Maths Learning Tool

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)

Team

Individual project supervised by

Dr. Pradeep G. Yammiyavar


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

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

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

63

Students

31 female, 30 male

31 from standard 6

32 from standard 7

3

Teachers

1 female, 2 male

2 teaching standard 6

1 teaching standard 7

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


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

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

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



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 Polyblocks

  • Participants 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

Limitations Future Work


What I Learned


Achievement

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


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

  1. Gardner, H. E. (2011). Frames of mind: The theory of multiple intelligences. Hachette Uk.
  2. Blessing, L. T., & Chakrabarti, A. (2009). DRM: A design reseach methodology (pp. 13-42). Springer London.
  3. 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.
  4. 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.
  5. Psychology Today. Retrieved January 14, 2021 from https://www.psychologytoday.com/blog-posts

More Projects