Information Age Education Blog
Three Math Education Conference Presentations
On October 18-19, 2013, I presented three talks at the Alberta Math Teachers Association Conference held in Edmonton, Alberta. The conference was very well designed and well run. I learned a great deal from the sessions I attended. This IAE Blog entry summarizes my presentations and some of my suggestions for improving math education. You will find Suggested Readings at the end of this IAE Blog entry.
My Keynote Address: Math Maturity
Summary: A good math education includes an appropriate balance between learning math content and gaining in math maturity. Some of the components of math maturity are: math communication (reading, writing, speaking, and listening in the language of math); learning to learn and relearn math; transfer of math learning to new and diverse problem situations; math as a human endeavor; math problem posing and solving, with special emphasis on word problems; using computers in combination with math modeling and computational thinking; persistence; and math intuition.
Some Observations: This concept of math maturity is slowly making its way into the world of math education. Or, should I have said slooooly? The Common Core State Standards in the U.S.—and the western Canada version of CCSS adopted a number of years ago—stress learning for understanding. However, these standards do not look at the overall discipline of mathematics and identify math-related knowledge and skills a student can develop that will last a lifetime. Increases in a student’s level of math maturity in areas such as learning to learn and relearn math, transfer of math learning to other disciplines, problem recognition and posing, and math-oriented habits of mind all have lifelong value. These and other important aspects of math maturity are not adequately assessed in the types of state/provincial and national math tests that are driving the day-to-day math teaching in our classrooms.
In addition, our math education system is falling further behind in the integration of computer-based tools used in the representation or solving of math-related problems both in math and in all other disciplines.
My Parallel Session: Math-related Games and Manipulatives
Summary: Many mathematicians themselves consider math to be a type of game. Here are quotes from two world-class mathematicians:
“Mathematics is a game played according to certain simple rules with meaningless marks on paper.” (David Hilbert; German mathematician; 1862—1943.)
We must regard classical mathematics as a combinatorial game played with symbols. (John Von Neumann; American mathematician; 1903–1957.)
And, of course, we have a steadily growing number of games in which the players use math and can learn math through using it. The game of Monopoly, available both in its traditional “hard copy” form and on a computer, provides a well-known and excellent example. Such games were stressed in this presentation.
Math-related games and math manipulatives facilitate student engagement in learning math by doing/using math and math-related ideas. The abacus is both an excellent aid to doing addition and subtraction, and an excellent math manipulative for learning to do addition and subtraction.
A key math education issue is teaching/learning in a manner that supports transfer of learning from the game and manipulative environment to the various content and math maturity goals of math education. This presentation used a very broad definition of math manipulative, so that calculators, computers, and math tools such as spreadsheets and computer algebra systems are included. The majority of participants in this session (some, grudgingly) supported this broad definition of a math manipulative.
Some Observations: There is general agreement that math-based games and simulations—especially ones that are “real-world” oriented—can help to make math learning more fun and more relevant to the lives of students. At the conference, the second day’s keynote presentation by Karin Ani focused on this topic.
While a variety of traditional (by hand) and virtual (by computer) math manipulatives are commonly used in math education, we have reached a major stumbling block when it comes to how to appropriately use calculators and computers. They are a type of math manipulative that can be used to solve problems, that actually “know” how to solve certain types of problems, and that can contain built-in instructions to help students learn to understand and solve certain types of problems.
Most current math educators have not yet carefully considered the implications of students having ready access to computer-based math manipulatives that can both help students learn math and can help students do/use math. Our math education content and assessment systems have not yet figured out how to appropriately integrate powerful computer-based manipulatives that can both teach and solve math problems.
A great many teachers of math (perhaps the majority?) believe that calculators are a major barrier to students learning what the teachers consider to be really important traditional components of math, such as how to do multiplication and division using pencil and paper. This is a strongly held belief, and is a good example of the barriers our math education system faces as it tries to maintain pace with continued rapid changes in technology. We are a loooong way from designing state and national math tests that require students to have a high level of competence in using calculators and computers as aids to representing and solving math problems, and applying this knowledge and skill to solving math-related problems in the other disciplines.
My Parallel Session: Brain Science and Math Education
Over the past hundred years we have made substantial progress in the study of brain science and its applications to teaching and learning math and other disciplines. We have increasing insight into IQ, multiple forms of intelligence, and cognitive development. We know considerably more about the specific math learning disability of dyscalculia. We also know more about the specific reading disability of dyslexia. Many children who have one of these conditions also have the other, and certainly having both is a major challenge to their learning math.
