Mathshop is an educational program that teaches mathematics to pre-school and school-aged children in Mongolia. The document discusses using Bayesian Knowledge Tracing (BKT) to model students' knowledge based on their use of the Mathshop program. BKT is shown to accurately model over 60,000 practice problems completed by 765 students on 275 math skills. The models are able to predict student performance and identify skills they have yet to master to aid improvement. Results demonstrate BKT is effective for evaluating student knowledge in Mathshop and helping teachers, parents and designers optimize the program.

1. Mathshop

2. OUR VISION & MISSION FOR EDUCATION

3. ЗОРИЛГО
МАТЕМАТИКИЙН СУРГАЛТЫГ ЦАХИМ ХЭЛБЭРТ ШИЛЖҮҮЛЭН СОНИРХОЛТОЙ
БАЙДЛААР ХҮҮХДЭД ХҮРГЭХ ...

4. MATHSHOP
ПРОГРАМЫН ОНЦЛОГУУД
 Монгол улсын бага, дунд боловсролын математикийн хичээлийн улсын хөтөлбөрийг үндэс
болгосон
 Англи, монгол хэл дээр суралцах боломжтой
 Бүлэг, сэдэв бүр хязгааргүй бодлогын сантай
 Орон зай цаг хугацаанаас үл хамааран интернэттэй болон интернэтгүй орчинд хэрэглэх
боломжтой
 Бие даан суралцах арга барил эзэмшүүлнэ
 Mathshop хэрэглэгч найзуудынхаа амжилтыг харж тэднээс суралцах боломжтой
 Математикийн хичээлийг хялбар аргаар судалж чөлөөт цагаараа сонирхолтой хэлбэрээр
мэдлэг олж авахад тустай
 Анги бүр цахим ном болон эцэг эхчүүдэд зориулсан булантай

6. Бага Дунд
БэлтгэлАхлах
Сургуулийн өмнөх
боловсрол
8-
12
анги
1-7
анги
Ерөнхий
боловсрол
ХАМРАХ ХҮРЭЭ

7. СУРГУУЛИЙН ӨМНӨХ НАСНЫ СУРАГЧДАД ЗОРИУЛСАН ТОО ТООЛЛЫН ХИЧЭЭЛИЙГ
ОЛОН УЛСЫН СТАНДАРТААР БАЯЖУУЛСАН
• Хэл яриа, сэтгэхүйн чадвар эзэмшүүлэх хүрээлэн байгаа орчин,
юмс үзэгдлийн талаар анхны мэдэгдэхүүнтэй болгох
• Хос хэлний суурь мэдлэг эзэмшүүлэх
• Аудио бичлэгтэй
• Бие даан суралцах арга барил эзэмшүүлэх
• Сургуулийн өмнөх тоо тооллын хичээлийн бүрэн мэдлэг олгох
ХАМРАХ ХҮРЭЭ

8. 1-7-р Анги
Энгийн
Бүлэг 1
Сэдэв 1
Сэдэв 2
Сэдэв 3Бүлэг 2
Дунд
Бүлэг 1
Сэдэв 1
Сэдэв 2
Сэдэв 3Бүлэг 2
Ахисан
Бүлэг 1
Сэдэв 1
Сэдэв 2
Сэдэв 3Бүлэг 2
ХАМРАХ ХҮРЭЭ

9. ХАМРАХ ХҮРЭЭ

10. ХАМРАХ ХҮРЭЭ

11. ХАМРАХ ХҮРЭЭ

12. BAYESIAN KNOWLEDGE TRACING
Bayesian Knowledge Tracing (BKT) is one of the most popular knowledge
inference models due to its predictive accuracy, interpretability and
ability to infer student knowledge. We present results from our ongoing
research which uses BKT tool to evaluate and model the knowledge of
students who use our Mathshop program. The Mathshop program gives
opportunity to pre and school age children to learn mathematics in an
engaging and interesting way based on new mathematics educational
standards, trends and curriculum of mathematical competence. By using the
application, children will develop the capacity to know and practice basic
concepts of mathematics by themselves, while also being provided with the
full opportunity to improve their learning techniques, confidence, ability
to express themselves and develop their intelligence and thinking skills.

