumcircle is 𝑅 what is 𝑏 and 𝑐𝑜𝑠𝐴 when 𝑎 = 2, 𝑐 =
4𝑐𝑜𝑠𝐵, 𝑐𝑜𝑠𝐶 = −1/3?
𝑞4 In △ 𝐴𝐵𝐶 ∠𝐵 = 60° 𝐴𝐵 + 𝐵𝐶 = 1. 𝑀 is the midpoint of 𝐵𝐶 . What is the length of 𝐵𝐶
such that the length of line segment 𝐴𝑀 is minimum.
Solving a math quiz requires knowledge of related concepts. For instance, to solve 𝑞1 in Table 1, the
students should know and be able to apply the knowledge of proof, law of sines, and etc. Understanding
how students master the underlying concepts of the quizzes help us estimate their knowledge states
more precisely, therefore, provide better remedial strategies.
Identifying the concepts required to solve the quizzes is not an easy task. Some of the concepts can
be identified in the textual information of the quiz and its standard answer while some cannot. In this
work, we take an initiative attempt to utilize the noun phrases as the concepts. For example, we deem
proof, equality, and triangle as necessary concepts to solve 𝑞1 . We denote the underlying concepts of
a quiz set as 𝐶. For each pair of 𝑞 and 𝑐, 𝑟𝑒𝑙𝑎𝑡𝑒𝑑𝑛𝑒𝑠𝑠(𝑞, 𝑐) denotes the relatedness between a quiz and
a concept, which indicates the degree to which the knowledge of a concept is necessary in solving the
quiz. For preprocessing, we use pdftotext2 to extract the plain texts of quizzes from PDF format. Then,
we adopt Janome3 to parse the Japanese terms in the quiz text. Last, we use a classic term weighting
method TFIDF [10] to compute 𝑟𝑒𝑙𝑎𝑡𝑒𝑑𝑛𝑒𝑠𝑠(𝑞, 𝑐), which is implemented in scikit-learn4.

3.2.2. Estimating mastery level on concepts.

Figure 2: An illustration on computing mastery level on concepts.

After extracting the concepts and their relatedness to the quizzes, we estimate the students’ mastery
level on the concepts 𝑚𝑎𝑠𝑡𝑒𝑟𝑦_𝑙𝑒𝑣𝑒𝑙(𝑐|𝑠𝑡 ) from their learning history in Equation (1).

∑𝑞∈𝑄𝑠 𝑟𝑒𝑙𝑎𝑡𝑒𝑑𝑛𝑒𝑠𝑠(𝑞,𝑐)∙𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑛𝑒𝑠𝑠_𝑟𝑎𝑡𝑒(𝑞|𝑠𝑡 )
𝑡
𝑚𝑎𝑠𝑡𝑒𝑟𝑦_𝑙𝑒𝑣𝑒𝑙(𝑐|𝑠𝑡 ) = ∑𝑞∈𝑄𝑠 𝑟𝑒𝑙𝑎𝑡𝑒𝑑𝑛𝑒𝑠𝑠(𝑞,𝑐)
(1a)
𝑡
(𝑞,1)
𝑠
𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑛𝑒𝑠𝑠_𝑟𝑎𝑡𝑒(𝑞|𝑠𝑡 ) = 𝑡(𝑞) (1b)
𝑠𝑡

where:
𝑄𝑠𝑡 = the set of quizzes in a student’s attempts
𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑛𝑒𝑠𝑠_𝑟𝑎𝑡𝑒(𝑞|𝑠𝑡 ) = the correctness rate of 𝑞 in a student’s attempts
(𝑞,1)
𝑠𝑡 = the correct attempts on 𝑞
(𝑞)
𝑠𝑡 = all the correct attempts on 𝑞
As illustrated in Figure 2, we compute the mastery level on each concept by looking at how the
student answered the quizzes which require the knowledge of this concept. Suppose the student had
attempted three quizzes 𝑞1 , 𝑞2 , and 𝑞3 , all of which require the knowledge of 𝑐1 . However, the student
failed on 𝑞2 at the first attempt and it is not counted in the computation of mastery level on 𝑐1 . Note
that for the unseen quizzes, their requirement on the concepts is not considered in the computation. In
other words, the mastery level only reflects the student’s understanding of the concepts in the context
of quizzes s/he had attempted.

2 https://github.com/jalan/pdftotext

3 https://mocobeta.github.io/janome/

4 https://scikit-learn.org/stable/
3.2.3. Estimating quiz difficulty and expected learning gain.

