Final Report

The initial purpose of this study group was to study the book "How The Brain Learns Mathematics" by David Sousa. We wanted to learn about the research that has been done in this area and then adopt/develop strategies to help students learn and retain mathematics concepts. Not only did we learn about new and different approaches to teaching and learning mathematics, but we were all pleased to learn that much of what we do in our classes agrees with the researched-based advice given in the book.

With that said, we are anxious to attempt to integrate new and different learning/teaching strategies into our lessons and classes. The following are some of the changes we have or will be making in our classes:

• Integrate more student writing activities in lessons and assignments.


• Be more aware of the timing in lessons ("degree of retention" model). Use the first "prime-time" 20 minutes for teaching new material instead of using it for going over homework. Revise lesson plans to incorporate this model.


• Take more care and consideration when explaining the mathematical meaning behind the concepts being taught rather than just teaching the procedure.
  

The effects of making these changes to our classes:

• Through integrating more writing activities in lessons, students will be able to learn math concepts more effectively and develop critical-thinking and problem solving skills. Students will have a permanent record of their thoughts where they can reflect on them. Students will be better able to organize ideas, develop new ideas and solve problems. Students will become active participants in their learning. Some examples of success in the classroom by integrating more writing activities:

In Geometry, the writing is very technical and there has been a considerable amount time spent learning to read and write technically. Evidence of understanding exists when there is more detail emerging in their writings. This should translate to improved long-term memory retention.

The applied senior class creates chapter summaries. Each student picks out what they feel are the most important concepts of the chapter. As review for the test, students compare the summaries with each other and make changes accordingly.

• Following the recommendations of this book, we will be guiding our students in building a stronger conceptual base through the grade levels. This should increase students confidence and decrease their math anxiety about moving into more advanced, abstract topics.


• Students will be able to better connect with the material they are learning and will be able to apply it to different mathematical situations.


• Changing the timing of our lessons to incorporate the "degree of retention" model, students will be learning new concepts during their "prime learning" time. This should help them make connections and have better retention of the concepts taught.
  

Our recommendations to other educators:

• Educators of all disciplines can see that if students cannot make sense of what they are being taught then they will not be able to make connections to what they already know.


• All teachers of mathematics should read this book. It really sheds a light on how students come to us with such different strengths and abilities in mathematics, based on the workings of the brain and how any difficulties have been addressed in the younger, developmental stages. According to the research presented in this book, the important work in development happens when students are quite young. We can hope that teachers of elementary students utilize these strategies, when there is a better chance to make an impact. Regardless, we, as math teachers of 8 - 12 grade, can come to our students with more understanding of the challenges students face in learning mathematics and try to plan our lessons to maximize their learning.


• As educators, we should continue to investigate the research in our discipline and attempt to integrate new and different learning/teaching strategies. Then we should take the time to reflect on what worked and improve on what did not work well with our students.


• According to the author, research indicates that students have difficulty learning too many different concepts in too little time. One of the concerns voiced by the participants in this group is that there are still too many topics in many of our math courses. We wonder if the folks at the state education level read any of the current research.

April 22 Conclusion

Effective teaching strategies cut across all content areas. For the teaching of mathematics, ...the following notions should be kept in mind:(pg 215)

• Everyone has the ability to do mathematical operations.
• Rote learning without meaning impedes long-term application of mathematical knowledge.
• Learning is easier when it makes sense and is meaningful to the learner.
• Learning mathematics is easier when the learner can connect mathematical operations and concepts to solving problems in the real world.
• Talking and writing about mathematics improves the depth of learning and recall.
• Learning mathematics involves a progression from the concrete to the representational to the abstract.
• People learn mathematics in different ways.

April 22 Chapter 8

Putting It All Together

"When teachers keep in mind what is now known about how the brain learns, they are more likely to develop lessons wherein students learn and remember the content objective while they enhance their process skills."(pg 201)

Questions to keep in mind when planning lessons:
1. Is the lesson memory-compatible?
less is more
keep lesson segments 15 to 20 minutes long in secondary classes
2. Does the lesson include cognitive closure?
"It is during closure that a student often completes the rehearsal process and attaches sense
and meaning to the new learning..." (pg 202)
Closure is different than review- in closure the student mentally rehearses and summarizes
the concepts and decides if it makes sense and has meaning.
Timing closure - start a lesson-have students think and discuss previous lesson
during a lesson - have students review a concept in their mind before
moving on
end of lesson - should almost always occur at the end of the lesson
3. Was the timing of the new learning taken into account?
See chapter 3- retention during a learning episode
4. Should a lesson start with mathematics homework?
"Do not use up valuable prime-time if the homework review is merely casual (about the
mechanics of doing it) rather than substantive (about its content)."
Teach new material first
Use downtime protion to have students practice the new learning or discuss it
Do cognitive closure during prime-time-2
5. What about practice?
Select smallest amount that will have the maximum meaning for learner
Model
Practice should occur in the presence of the teacher
Assign limited independent practice
6. What writing will be involved?
Writing is important in communicating mathematical concepts
7. Are multiple intelligences being addressed?
8. Does the lesson provide for differentiation?
Differentiate content, process, and/or student demonstration of content

April 22 Chapters 7 and 8

Recognizing and Addressing Mathematics Difficulties

Do some of the mathematics difficulties come from trying to cover too much material each year?As teachers, we don't have control over that, but do agree there is too much material to address in depth. The old saying "a mile wide and an inch deep" still holds true.

