MATH THAT EXCITES AND MOTIVATES? YES, IT’S WITHIN YOUR REACH

Our founder has a long history of interest in mathematics. Here, he reflects on how, congruent with the Growth Mindset [1] approach to teaching, interest, and motivation awakened by teachers and parents, and not innate ability, led to his efforts and achievements. Mathematics, including statistics, is a foundational element in navigating life well and excelling in many careers. The founder details techniques parents and teachers can use to help students of all abilities activate their interest and maintain their motivation for learning mathematics. We have found that these techniques help create mathematically accomplished learners.

The Challenge for Parents and Teachers – How to Excite and Motivate

My first recollection of being interested in mathematics comes from second grade. We had a self-paced mathematics workbook and I found myself competing against a classmate named Wally to see who would finish first. I don’t remember now who won, but I realize that, even as a second grader, that feeling of competition pushed me to try harder and do more. Reflecting back, I am guessing that I was guided by a wise teacher who knew how to get the most out of me while also keeping me out of trouble.

Parents and teachers today are challenged with exciting and motivating their students, with their varying levels of abilities and motivations, to achieve in mathematics and other subjects. Today, I find myself the coach of a math team comprised of amazing students of varying levels, all really interested and excited about mathematics, and I wonder how their learning path led them to join the math team. Psychologists tell us that, to understand this subject, we should take a step back and review motivation for cognitive tasks such as learning and, even before motivation, understand how an interest in a subject starts.

Why the focus on interest and motivations? Because it matters. While, for years, America has focused on the teachers’ capabilities and depth of knowledge in the materials they are teaching, no surprise, students’ own beliefs and motivations form a significant part of effective learning. Carol Dweck’s Growth Mindset research shows that, like compound interest, differences in attitude can accumulate to significantly different accomplishments over time. This research holds true across different ability levels, cultures, and socio-economic groupings.

First, Activate Interest

Researchers, such as Paul Silva from the University of North Carolina, have been making progress on examining the science of interest, understanding what interest is, determining how topics become interesting and learning how we can cultivate interest in ourselves and those around us [2]. Interest helps the brain to focus and can drive everyone to think more clearly, focus better and achieve more in any particular area, regardless of their ability.

Paul Silva’s research details how, for a subject to be deemed interesting, it must be novel, complex, but still comprehensible. The tools to help make math interesting can take many forms, including:

• Make mathematics relevant to the family [3]- Can you estimate how much money is needed to purchase a group of items? Which is cell phone plan right depending on how much data everyone uses? What is the effect of just a 0.2% expense charge on your retirement after compounding for 30 years?
• Mathematics through logic puzzles and workbooks – A huge array of math and logic puzzles and workbooks is available for all levels. Browse in the library or bookstore and bring home what captures your student’s attention. These are some of the founder’s favorites: https://goo.gl/d66ji4.
• Amazing Results, Paradoxes & Fallacies [4]- How much is $0.01 doubling each day for a month [5]? Prove that 1 = 2 [6]. And, consider this favorite of my nephew Mitchell, prove that 1+2+3+… infinity = -1/12 [7].
• Crazy Math Challenges [8]- How many marshmallow bags would we need to fill up your brother’s room? How fast must Santa be traveling to deliver presents to all those homes within 24 hours?
• Math using projects – This is probably the most useful form of instruction as the retention rate for hands-on learning achieved through projects is very high. Consider this example: If you built a marshmallow cannon, how fast would the marshmallows have to travel to go up two stories [9]? How high must a track’s starting point be to accomplish a 2’ diameter loop-de-loop for the racers [10]?

To make these activities novel and complex, present content from a wide variety of sources and levels to see what engages students and challenges them. For classroom teachers, this means having items at all levels available. Parents can more precisely gauge their child’s interest and abilities by trying different content at different levels.

As parents and educators, we soon find the delicate balance in keeping content comprehensible. We must encourage persistence and innovative thinking, but not frustrate the student at the same time. We can subtly monitor progress and ask our students leading questions, and help them understand the material while not taking away from their achievements. While the student may need hints to reach the right solution, the key is that the student can approach the problem on their own.

