Learning Materials for Math: An evidence-based look into the most effective early grade math materials and how they

can be replicated, including the use of ICT Sarah Pouezevara, on behalf of Carmen Strigel,

RTI International December 5, 2013

Introduction and overview

• Sarah Pouezevara, ICT Specialist, RTI International

• Presentation will review:

– Some background about early learning and math

– Look at concrete math materials

– Examples of ‘real world’ math

– ICT and math

Early Grade Math

• Young children experience and explore not only mentally, but also physically.

• Being numerate means being able to use knowledge and understanding about numbers, calculation strategies and data-handling techniques to solve problems and make decisions in many different contexts.

Various pedagogies

• Traditional vs. “Reform math”

• Bourbaki vs. Poincaré

• Montessori math

• Conceptual-based curriculum such as Singapore Math and Saxon math

• Marilyn Burns’ “Math Talk” program

• Literature and games integration

Types of Materials

• Workbooks

• Teacher guides

• Images / visual representations

• Manipulatives

• Games and songs

• Everyday objects

• Technology

What do good math materials do?

• Conceptual understanding through visual representation

• Multisensory experience

• Recognize patterns , analyze relationships

• Practice concepts, problem solving

• Opportunities to communicate and describe

• Support a coherent developmental plan and assessment

Case Study: Jordan EGMA

• Students performed better on procedural problems than those requiring application

• Led to curriculum and teacher education reform towards more meaningful application of skills

• The materials include: teacher manual, the daily lesson notes and a workbook

• Reproduce structures from daily life to create abstract designs with pattern and symmetry

• Opportunity for a multisensory experience

• Learners see and discover relationships, patterns

Concrete Materials

Concrete Materials- Examples

Abacus Relational rods Pattern blocks

Attribute blocks Geoboards Pentominoes

Balance and weights Graduated beakers Stackable blocks

Base 10 Materials Hundreds chart Stamps with denominations

Playing cards Materials for counting and sorting

Tangrams

Connecting cubes Measuring spoons Thermometers

Plastic shapes Measuring Tape Two-colored counters

Clocks Plastic transparent tools 3D solids

Colored tiles Money Trundle wheel

Source: Early math strategy: The report of the expert panel on early math in Ontario. (Canada Ministry of Education, 2003)

Colored counters

Concrete Materials- Examples

Abacus

Pentominoes

Relational rods

Trundle wheel

Base 10 Blocks

Money

Dice Tangram

Playing cards

Geoboard

• Bottle caps can be used for counters, sticks can be used for relational rods, geoboard is easy to create with nails and a board, etc.

• Teachers need support, positive examples from other teachers, and policy-makers’ commitment to effectively make use of such materials.

Replicating concrete materials

• Avoiding rote algorithms through replication of concrete materials

• Opportunities to learn the same concept through different strategies

• Materials include sticks, stones, charts

Case Study: Kenya

What the Research Says

• Long-term use of concrete materials is positively related to increase in student mathematics achievement and improved attitudes towards mathematics

• Manipulatives on their own do not teach -- teachers do.

Real-world math applications

• Materials come from the environment, real situations

• For example, counting and weighing olives from a school-based farm

• Geometric forms produced by local artisans (tiles, rugs)

• “Garbage City” trash collection and plastic recycling

• Use records of daily collections to graph, estimate profit, etc.

Case Study: Egypt

• Engaging software such as GeoGebra Virtual Manipulatives, BrainPOP! and Motion Math

• Various web applications and mobile applications across platforms

• Adaptive math software

• Assessment and personalized instruction

ICT and Math

• Give unprecedented access to teachers and students around the world

• Devices with a range of features from simple to complex

• Mobile=portable

• Mobile=on the move

Mobile Learning

Electronic Manipulatives

• Stores and retrieves configurations

• Manageable, clean, flexible

• Recording and replaying students’ actions

• Linking the concrete and the symbolic with feedback

• Changing the nature of the manipulative

• Making the leap from concrete to abstract

Next Steps

• Increasing tactile experiences through haptic technology

• Room for more research in mobile learning with early grade numeracy– currently focus is on higher education and the US and Europe

What the Research Says

• Developmental progression matters

• Tailoring instruction through continuous assessment helps build on prior knowledge

• Organizing and representing concepts is important

• Link concepts to informal knowledge and experiences

• Embed math across the curriculum every day

Questions and comments? Examples from the region?