Math Teaching Strategies that Challenge Students
Critical Thinking Techniques Students Use to Link Math Concepts
The road to learning math is pitted with potholes full of students who could not grasp the connecting links between math concepts. One reason for these students failing to understand math was being peppered with concepts, similar to a pitching machine throwing baseballs to a batter. The batter misses the first ball and while trying to discover why the first ball was missed after swinging the bat, two more balls whiz by the batter's bat. Now this student is becoming overwhelmed and lost.
The key to teaching math so students internalize and transfer their knowledge is to make learning math personal. No matter how many worksheets students complete, they will never make the connection between math concepts until it is concrete and relates to their personal environment. Math needs to be real and not just a set of numbers or endless problems to calculate. Personal math allows students to link concepts as whole and not a lot of independent ideas (or baseballs) with no connection.
The following four techniques aid students transferring math concept knowledge to other math concepts for linking concepts.
Problem-Based Learning (PBL)
The best strategy in PBL is the use of case studies which present students with real life problems that require applications of math to solve or find a solution. Students:
- determine what they know by identifying what is known, what needs to be find out, what they want to learn (KWL) based on a given case study scenario.
- develop a problem statement which contains steps for solving the problem and factors for determining successful completion.
- gather information through online resources, surveys, interviews, observations, measurements, etc.
- develop possible solutions using concept maps, Venn diagrams, graphic organizers, etc.
- present a solution to the case study based on what was learned.
Interactive Math Tools
The use of online interactive learning tools in math for solving and creating math problems is essential for allowing students to make connections in math. Choose an interactive tool that requires students to use problem solving strategies that use formal operational skills and proportional reasoning. The best interactive math tools require students to solve problems by applying more than one math concept.
Interactive math addresses the problem of engaging students through the use of virtual manipulatives to help them visualize math relationships. Virtual math learning environments allow students to apply logic and reasoning for problem solving.
Using Manipulatives to Model Math Problems
Learning and understanding mathematics, at every level, requires student engagement. Mathematics is not a spectator sport. Students must be engaged in the learning process through practical applications of math. Whether the manipulatives are purchased in kits or created from available materials, this hands-on learning approach engages students’ minds as they use manipulatives to create models and representations to solve math problems.
Explain How to Solve Math Problems in Writing
This technique involves students solving a problem and then writing a story describing how the problem was solved. Writing provides students with a creative method to think and internalize how they linked math concepts in real life problem solving situations. These student writings also provide teachers with an insight into a student’s true understanding of math that a dozen work sheets could never provide.
Making Connections
When students are engaged in learning math that is personal to them, they are engaged in the learning process. Problem solving situations, case studies, and traditional math problems focused on students provide increased opportunities to internalize and make connections. Students like to participate and not watch demonstrations of how to solve problems; true understanding comes from hands-on, minds-on math.
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