Figure 3: An illustration on computing quiz difficulty and expected learning gain.

To improve the acquisition of knowledge, the student needs to practice on quizzes that are of
appropriate difficulty and provide learning gain at the same time. Therefore, we propose two criteria—
quiz difficulty and expected learning gain— to decide which quizzes to recommend. Quiz difficulty
reflects the probability that the student will give a wrong answer. As shown in Equation (2) and Figure
3, it is inferred from the student’s mastery level on the concepts required in this quiz. Taking 𝑞1 for
example, the students’ mastery level on 𝑐1 , 𝑐2 , and 𝑐4 indicates how possible s/he is able to solve 𝑞1 .
By subtracting it from 1, we obtain the probability that the student will fail to solve 𝑞1 , i.e., the difficulty
of 𝑞1 . Note that for the unseen concepts, we set the mastery level as 0 to simplify the computation.

∑𝑐∈𝐶 𝑚𝑎𝑠𝑡𝑒𝑟𝑦_𝑙𝑒𝑣𝑒𝑙(𝑐|𝑠𝑡 )∙𝑟𝑒𝑙𝑎𝑡𝑒𝑑𝑛𝑒𝑠𝑠(𝑞,𝑐)
𝑞𝑢𝑖𝑧_𝑑𝑖𝑓𝑓𝑖𝑐𝑢𝑙𝑡𝑦(𝑞|𝑠𝑡 ) = 1 − ∑𝑐∈𝐶 𝑟𝑒𝑙𝑎𝑡𝑒𝑑𝑛𝑒𝑠𝑠(𝑞,𝑐)
(2)

The expected learning gain of a quiz at step 𝑡 is the average mastery level update on the concepts if
the student successfully solves the quiz at the next step 𝑡 + 1, as computed in Equation (3).

where 𝐶𝑞 is the set of concepts required in 𝑞. As illustrated in Figure 3, when computing the expected
learning gain of 𝑞2 , we first update the student’s mastery level on concepts assuming s/he successfully
solved 𝑞2 . Then the total improvement on the mastery level is normalized by the number of concepts
required in 𝑞2 .

3.2.4. Recommending quizzes.
We recommend quizzes based on the estimated difficulty and expected learning gain. Since both of
quiz difficulty and expected learning gain are computed from students’ mastery level of the concepts,
they are intertwined with each other. Intuitively, a more difficult quiz may provide more learning gain
if the student successfully solved it. Meanwhile, it requires the students to have more tolerance of
uncertainty and to seek extra assistance in solving the quiz. Therefore, we adopt a recommending policy
that the quiz is neither too difficult nor too easy to the students, yet provides learning gain as much as
possible. As a result, the quiz to be recommended is not necessarily the one with the highest expected
learning gain.
To do so, we select the quizzes in a proper range of difficulty and then rank them based on the
expected learning gain in descendant order. Given a predefined number 𝑛 of quizzes to recommend, the
recommended set of quizzes and their order is 𝑅𝑒𝑐𝑜𝑚𝑚𝑒𝑛𝑑(𝑄|𝑠𝑡 ) = (𝑞1 , . . . , 𝑞𝑛 ) such that for any
1 ≤ 𝑖 ≤ 𝑛 , 𝛼 ≤ 𝑞𝑢𝑖𝑧_𝑑𝑖𝑓𝑓𝑖𝑐𝑢𝑙𝑡𝑦(𝑞𝑖 |𝑠𝑡 ) ≤ 𝛽 , and for any 1 ≤ 𝑖 ≤ 𝑗 ≤ 𝑛 ,
𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑_𝑙𝑒𝑎𝑟𝑛𝑖𝑛𝑔_𝑔𝑎𝑖𝑛(𝑞𝑖 |𝑠𝑡 ) ≥ 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑_𝑙𝑒𝑎𝑟𝑛𝑖𝑛𝑔_𝑔𝑎𝑖𝑛(𝑞𝑗 |𝑠𝑡 ) , where 𝛼 and 𝛽 are the
thresholds of difficulty. In the example of Figure 3, given the estimated difficulty and expected learning
gain, we recommend 𝑞2 if the acceptable difficulty is no greater than 0.3.

