Tuesday, April 28, 2009

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.

Monday, April 27, 2009

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)