Teaching Mathematics to the Adolescent Brain

Teaching Mathematics to the Adolescent Brain

By Stacy Simmons

Searching for Novelty in Mathematics

Increases with Adolescence

Adolescence marks an increase in the need for novelty to maintain interest. A challenge is only interesting until the novelty wears off, once it does, the search for a new challenge begins. How does this affect new learning?

Mathematics and the Adolescent Brain

Creating Novelty

Letting students ask the questions

1. Give students a situation

2. Students pose a question

3. Students create a mathematical model​

4. Perform a calculation

5. Check to see if the model/calculation answered the original question​

Mathematics and the Adolescent Brain

How Does the Brain Process Novelty?

Mathematics and the Adolescent Brain

• ​Face new learning situations

• Create new drawings

• ​Think abstractly

Right Hemisphere

• ​Practiced tasks

• Routine operations

• Language

Left Hemisphere

Multiple Choice

If new learning is primarily handled by the right hemisphere, how is information moved to the left hemisphere where it becomes a learned or routine process?

• Through the same amount and type of practice for all students

• Through continuous exposure to new situations

• Through time and varied practice with the new material, the amount needed differs from student to student

• Through continuous exposure to the exact same type of practice in class and in homework.

​- David Sousa

"It may be that one component of mathematical aptitude is the ability of a student's brain to make right-to-left transitions involving mathematical operations in less time and with fewer exposures than average."

Poll

Do you believe that mathematical aptitude as described in the previous quote supports a mathematical mindset as described by Jo Boaler? Choose the statement you agree with most.

• Yes, mathematical aptitude is described as faster than average transfer from right to left hemispheres. All students are capable of the same transfer with adequate practice and time.

• No, a mathematical mindset does not recognize aptitude, only achievement through effort.

• Prefers concepts to procedures

• ​Prefers models over numbers

• May have difficulty following through to a solution

Qualitative

• ​Approach math in a routine fashion

• Prefer working with numbers

• May have difficulty with multistep problems​

Quantitative

Learning Styles

Mathematics and the Adolescent Brain

Make connections and emphasize how the steps and numbers connect to the overall concept.

​

Table from pg. 133, Sousa, How the Brain Learns Mathematics

Strategies for Quantitative Style

Multiple Choice

What strategy is best suited for a student who emphasizes component parts rather than the larger mathematical constructs?

• Use simulations to show application of a concept to different situations.

• Look for ways to link parts to the whole.

• Emphasize the meaning of each concept or procedure in verbal terms.

• Provide a variety of manipulatives and models to support numerical operations.

Connect models and simulations to the concepts, then to the procedures, and then introduce algorithms

​

Table from pg. 134, Sousa, How the Brain Learns Mathematics

Strategies for Qualitative Style

​

Multiple Choice

What strategy is best suited for a student who has difficulties with precise calculations and explaining procedures for finding the correct solution?

• Encourage explicit description of each step used.

• Highlight the concept and overall goal of the learning.

• Emphasize how individual components contribute to the overall design of the geometric figure.

• Start with the larger framework and use different approaches to reach the same concept.

Multiple Select

Select all correct statements about teaching strategies for quantitative and qualitative learning styles.

• Teaching strategies for different learning styles help address mathematical behaviors in individual students.

• Teachers must differentiate lessons for every student based on their mathematical behaviors.

• It is unrealistic to expect that teachers can address every mathematical behavior within a single lesson.

• A few instructional strategies should be selected for successful learning for all students

Begin with inductive reasoning (suited for qualitative learners) and then move on to deductive reasoning (suited for quantitative learners). ​

​

Table from pg. 135, Sousa, How the Brain Learns Mathematics

Mathematical Reasoning

Multiple Choice

Putting it all together. How can we help students make connections regardless of their learning style?

• Homework, lots of practice to make perfect

• Grades can be used to motivate learning and greater focus

• Graphic organizers to connect concepts, procedures, and algorithms

• Straightforward, simple examples to avoid confusion

Why Graphic Organizers?

Graphic organizers give students a visual representation that can help qualitative learners connect concepts to procedures and algorithms while also helping quantitative learners connect algorithms and procedures to the concepts they are learning.

​

The adolescents of today are immersed in a visual world, it is only natural that a visual tool would be invaluable to their success.​

Mathematics and the Adolescent Brain

Multiple Select

How can we help adolescent students move new learning from the right hemisphere to the left hemisphere? Choose all that apply.

• Allow students to pose their own mathematical questions about a situation.

• Use teaching strategies that bridge the gaps between qualitative and quantitative learners.

• Use graphic organizers to connect concepts, procedures, and algorithms.

• Focus on calculations and math facts to lead students toward correct answers.