# Maths Learning Tool

**1. Overview**

**1. Overview**

Bachelors thesis project at Department of Design, Indian Institute of Technology (IIT) Guwahati.

I found that students with low logical-mathematical intelligence [1] struggle to learn Maths in conventional ways. To address this problem I designed and evaluated two physical tools and an educational board game that draw upon users' multiple intelligence to aid learning geometry, algebra, and calculation. I found that the interventions helped visualize spatial concepts, understand abstract concepts, and ease anxiety related to calculation.

I got the top grade (A+) for this project at IIT. IIT is the **number 1 ranked** engineering institute in India. Being the best, it has a low acceptance rate of around 2%.

**Duration**

August 2015 - April 2016

(9 months)

**2. Methodology**

**2. Methodology**

I followed the design research methodology [2] to discover, redefine, and investigate the problem by designing and evaluating interventions based on empirical and secondary research data.

**Objectives**

**Objectives**

**Tasks and Methods**

**User research**

Contextual inquiry

Observation

Fly-on-the-wall

Think aloud

Interviews

Focus groups

Surveys

Affinity analysis

Statistical analysis

**Secondary research**

Literature research

Competitive analysis

Mind map

Reference model

Problem framing and scoping

**Design**

Idea generation

Selection matrix

Idea detailing

Evidence-based design

Parallel prototyping

Physical prototyping

Game design

**Evaluation**

Case study

Contextual inquiry

Lab study

Observation

Think aloud

Interviews

Surveys

Affinity analysis

Traingulation

Play testing

**3. Problem Framing**

**3. Problem Framing**

I did a **literature review** covering four major domains.

I analyzed the findings using a **reference model** to identify research gaps and frame the problem.

**Theoretical Framework**

I used the theory of multiple intelligence by Howard Gardner [1] to guide my research. According to this theory, humans possess seven types of intelligence with varied strengths of each.

**Identified Problem**

Conventional ways of learning Maths rely on learners' logical-mathematical intelligence [1,3]. This results in disengagement, reduced learnability, and eventually Maths anxiety for students with low logical-mathematical intelligence [4].

**Identified Opportunity**

Facilitate learning Maths for students with low logical-mathematical intelligence by utilizing their stronger intelligence types.

**Problem Scoping**

I focused on

National Council of Educational Research and Training (NCERT) Maths.

Standard 6 and 7 of Indian schooling system.

Learners with strong spatial-visual intelligence and bodily-kinesthetic intelligence.

**4. User Research Process**

**4. User Research Process**

**63**

**63**

**Students**

31 female, 30 male

31 from standard 6

32 from standard 7

**3**

**3**

**Teachers**

1 female, 2 male

2 teaching standard 6

1 teaching standard 7

**6**

**6**

**Schools**

Guwahati, Assam

**Objectives**

Identify standard 6 and 7 NCERT Maths

**topics**that students usually find challenging to learn.Identify some of the key

**challenges**faced by students in learning these topics.Access students'

**multiple intelligence profile**[1].Explore

**relation**, if any, between students' multiple intelligence profile [1] , topics found to be challenging, and challenges faced.

**User Screening**

Students who find it

**challenging**to learn Maths, by asking teachers to identify.Students with

**strong**spatial-visual intelligence and bodily-kinesthetic intelligence.

**Data Collection**

**Surveys**with students and teachers to identify topics that students find challenging to learn.

Individual semi-structured

**interviews**with teachers involving open-ended questions like -

*Can you tell me about a recent challenge you faced when teaching Maths?*

*How did you navigate it?*

Individual semi-structured

**interviews**and**focus groups**with students involving open-ended questions like -

*In the survey, you mentioned that you find the chapter "Algebraic Expressions" to be challenging. **Can you tell me about what a particular challenge you face in the chapter?*

*Can you tell me about your experience of learning this topic in class?*

**Observation**of students solving, using**think-aloud**protocol, the questions they identified to be difficult.**Contextual inquiry**of maths lecture being delivered in school and in tuition classes. I used the**fly-on-the-wall**method and took**observational notes**of the activities, teaching approaches, tools used, and student engagement. For example, I observed how the teacher helped students one-on-one when they were unable to solve questions.

**Surveys**to access students' multiple intelligence profiles [5].

**Data Analysis**

**Affinity analysis**of the qualitative data such as the interview transcripts.**Statistical analysis**of the quantitative data such as the survey responses.

**5. User Research Insights**

**5. User Research Insights**

Students' displayed **varied strengths** for the 7 types of intelligence across a class.

Topics found difficult by students varied with their intelligence profile. The diagram below shows the **dominant intelligence** type of the students who marked the chapters as difficult.

**6. Design Process**

**6. Design Process**

Based on the insights from the user research, literature review, and **competitive analysis** of existing tools for teaching and learning Maths, I generated several **ideas** to address the identified user needs.

