---
theme: metropolis
title: BCME - Research Presentation
subtitle: Learning fractions through visual representations - a Ph.D. research with low-achieving secondary students
author: 'Leonardo Barichello, Supervisors: Dr. Peter Gates and Dr. Colin Foster'
institute: 'University of Nottingham, Funders: CAPES and UoN'
date: April 04th, 2018
toc: false
slide_level: 2
header-includes: \metroset{progressbar=frametitle,sectionpage=progressbar}
---
# Introduction
## Motivation
>> Achievement is not equitably spread throughout society; children from less affluent homes do disproportionately worse than those bought up in relative affluence. […] Much research has attempted to articulate this relationship, whilst much more has ignored it, through denial, or the misguided belief that by supporting the affluent all will benefit through the ‘trickle down’ principle. (Gates, 2015)
- Research with low achieving students for low achieving students.
## Context
- Students from three low sets in an underperforming secondary school in East Midlands;
- Teachers were investigated by Rita Santos Guimaraes[^1]
- Topic: Addition and subtraction of fractions.
[^1]: F12 - Investigating teachers' changes in practice with low-achieving students
# The lessons
## The lesson plans
- 12 lessons plans grouped into 3 packs (one per term);
- Worksheets + Comments for the teacher + cut-outs;
- Topics covered:
- equivalent fractions,
- comparison of fractions,
- addition and subtraction,
- mixed numbers and improper fractions,
- word problems.
## Three design principles
1. The lessons should enable students to build their knowledge about fractions on visual representations;
2. Students should have opportunities to solve the tasks without being told how to do it beforehand;
3. Keep the lesson plans coherent with participant teachers’ current practices.
## Outline of the lessons (1)
You can download the second version of all the lesson plans at [barichello.coffee/bcme2018](http://barichello.coffee/bcme2018).
- Pack 1:
- Lesson 1.1: introduction of rectangular area model,
- Lesson 1.2: fractions (1/2, 1/4, 1/8 and 1/16),
- Lesson 1.3: fractions (1/3, 1/6, 1/9 and 1/18),
- Lesson 1.4: new denominators,
- Lesson 1.5: diagrams.
# Data analysis and conclusion
## 1 - Interference of visual abilities
![Rotating cut-outs was very demanding](image2.jpg){width=90%}
## 5 - Whole number bias
- Gone!
- Just a few mistakes related to the whole number bias;
- Some "doubling", but only when questions were conducive.
Why?
- Meaning beyond symbolic.
## References
Ainsworth, S. (2006). DeFT: A conceptual framework for considering learning with multiple representations. Learning and Instruction, 16(3), 183–198.
Gates, P. (2015). Social Class and the Visual in Mathematics. In S. Mukhopadhyay & B. Greer (Eds.), 8th Mathematics Education and Society Conference (pp. 517–530). Portland State University.
Lakoff, G., & Núñez, R. (2000). Where mathematics come from: How the embodied mind brings mathematics into being. Basic books.
Pye, J. (1988). Invisible children: who are the real losers at school? Oxford University Press Oxford.
## {.standout}
Thank you!
barichello@gmail.com
http://barichello.coffee/bcme2018