"Despite higher standards and high-stakes testing, student attitudes about mathematics have not improved much." pg (170)

Alleviating math anxiety in the classroom:

• Teacher attitudes -
  Show the value of mathematics
  Create opportunities for success - "studies suggest that teachers need to build in a 70% percent success rate in order for students to remain engaged with work that is challenging enough to demand effort but easy enough to expect success." (pg 173)
  Display confidence in teaching mathematics
• Curriculum-
  Provide activities that train students to apply their knowledge
  Devote more time to new material, discovery and application
• Instructional Strategies -
  Develope meaning by showing practical applications that are relative to students
  Encourage students to make sense of what they are learning rather than memorize steps or procedures
• Assessments -
  Limit the number of tests and do not have timed tests
  Assess students on how they think about mathematics
  Use multiple methods of assessment-oral, written, or demonstration formats
  
  
  "Several research studies have shown process mnemonics to be particularly effective with students who have difficulties in mathematics." (pg 189)

March 10: Chapter 6

Teaching Mathematics to the Adolescent Brain

"The researchers found that adolescents used more of their prefrontal cortex than adults. Actually, the amount of prefrontal cortex used was simiilar to what adult brains use when performing much more complex tasks." (pg 134) Possible implications to these findings are "overworking of the frontal lobes leads to impulsive and more emotional (rather than rational) responses during problem solving." (pg 135)

Teens in other countries spend much more time with adults than with their peers, and do not exhibit the immature behavior of teens in North America.

The adolescent brain may actually have an enhanced aptitude for learning algebra more easily than the adult brain.

Students are more likely to be successful in learning math if teachers use instructional strategies that are compatible with their students' cognitive styles.

Since adolescents are surrounded by visual images, it makes sense to use visual tools in the mathematics classroom. Graphic organizers are one type of visual tool.

Homework assignments should not have a heavy weight in a student's class average.

Feb 10: Chapter 5

Teaching Mathematics to the Preadolescent Brain

Students should write in a journal reflecting on what they learned in math that day.

When you give students writing activities you need to scaffold them and be specific.

Students don't always understand that the "=" sign means equal. The notion of "equal" is complex and difficult for students to comprehend, yet it is a central math idea within algebra.


"Layering the curriculum is a simple way to differentiate instruction, encourage higher-level thinking, prepare students for adult-world decision making and hold the accountable for learning."(Pg 144)

Jan 13: Chapters 3 and 4

Reviewing the Elements of Learning/Teaching Mathematics to the Preschool and Kindergarten Brain

Students learn best at the beginning of class and at the end of class. In a 40 minute period, the highest degree of retention is during the first 15 minutes of the class. The next 10 to 15 minutes of the 40 minute class is "downtime", followed by the last 10-15 minutes of the 40 minutes which students have a degree of retention close to the first 15 minutes of the class.

"During a learning episode, we remember best that which comes first, second best that which comes last, and least that which comes just past the middle". (pg 61)

Rehearsal is very important for students to maintain information in their memory.

Working memory connects with the learner's past experiences and needs to answer to question: "Does it have meaning?"

Teachers need to spend time building meaning of concepts.


Through writing activities, teachers help students to learn a math concept more effectively and develop crititcal-thinking and problem solving skills.

Young students learning math should look for patterns.

Dec 9: Chapters 1 and 2

Developing Number Sense/Learning to Calculate

Our language is a barrier to how we learn numbers.
"Our ability to approximate numerical quantities may be embedded in our genes, but dealing with exact symbolic calculation can be an error-prone ordeal." (pg. 35)

Memorizing facts is not intuitive.

We are born with a built in number sense, genetically pre-disposed.

Survival Skill(counting number of predators)

English words make learning arithmetic harder.

The further apart numbers get the longer it takes to add them mentally.

On the mental number line, the numbers get closer together the larger they get.(See diagram pg 23)

The region of the brain we use for counting includes the same part that controls our fingers.

Just as phonemic awareness is a pre-requisite to learning phonics and becoming a successful reader, developing number sense is a pre-requisite for succeeding in math(pg. 26)

"Number sense can be considered the innate beginnings of math intelligence. But the extent to which it becomes an individual's major talent still rests with the type and strength of the genetic input and the environment in which the individual grows and learns."(pg 33)

Calculations are difficult for the human brain. Only number sense is innate.

Children in the primary grades suffer from a shift from intuitive number sense to rote memorization.

* "The idea is to use the students' innate sense of patterning to build a multiplication network without memorizing the tables themselves." (pg. 46)