Using a **selection matrix**, I narrowed down to three ideas for further exploration using **parallel-prototyping**. I iteratively detailed and prototyped these three ideas using methods such as **hands-on exploration** and **playtesting**. For example, I tried out various types of building blocks, materials, and joints while detailing the idea of a tool for constructing geometric shapes.

The final three ideas involve two physical tools and an educational board game** **to learn algebra, geometry, and calculation, respectively. These interventions utilize **learners' strength** by relying on their spatial-visual intelligence and bodily-kinesthetic intelligence.

**7. Intervention 1 - Polyblocks**

**7. Intervention 1 - Polyblocks**

Polyblocks is a physical tool to aid students in understanding, visualization, and problem-solving when learning Geometry. It involves wooden building blocks and joints that can be used to build 2D shapes and cuboids.

**Design Features**

**8. Evaluation of Polyblocks**

**8. Evaluation of Polyblocks**

**Research Questions**

*In what ways do Polyblocks***help***users to solve questions from the "Congruence of Triangles" chapter?**What***challenges***do users face when using Polyblocks?*

**User Screening**

Based on the survey data I collected previously, I screened participants who had strong bodily-kinesthetic intelligence and found the "Congruence of Triangles" chapter difficult.

**Data Collection**

**Task and Procedure**

I introduced Polyblocks and asked participants to use it, while I guided them when necessary, for solving a question from the "Congruence of Triangles" chapter that was rated by teachers as easy.

**Task and Procedure**

*In ΔABC, AB = 6 cm, BC = 6 cm, AC = 9 cm. In ΔPQR, PQ = 9 cm, QR = 6 cm, PR = 6 cm. *

*(i) Are the two triangles congruent? Give reasons. *

*(ii) If the two triangles are congruent, write it symbolically. *

*(iii) Write the corresponding angles and the relationship between them. *

*(iv) Write the corresponding sides and the relationship between them.*

I then provided the participant with a question from the "Congruence of Triangles" chapter that was rated by teachers with medium level difficulty. I chose a question that had two solutions.

I asked the participant to first solve the question using pen and paper only and then to solve it using Polyblocks. They solved the question using

**think-aloud**protocol, while I**observed**them and answered their questions when necessary.I took

**observational notes**of participants' activities, comments, questions, ability to solve the question, issues they faced etc.After the task was completed, I conducted semi-structured

**interviews**involving open-ended questions like -

*In what ways, if any, do you think Polyblocks helped you in solving the question?*

*If we were to redesign Polyblocks for you, what are some of the changes you would like to see?*

**Data Analysis**

I did **affinity analysis** of the interview data and observational notes. I analyzed the video recordings of the sessions looking for more details and for **triangulation**.

**Insights**

Participants

**quickly learned**to use PolyblocksParticipants

**enjoyed**using Polyblocks, as it allowed them to actively engage through hands-on activity, compared to using only pen and paper.**Hands-on manipulation**such as rotating, flipping, and overlapping the triangles helped participants to visualize and understand. This in turn helped them to solve certain parts of the question that they were unable to solve using pen and paper.

*"This [Polyblocks] is fun to use. I like to build things and play with it, it helps me think."*

**Challenges Faced by Participants**

Conversion of side lengths in terms of the 3 cm blocks was time-consuming and error-prone.

Visibility was hindered by the protractors when the triangles were overlapped, which resulted in errors.

**Design Recommendations**

Use an analog object which can be pulled to the desired length for constructing the sides.

Use transparent material for the protractor.

**9. Conclusion**

**9. Conclusion**

**Limitations Future Work**

**What I Learned**

**Achievement**

*I got the top grade (***A+***) for this Bachelors thesis project*

**Where are the Other Interventions?**

**Where are the Other Interventions?**

To keep the length of this post reasonable, I will soon create separate posts to discuss the design and evaluation of the other two interventions. For now, you can access an old version here.

References

- Gardner, H. E. (2011).
*Frames of mind: The theory of multiple intelligences*. Hachette Uk. - Blessing, L. T., & Chakrabarti, A. (2009).
*DRM: A design reseach methodology*(pp. 13-42). Springer London. - Wright, T. (2001). Karen in motion: The role of physical enactment in developing an understanding of distance, time, and speed.
*The Journal of Mathematical Behavior*,*20*(2), 145-162. - Arslan, C., Deringol-Karatas, Y., Yavuz, G., & Erbay, H. N. (2015). Analysis of research on mathematics anxiety in selected journals (2000–2013).
*Procedia-Social and Behavioral Sciences*,*177*, 118-121. - Psychology Today. Retrieved January 14, 2021 from https://www.psychologytoday.com/blog-posts

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