AN INTERACTIVE LEARNING TOOL FOR EARLY ALGEBRA EDUCATION

Masters ThesisSiva Meenakshi Renganathan

Advisor: Dr. Christopher StewartCommittee: Dr. Arnulfo Perez and

Dr. Radu Teoderescu

Siva Meenakshi RenganathanGraduate Research Associate, The Ohio State University

Previously:– B.E. in Computer Science and Engineering,

College of Engineering Guindy, India.– Software Development Intern,

Expedia Inc., Chicago.Publications:

– A. Perez, K. Malone, S. M. Renganathan, and K. Groshong “Computer modeling and programming in algebra”, in Proceedings of the 8th International Conference on Computer Supported Education, 2016, Volume 1, pp. 281-286.

– N. Morris, S. M. Renganathan, C. Stewart, R. Birke and L. Chen “Sprint Ability: How Well Does Your Software Exploit Bursts in Processing Capacity?”, IEEE International Conference on Autonomic Computing (ICAC), 2016, pp. 173-178.

– A interactive learning tool for early algebra education – Paper accepted in Frontiers in Educations, 2017.

Overview

■ We designed a web-based learning tool for an Algebra curriculum created in the T&L department

■ We deployed our tool at 5 schools for 700 students. It is currently in use.

■ We learned key principles to support interactive learning tools for curriculum that aims to show the duality of abstract concepts

– Co-designing curriculum and systems– Regulated data transfer between client and server– Integration with Classroom Management systems

Outline

■ Engineering driven curriculum

■ Curriculum’s Technical requirements

■ System Design and Design principles

■ Evaluation and Optimizations

■ Deployment and Analysis

■ Conclusion

Outline

■ Engineering driven curriculum■ Curriculum’s Technical requirements

■ System Design and Design principles

■ Evaluation and Optimizations

■ Deployment and Analysis

■ Conclusion

Issues with Traditional Curriculum

■ Divorces mathematical concepts from their STEM applicationsFor example: Linear Algebra is not taught alongside Ohm’s law.

■ Insufficient STEM experience in high school drives students away from STEM in college [1]

■ Hinders students’ understanding of STEM and its applications in real world

■ Does not leverage technology to teach students

Solution: Science and Engineering Driven Mathematics Curriculum■ We designed a new engineering driven Algebra curriculum [2]

■ Explores STEM concepts and applications simultaneously

■ Engage, Investigate, Model and Apply framework [3]

■ Uses computers and technology to bridge the gap between different representations of data: Equations, Graphs and Physical data.

Science and Engineering Driven Mathematics Curriculum■ Guide students to setup the apparatus for scientific

experiments

■ Repeat each experiment with different inputs and measure corresponding output

■ Plot this data on to graph and view its equation

■ Generate a regression curve and Observe the variation of curve in the graph as the parameters like slope and y-intercept changes

■ Understand the different representations of data: physical points, graph and equations

Chapter 1 – Linear Algebra and its ApplicationsBasic Linear Algebra:

Y = ( m * x ) + c– m is the slope of the line– C is the y-intercept of the line

Applications:– Ohm’s law– Measuring velocity of a moving vehicle

Ohm’s Law Experiment (V = I * R)Linear algebra correspondence:

Y = ( m * X ) + c I = ( 1/R * V )– I is the current in the circuit– V is the voltage in the circuit– R is the resistance in the circuit– m = 1/R , is the slope– c = 0, is the y intercept

■ Students measure different current outputs for different input voltages (batteries) and use the graph to find an unknown resistor.

Velocity Experiment (Velocity = Dist / Time)Linear algebra correspondence:

Y = ( m * X ) + c D = ( V * T )– D is the distance covered by the car– T is the time taken in seconds– m = V is the velocity (speed) of the car– c = 0, is the y intercept

■ Students measure the distance covered by the car in time T seconds in multiple runs and calculate the velocity of the car.

Outline

■ Engineering driven curriculum

■ Curriculum’s Technical requirements■ System Design and Design principles

■ Evaluation and Optimizations

■ Deployment and Analysis

■ Conclusion

Curriculum Technical Requirements

An Interactive Smart Classroom setup where students:1. Enter their experimental data2. Visualize it on to a graph3. Generate regression lines and their equations4. Interactively manipulate slope and y-intercept5. Observe the instant feedback upon changing slope and intercept6. Update axes to better understand negative slopes7. Save work and retrieve it later8. Collaborate and share data with other students

Curriculum Technical Requirements in Computer Science Abstraction■ Data Input

■ Data Visualization

■ Interactive updates on the visualized graph

■ Share data between users in real time

■ Save data and session to continue later

■ Integration with classroom management systems for easy adoption

Portal Demo

Portal Demo

Outline

■ Engineering driven curriculum

■ Curriculum’s Technical requirements

■ System Design and Design principles■ Evaluation and Optimizations

■ Deployment and Analysis

■ Conclusion

Interactive Linear Algebra Tool

Design Principles:– Client programming– Curriculum and System co-design– Asynchronous data transfer between