3.3. Strengths and limitations
Compared with previous works that recommend quizzes (or exercises in other contexts), our
proposed recommender system has the following strengths:
 Our recommendations are user-interpretable.
As described in Section 3.2, every step in the recommender system is intuitive and simple, which
makes it easy to provide explanations for the recommended quizzes. For example, we recommend
𝑞2 to the student since s/he does not fully understand 𝑐3 and by attempting 𝑞2 s/he may deepen the
understanding of 𝑐1 and 𝑐3 . This type of information is difficult to extract in deep knowledge tracing
methods [5–8] since the quizzes and knowledge states are usually embedded as vectors and
processed in complex computation.
 Our model takes the future learning gain into consideration.
In a knowledge tracing model, the main goal is to model and trace the changes of knowledge states
when students attempt quizzes. As a result, these models output the probability that a student can
solve a quiz successfully while they do not consider whether and how the knowledge state improves
by solving the quiz. In contrast, our model recommends quizzes taking the expected learning gain
into account, which is an effort to optimize the learning outcomes.
 Our model does not rely on the data of other students.
Unlike data-driven methods which rely on a large dataset of student attempts on the quizzes, our
model is content-based and is able to recommend quizzes merely using the data of one student. This
is important when implemented in a real classroom setting that usually does not have sufficient
student data on the quizzes.
 Our model is flexible and easy to modify.
Except for the two criteria we use in this work, our model is flexible to accept other criteria and
modifications. For example, we can recommend a quiz which improves the understanding of the
weakest concept instead of the overall understanding of the concepts. Or as in [1], we can set a target
of concepts as a learning goal, then the quizzes supporting the understanding of these concepts will
be prioritized.
Being intuitive and simple brings limitations too. For example, we do not consider the students’
ability to apply their previous knowledge when solving a new quiz. Besides, we simply assume the
students know nothing about unseen quizzes or concepts, which is not the case in real situations since
the unseen concepts may be related to the known concepts. As described in Section 3.2.1, we focused
on explicit noun phrases as the necessary concepts for solving a quiz. To obtain more underlying
concepts, methods such as topic models can be integrated in our recommendation framework. However,
interpreting the latent vectors could be another challenge. To address these limitations, considering the
relationships between concepts and introducing parameters that model more complex learning
behaviors are future works.

4. Pilot in high school classroom
Figure 4: The interface of the recommender system used in the pilot.

We conducted a pilot of the proposed recommender system in a real classroom setting as preparation
for a well-designed comparative experiment. In the pilot, one class of students of a Japanese high school
was invited to use the recommender system to solve quizzes during summer vacation from July 20th to
August 23rd, 2021. The teacher had assigned 54 quizzes and asked the students to finish the quizzes
and check the answers by themselves. Note that the students were highly recommended to solve the
quizzes and report their answers in the learning system. However, they were not required to do so since
they also can choose to solve quizzes in paper-based textbooks. In the BookRoll system, the students
can access the quizzes from a book directory, a list of quiz assignment, or from the recommender system
tab. While the students started to attempt the quizzes in the system, we recommended the assigned
quizzes accordingly. We set the acceptable quiz difficulty in the range of [0.1, 0.6]. Figure 4 shows the
interface of the recommender system where the estimated mastery level and the reasons why a quiz is
recommended were shown to the students. During the summer vacation, the log data of quiz answers
and recommendation clicks were collected5. After the summer vacation, we conducted a questionnaire
survey on the students’ perceptions of the recommender system.

4.1. Students’ reactions
Table 2.
Statistics of the usage of the recommender system.
Number of Students
Total students 38
Accessed the learning system 22
Clicked the recommended quiz 2
Answered the recommended quiz 1

Table 2 shows the statistics of the system usage during the pilot period. 57.9% of the students
accessed the learning system and only two students ever clicked the recommended quizzes. To further
investigate the reason of the usage of the recommender system, we analyzed the questionnaire survey.
The questionnaire contains 42 questions regarding the students’ perceptions of the recommender system
and attitudes towards math learning. Among the questions, 8 are descriptive and 34 are 5-likert scale
questions, which were found to have good reliability ( 𝛼 = 0.836 ). 30 students answered the
questionnaire and 3 incomplete answers were excluded in the following analysis. We separated the
students into two groups based on whether they reported that they ever used the recommender system.
The students whose answers were equal to or greater than 3 are treated as self-reported users (𝑛 = 6),
while the rest of the students are treated as self-reported non-users (𝑛 = 21). Note that the following
analysis is based on an assumption that we “trust” the self-reported results. We then conducted 2-tailed
t-test on the answers of the other questions between these two groups. Table 3 lists the questions that
had a significant difference (𝑝 < 0.05) between the two groups. We found that the self-reported users

5 The log data of quiz answers during August 12th and August 18th was not recorded due to a system bug.
demonstrated more positive attitudes towards the usefulness of the recommender system, more trust
towards the explanations and the recommender system, and more motivation to do math quizzes.
However, we are aware of the limitations such as the small sample size and the low reliability of self-
reported results.