13. BAYESIAN KNOWLEDGE TRACING
BKT
+Forgetting
+Item difficulty
+individualization
Logistic models
Performance factor analysis
Addictive factors model
Elo rating system
Generalizations
Feature aware student modeling
Latent-factor knowledge tracing
Mixture modeling
Fig. 1. Overview of basic approaches for modeling learning

14. BAYESIAN KNOWLEDGE TRACING
10 1 10 1
0 0 11 1
Knowledge
component
1
Knowledge
component
2
✓ ✓ ✓ ✓✕ ✕
✓ ✓ ✓
✕✕
Fig. 2. Knowledge components
p(L1)u
k=p(L0)k
(1a)
p(Lt+1|obs=wrong)u
k
=
p(Lt)u
k∗(1−p S)k
p(Lt)u
k∗(1−p S)k +(1−p Lt)u
k ∗p(G)k
1b
p(Lt+1|obs=wrong)u
k=
p(Lt)u
k∗p(S)k
p(Lt)u
k∗p(S)k+(1−p Lt)u
k ∗(1−p(G)k)
(1c)
p(Lt+1)u
k=p(Lt+1|obs)u
k+(1−p Lt+1 obs)u
k ∗p T)k
(1d)
p(Ct+1)u
k=p(Lt)u
k∗(1−p S)k +(1−p Lt)u
k ∗p(G)k
(1e)
p(L0) Probability of initial knowledge
p(T) Probability of learning
p(G) Probability of guess
p(S) Probability of slip.
(1a) - The initial probability of student u mastering
skill k
(1b) – The correct probability of student u applied
skill k
(1c) - The incorrect probability of student u applied
skill k
(1d) - The conditional probability is used to update
the probability of skill mastery
(1e) - the probability of student u applying the skill

15. KNOWLEDGE COMPONENT IN THE MATHSHOP
For this work, we have used skill score data of primary school
students of two schools, a public school and a private school.
The dataset consists of Mathshop program’s test results of 63300
transactions belonging to 765 students' work on 275 different
skills. We have developed student model using BKT for each
primary school class. The preliminary result show possibility of
using BKT in interpretation of math skills earned with Mathshop
program.
Fig. 3. An example task of Mathshop software.
Model Number of Rows RMSE Accuracy
Class01
A
2470 0.351916 0.843320
Class01
B
960 0.386457 0.785417
Class01
C
600 0.383071 0.795000
Class02
A
6040 0.356172 0.831126
Class02
B
1710 0.350951 0.830409
Class02
C
1090 0.388684 0.784404
Class03
A
9350 0.309066 0.885561
Class03
B
4080 0.353069 0.828676
Class03
C
1650 0.357539 0.830303
Class04
A
9970 0.322438 0.866700
Class04
B
1630 0.305653 0.884049
Class04
C
580 0.298566 0.862069
Class05
A
13140 0.246912 0.926332
Class05
B
2320 0.360068 0.817316
Class05
C
7460 0.359890 0.822252

16. KNOWLEDGE COMPONENT IN THE MATHSHOP
The aim of this research was to show the advantages of learners’ knowledge modeling using BKT
and therefore develop an automatic skill development recommendation to bridge the knowledge gap for
the users of the Mathshop program. If the learner’s initial knowledge and the transition parameters
are less than the slip and the guess parameters in knowledge model, Mathshop recommends returning
to the task for later. For example, this was the case in the task Fractions and Decimals” shown in
figure 4.
Fig. 4. Comparison of different tasks in the 4th grade

17. CONCLUSION
In the first test, we have used the Brute-force algorithm. It takes about 15 minutes to estimate
knowledge parameters of 13200 records. It was established that Brute force algorithm is expensive
in computational cost. Therefore, we have used standard BKT tool by EM method to avoid these costs.
In this case BKT tool’s processing time was 0.203 seconds for the same data.
Results of the tests show that Bayesian Knowledge Tracing is an effective way to evaluate the
students' knowledge in Mathshop program. A student model can represent a wide range of students’
characteristics.
Visualization of student learning processes with the BKT tool creates the following advantages:
1. Visual results of BKT based knowledge model could be used to improve base curriculum of the
subject and they also could help teachers to assess student knowledge.
2. Gathering the knowledge track of each student helps parents to see their child's actual level of
knowledge and find out what subject they need to focus on.
3. By collecting the statistics of student’s knowledge, the Mathshop designers and advisors can
continuously improve the program contents and its way of presentation and other tactics.

18. CONCLUSION

19. CONCLUSION

20. CONCLUSION

21. CONCLUSION

22. АНХААРАЛ ТАВЬСАНД
БАЯРЛАЛАА!
ЦАХИМ ХУУДАС: MATHSHOP.MN
ХАЯГ: СБД, 8-Р ХОРОО, ОЮУТНЫ ГУДАМЖ, ЮНИТИ ЦЕНТР, 405 ТООТ
УТАС: 88272796, 99997326
FACEBOOK:MATHSHOP ХЭРЭГЛЭГЧДИЙН ГРУПП