We are also making considerable progress in understanding brain chemistry and the effects of drugs such as caffeine and Ritalin on brain functioning. These two drugs can help a brain maintain focus (pay attention) in class and while studying. Ritalin, which is widely prescribed for ADHD, is now being increasingly used by non-ADHD students to give them an advantage. We face a future in which more and more legal and illegal drugs will be routinely used by students to increase their academic performance. For example, with the aid of such drugs a student can “pull an all-nighter” and still be able to function well on a test during the next school day.
Some Observations: The participants in my brain science session displayed considerable interest in how recent research in brain science is applicable to math education. For example, research shows that multitasking while studying is a very poor study habit. Our teaching methods often overload a student’s working memory, and thus produce poor learning results. Stress, coming from living in poverty, test anxiety, and other sources, significantly degrades brain performance. It is clear that continuing progress in brain science now offers new understandings of considerable value to teachers and their students.
What You Can Do
Today’s math classroom teachers are caught between a rock and a hard place. The “rock” is the carefully prescribed curriculum to be covered, the tests based on this curriculum, traditional math teaching methodologies, ingrained expectations from parents, and math requirements for moving up from one grade to the next and/or to graduate from high school.
The “hard place” is the difficulty of “going it alone,” deviating from the prescribed math education path in ways that you (a teacher) are quite sure will improve the overall quality of the math education your students are receiving.
As a teacher, you can decide the extent to which you will “toe the line” and the extent to which you will use your best judgment—including knowledge and skills both of the current math education system and of alternatives. I strongly recommend that you be venturesome. Continue to experiment with new ideas. Increase your knowledge of brain science as it relates to teaching and learning. Push your personal envelope in ways that will help both you and your students to grow.
Both the U.S. and Canada are striving to improve their math education systems. Both countries are having trouble finding an appropriate balance between high-stakes testing and the need for good formative assessment that provides rapid and relevant feedback to students, teachers, and parents. In my opinion, both countries are weak in appropriately integrating potential advances based on continuing research in math education and brain science. Both countries are weak in integrating computer technology as a combination math manipulative and tool that serves both as an aid to learning and as an aid to doing/using math.
Suggested Readings from IAE and Other Publications
You can use Google to search all of the IAE publications. Click here to begin. Then click in the IAE Search box that is provided, insert your search terms, and click on the Search button. Click here to search the entire collection of IAE Blog entries.
Here are some examples of publications that might interest you. All of these materials are available free from the Information Age Education websites.
A Compendium of Free IAE Math Education Materials. See http://iae-pedia.org/Free_Math_Education_Materials.
Math Digital Filing Cabinet. See http://iae-pedia.org/Math_Education_Digital_Filing_Cabinet.
Math Education Quotations. See http://iae-pedia.org/Math_Education_Quotations.
Math Maturity Introduction and Overview. See http://iae-pedia.org/Math_Maturity.
Math Maturity Workshop. See http://iae-pedia.org/Math_Maturity_Short_Workshop.
Moursund, David (2007). Introduction to Using Games in Education: A Guide for Teachers and Parents. See http://iae-pedia.org/David_Moursund_Books.
Moursund, David (2011). Play Together, Learn Together: STEM. See http://iae-pedia.org/David_Moursund_Books.
Moursund, David, and Albrecht, Robert. (2011). Using Math Games and Word Problems to Increase Math Maturity. See http://iae-pedia.org/David_Moursund_Books.
Moursund, David. Using Brain/Mind Science and Computers to Improve Elementary School Education. See http://iae-pedia.org/David_Moursund_Books.
Overview of Brain Science. See http://iae-pedia.org/Brain_Science.
Quotations Collected by David Moursund. See http://iae-pedia.org/Quotations_Collected_by_David_Moursund.
Two Brains Are Better than One. See http://iae-pedia.org/Two_Brains_Are_Better_Than_One.
Understanding and Mastering Complexity: Understanding Our Brain and Applying that Knowledge. See http://i-a-e.org/newsletters/IAE-Newsletter-2013-120.html.
We Have Several Brains. See http://i-a-e.org/newsletters/IAE-Newsletter-2012-92.html.
What the Future Is Bringing Us. See http://iae-pedia.org/What_the_Future_is_Bringing_Us.