Client and Server– Integration with classroom management

system

1. Curriculum and System Co-Design

■ Graphing tools like excel does not provide interactive charts

■ Primary focus should be curriculum demands more than other features

■ Co-design a system with graphing and Interactivity at corethat guarantees minimal update times

■ Key to instantaneous visualization – Client programming

Curriculum and System Co-Design

Client Programming– JavaScript enabled client that uses D3.js visualization library– Client visualization enables client to graph data without sending requests to

server– No RTT latency in visualization– All updates to graphs are processed by client in few milliseconds

Curriculum and System Co-Design

2. Data Transfer Between Client and ServerFlow of data demanded by curriculum:

Data Transfer Between Client and ServerProblem Solution

Synchronous requests require page reloads and redundant HTML element transfers

AJAX (Asynchronous JavaScript and XML) can send and receive data without reloading page

User interactions like mouse movements and keystrokes help simulate users session. Butcannot send a request for every interaction

Use Batching to collect user interactions and send them after x seconds

Constantly updating Shared tables requires a huge number of requests

Refresh tables and pull data on-demand

Data Transfer Between Client and Server

3. Integration with Classroom Management Systems■ Classroom Management Systems like Moodle and Carmen provide

– Signup and User Management– Login APIs– Platform to upload and share academic materials– Grading and Surveying APIs

■ We extended moodle, an open source classroom management system to take advantage of these APIs.

■ This integration with classroom management systems allow easy adoption of our tool in schools

Integration with Classroom Management Systems■ Re-use user profiles and user-ids in moodle

■ Add school-id and generate unique class-id for every class

■ Class-id allows one to many relationship (a teacher can handle many sections in same or different school)

■ Separate database to store student’s experimental data(Dependent on moodle but also gives flexibility to use other databases that scale)

■ Shared flag to indicate whether a table is shared

Integration with Classroom Management Systems

Adding More Experiments

■ Curriculum has many chapters and each chapter has many experiments

■ Leveraging familiar UI to extend to numerous experiments

■ Only the axes labels and axes units differ for each experiment(voltage, time, distance, current etc)

■ Experiments are presented as tabs in same web page

■ Each experiment has an id and all tables created contain this field

■ Tables related to only that experiment are shown in each tab

Outline

■ Engineering driven curriculum

■ Curriculum’s Technical requirements

■ System Design and Design principles

■ Evaluation and Optimizations■ Deployment and Analysis

■ Conclusion

Evaluation

Response times for interactive graphing:

Less than 10 milli seconds for 100 points

Optimizations

1. Caching– Since page has mostly static content, browser caching can significantly reduce

number of requests to server– Graphing page has 32 elements and 30 of those can be cached

2. Compression– Reduces number of bytes transferred over network by about 25%

3. Themes and Styling– Disabling moodle user-themes and providing a simple UI reduces page load

times by about 30%

Outline

■ Engineering driven curriculum

■ Curriculum’s Technical requirements

■ System Design and Design principles

■ Evaluation and Optimizations

■ Deployment and Analysis■ Conclusion

Deployment and Analysis

■ Piloted our curriculum and tool in summer 2016 with 20 teachers

■ Updated curriculum and tool with feedback from teachers

■ More than 80% of piloted teachers adopted our curriculum and tool

■ Currently used by more than 700 students in 5 schools in Cbus

Deployment and Analysis

System traffic pattern over a single classroom session

Deployment and Analysis

Inferences:

■ Different types of network requests– Login requests– Graph-page loads– Table creation & updates – Batched user tracking

■ Peak load during login and data-input phase

Deployment and Analysis

Tail latency analysis:

99% requests served in lessthan 0.1 second

Deployment and Analysis

Number of interactions across different classes

Related Work

Speeding up processing and reducing response times has been explored in 1. ApproxHadoop : Processing is reduced by dropping map tasks and reducing

computations2. Sprinting: Increases processing rates by exceeding budgets for short bursts

and reverting back to safe processing rates

Outline

■ Engineering driven curriculum

■ Curriculum’s Technical requirements

■ System Design and Design principles

■ Evaluation and Optimizations

■ Deployment and Analysis

■ Conclusion

Conclusion

■ Developed an engineering driven curriculum

■ Discussed issues in developing a system that supports the curriculum

■ Built a system with key design principles discussed

■ Deployed and Analyzed our system

■ Can be extended to add more chapters like Polynomial Algebra and Geometry

References

1. E. Seymour and N. M. Hewitt, “Talking about leaving,” 1997.

2. A. Perez, K. Malone, S. M. Renganathan, and K. Groshong, “Computer modeling and programming in algebra”, CSEDU, 2016.

3. C. V. Schwarz and Y. N. Gwekwerere, “Using a guided inquiry and modeling instructional framework to support preservice k-8 science teaching,” Science Education, 2007.