| NSF Org: |
DRL Division of Research on Learning in Formal and Informal Settings (DRL) |
| Recipient: |
|
| Initial Amendment Date: | August 5, 2020 |
| Latest Amendment Date: | February 9, 2023 |
| Award Number: | 2031490 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Michael Ford
miford@nsf.gov (703)292-5153 DRL Division of Research on Learning in Formal and Informal Settings (DRL) EDU Directorate for STEM Education |
| Start Date: | January 1, 2021 |
| End Date: | December 31, 2024 (Estimated) |
| Total Intended Award Amount: | $498,276.00 |
| Total Awarded Amount to Date: | $498,276.00 |
| Funds Obligated to Date: |
|
| History of Investigator: |
|
| Recipient Sponsored Research Office: |
1000 CHASTAIN RD NW KENNESAW GA US 30144-5588 (470)578-6381 |
| Sponsor Congressional District: |
|
| Primary Place of Performance: |
1000 Chastain Road Kennesaw GA US 30144-5591 |
| Primary Place of
Performance Congressional District: |
|
| Unique Entity Identifier (UEI): |
|
| Parent UEI: |
|
| NSF Program(s): | CSforAll-Computer Sci for All |
| Primary Program Source: |
|
| Program Reference Code(s): |
|
| Program Element Code(s): |
|
| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.076 |
ABSTRACT
This research project studies conjectures about the learning of computational thinking through the development of a curricular and pedagogical intervention. The intervention adds a computational environment to a successful effort called the Algebra Project, and is focused on engaging all students in a predominantly African American middle school in computational thinking. In so doing, this work seeks to develop a remedy for the fact that many low-performing students lack a sufficient contextual understanding of the symbols that they are taught to manipulate in their mathematics courses. This research seeks to demonstrate how the use of various types of computational thinking can increase conceptual understanding, visual reasoning, and representational logic. In pursuit of this outcome, this project is seeking to determine to what extent a specific type of simulation and modeling application can enable teachers and middle-school students to use visual reasoning and spatial logic when analyzing mathematical functions. Students in this intervention will work collaboratively in small groups among themselves, and with near peer mentors and tutors, to examine shared experiences that are grounded in mathematical and computational logic. Through their ongoing collaboration and discourse, the students will determine solutions for various tasks and challenges that they are presented. In addition to using visual reasoning and spatial logic in this work, students will also learn to use Python scripts and functions to aid them in their analyses.
This research study will be carried out by using a specific type of Python-based microworld, that combines enactive-iconic representations with an experiential math curricular approach developed by the Algebra Project. The Algebra Project?s curricular approach uses a 5-step collaborative model for mathematics inquiry in the classroom. The first step begins with the students experiencing a shared event. Next, students examine the experience by representing the event pictorially, then through everyday language, then through an agreed upon regimentation of everyday language, and finally through the use of iconic and conventional symbolic representations and equations. This research will extend the Algebra Project?s curricular and pedagogical approach by providing students with enactive-iconic and diagrammatic mathematical constructions that they can manipulate virtually in a computational environment that they can use to further examine the mathematical features and logical structures involved. The results of the previous work of this research team that piloted this approach with a very small number of students in an urban context, found that the students involved developed a greater conceptual understanding of core mathematical ideas, namely equation and function, grounded in visual reasoning and representational logic. Furthermore, indicators suggested improvements in ownership and engagement. The research team had not yet examined the extent to which core elements of computational thinking were developed by the students, and this research will address that issue, as well as expand the content of the mathematics and computational material involved. This project is supported by the CS for All: Research and RPPs program.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
Note:
When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external
site maintained by the publisher. Some full text articles may not yet be available without a
charge during the embargo (administrative interval).
Some links on this page may take you to non-federal websites. Their policies may differ from
this site.
PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
Title: Supporting computational thinking for middle school mathematics students through diagrammatic reasoning and representational logic
In this project, our aim was to introduce a new mathematics literacy paradigm to a typical school mathematics classroom. We integrated the Algebra Project’s 5-step curricular process along with computational thinking and coding activities, with the goal of engaging middle school students with new opportunities for creativity, imagination, and self-expression in a mathematical context. We believe this leads to an experiential learning cycle, and to opportunities for creative mathematical expression that broadens a young person’s development of voice, agency, and positive mathematical identity.
In our work over the past three years at Forest Park Middle School (FPMS) in Clayton County, Georgia, USA, we have demonstrated that by combining computer science concepts with mathematics, mathematics can be taught with a pronounced creative, imaginative, and expressive component. We combined computational thinking content, interactive iconic mathematics simulations, and a Python microworld with a project based math curriculum designed by the Algebra Project, for 6th, 7th and 8th grade students.
In each year the students used the Algebra Project's 5-step curricular process. that involves: (1) engaging in a shared event to model mathematically, (2) representing the event pictorially, (3) informal People-Talk discussions about the event, (4) formal Feature-Talk discussions about the event, and (5) symbolically representing the event using equations. This process encourages students to talk and write about their shared experiences in the classroom in their own words, creating a space for students to fill with their own thoughts and their own ways of expressing themselves. In short, with their own imagination and creativity.
The 5-step curricular process takes the student from a concrete experience to an abstract symbolic conceptualization. However, the 5-steps don’t explicitly address where the student goes from there. We sought to deepen the student's learning experience by having the students engage in iconic simulations to explore the symbolic conceptualization and play with them until the students were comfortable using them creatively, imaginatively, and for self-expression.
For the 6th graders we did this in units that addressed concepts like ratios and propability. Our iconic simulation work was done at the following link:
https://ksuweb.kennesaw.edu/~ashaw8/Counters/
In that year, students also worked on solving simple word problems using double number lines, and our iconic simulation work was done at the following links:
https://ksuweb.kennesaw.edu/~ashaw8/DoubleNumberLine/
https://ksuweb.kennesaw.edu/~ashaw8/DoubleNumberLine2/
For the 7th graders, the units focused on linear equations, cartesian coordinates, directed graphs, arrow diagrams and ordered pairs. The students worked with our iconic simulation at the following links:
https://ksuweb.kennesaw.edu/~ashaw8/RoadColoring/
https://ksuweb.kennesaw.edu/~ashaw8/RaceAgainstTime/
For the 8th graders the units focused on Pre-Algebra and Algebra and concepts like multi-variable equations and functions. In this year, with the focus on functions, students began working in our Python microworld, and they learned how simple programming concepts like variables, equations, boolean logic functions, have a direct match with those ideas in Pre-Algebra and Algebra . The students worked in the Python Microworld to write simple Python code and to learn functional notation to create their own with our iconic simulations. The eigth grade work ends with the students translating functions using math equations into functions using Python. This Python microworld work was done at the following link:
https://ksuweb.kennesaw.edu/~ashaw8/CS4Algebra/
Our work points towards a systematic way to create an overlap between math ideas and ideas related to computational thinking and programming.
Last Modified: 05/01/2025
Modified by: Alan Shaw
Please report errors in award information by writing to: awardsearch@nsf.gov.