Table 3.
Analysis on the questionnaire survey.
Self-Reported User Self-Reported Non-
(𝑛 = 6) User (𝑛 = 21)
mean sd mean sd 𝑡
Perception of the recommender system
I used the recommender system 3.33 0.82 2 0.95 3.40***
because it was easy to use.
The recommender system was 3.33 0.82 2.38 0.80 2.53*
useful.
I wanted to use the recommender 3.17 0.41 2.33 0.80 3.46***
system more.
I trusted the recommender system. 3.83 0.75 2.71 0.85 3.12**
I used the recommender system 3.67 1.03 2 1 3.51***
because the quizzes fitted to me.
I understood why I need to do the 4 0.63 2 1.05 5.80***
recommended quizzes.
I trusted the explanations of why 3.67 0.52 2.29 1.01 4.53***
the quizzes were recommended.
Attitude towards math learning
I became better at math because of 3 0.89 1.76 0.70 3.12**
the recommender system.
I enjoyed learning math more 3.33 1.21 1.95 1.02 2.55*
because of the recommender
system.
The system pushed me to do math 3.67 1.03 2.14 1.11 3.13**
quizzes.

4.2. Challenges
Based on the results of the pilot, we found the following challenges to implement a recommender
system in our specific classroom setting:
 The inertia of the students to do quizzes in paper-based methods.
Doing math quizzes and self-checking the answers require a large visual space to write down the
answer and then compare it with the standard answer. The current e-book reading system and the
device could not fully support this usage, which leads to extra work for the students to report their
answers in the system after solving them in the paper version. As some of the students reported in
the questionnaire, it was annoying to find the same quiz in digital-version and the paper-version. To
encourage more usage in the digital version, we need to improve the convenience of the e-book
reading system so that the students can easily switch between both versions.
 The compatibility with the standard teaching schedule.
As a request from the teacher, we limited the recommendations to an assigned set of quizzes in the
pilot. This reduces the meaning to use the recommender system as the students had to finish all the
quizzes at the end. However, there does exist a concern that if the recommended quizzes for each
student are distributed over diverse topics, the teacher may fail to keep a standard teaching schedule
and to give feedback instantly. In the future, we need to balance the standard teaching schedule and
the personalized learning.
 The definition of the usage of the recommender system.
In our recorded log data, only two students clicked the recommended quizzes. However, 6 students
reported they ever used the recommender system. One of the two students who clicked the
recommended quizzes reported s/he never used the recommender system. Obviously, there is a gap
between our and the students’ perceptions of “usage”. Besides, the students may provide unreal
answers both intentionally and unintentionally. As Fredricks et.al [4] suggest, engagement is a
multifaceted construct that relates to behavior, emotion, and cognition. In future work, we plan to
record more students’ engagement with the system in a more objective manner.

5. Conclusions and future works
In this work, we proposed a quiz recommender system which not only considers the difficulty of the
quiz but also the expected learning outcome of solving that quiz. To increase the students’ motivation
of accepting the recommendations, our system provided interpretable information, i.e., the difficulty
and expected learning gain of a recommendation, to the students. Our system has advantages over
existing methods as a) the recommendations are user-interpretable, b) the future learning gain is
considered, c) it does not rely on large sets of student data, and d) it is flexible to modifications.
We also conducted a pilot to implement this recommender system in a Japanese high school
classroom. The log data demonstrated a low usage of the system during the pilot. However, we did find
some positive signals between the attitudes toward the system and the self-reported usage of it from the
limited questionnaire data. More importantly, we identified some challenges such as the inconvenience
of the current e-book reading system, the incompatibility with the standard teaching schedule, and the
gap between the intended usage of the system and the students’ perceptions of it. In future work, we
plan to redesign the evaluation experiment with more clear instructions and more thorough and
objective ways to record students’ engagement and learning performance improvement.

6. Acknowledgements
This work was partly supported by JSPS Grant-in-Aid for Scientific Research (B) 20H01722, JSPS
Grant-in-Aid for Scientific Research (Exploratory) 21K19824, JSPS Grant-in-Aid for Scientific
Research (S) 16H06304 and NEDO JPNP20006 and JPNP18013.

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