Then Maintain Motivation

“If Kids Don’t Want to Learn You Probably Can’t Make ‘em” – Jack Frymier

My wife, a very talented classroom teacher, sees her job, at the beginning of each school year, as getting to know each child, discovering what motivates them and then using that knowledge to teach them more effectively during the year. As humans, parents, and teachers, evolution has left many of us with instinctual approaches to motivation better suited for motivating physical tasks and encouraging behavioral modification, e.g. take out the garbage or you don’t get your allowance. While effective for simple tasks, this form of motivation falls short in motivating us in highly cognitive tasks such as learning. We need to take care. Pressure, unfair competition, threats, or punishments can all disrupt the learning process. Teachers and parents can accelerate the learning process by weaving in techniques such as autonomy, rewards for effort and achievement, and the delivery of more positive than negative feedback. Students respond well to our genuine interest in their learning pursuits and our reinforcement of the relevance of their study materials too [11].

James Middleton goes a bit further and details how, to maintain interest, the student must continue to see how the activity provides continued stimulation while also remaining in their control [12]. In practice, that means letting the student choose. All parents and teachers know how addictive and enticing electronic devices can be; so, for most students, all this must be accompanied by some sort of non-electronic relaxation time, where playing Call of Duty on your phone or texting friends is not an option.

A very useful tool for parents can be to utilize the Pomodoro technique and combine study time, e.g. study for the first 45 minutes of the hour, and use the remaining 15 minutes for non-electronic relaxation and explore some of the learning activities explained above. Teachers can ask students to select from these activities during these breaks from structured learning. Even though it’s the equivalent of asking your child: “would you like to take a bath or go to bed?”, it still allows them to retain control.

Parents and teachers may want to try some of these motivational tools:

• Learning Gamification – Reward for progress and efforts – While sourced from the mortal enemy of learning, gaming, the techniques work just as well in incentivizing learning as they do in encouraging gaming addictions. In this case, at least, the student might find him/herself hooked on something useful [13].
• Reward Systems that work in a student’s home – A properly designed reward structure can help bring focus to students who find it hard working for longer-term goals (e.g. ADHD/ADD). Teachers can convey home the students’ awards while parents can deliver the actual reward. These rewards can take the form of money, screen time (with limits), or even tasks performed by the teacher/parent such as doing the dishes at home or cleaning up their students’ desks.
• Drawing practical inferences – Students can benefit from periodically linking the learned material back to real-world applications, e.g. using probability to determine if you should bother checking Google Maps for traffic on the way to school.
• Project-Based Learning [14]- A huge subject beyond the scope of this article, it’s been shown that accomplishing learning through projects is one of the most important elements in maintaining motivation. The theory is that the project learning helps link the learning to practical inferences.
• Demonstrate genuine interest in their learning – We need to show a genuine interest in what our students are learning. This recognition and attention will provide much-needed reinforcement for students.
• Engage in well-matched competitive efforts – Competition is a motivator. When engaging our students in a competition, we need to make sure that both students believe that, with effort, they could succeed. This could be tiered competitions in the classroom, competitions formed through a website like chesskids.com, or even employing a system of handicaps so that the less accomplished learner can still win.
• Engage/relate items they are already interested in – This could be as simple as labels. E.g. How many phases does it take to burn a …
• Encouraging revision and learning from initial mistakes – This is quite simple to do at home, but a real challenge for the traditional classroom environment. Allowing students to revise their work is a significant learning and motivational tool.
• Value/Reward/Recognize the knowledge acquisition itself – Have acknowledgments in the family or classroom for knowledge progress regardless of level. Psychologically, it is quite simple to fall into the pattern of always recognizing the most accomplished students, but implementing some tools that help force you to spread the praise can combat this tendency, and motivate the students who really need it.
• Address anxiety surrounding tests or studying – Sometimes, anxiety due to previous failures, whether perceived or real, can interfere with future progress. Work with a teacher, coach or other professional to help with organizational abilities and study habits. Addressing anxieties and providing encouragement can go far in removing this blocker of motivation.

Summary

Teachers and parents have many available tools to activate interest and maintain motivation for learning in students. Research shows that applying just a few of these techniques regularly can result in a significant difference in student engagement and, ultimately, accumulated learning. Teachers can engage parents to educate through these tools and activities and personalize them for their children while parents can assist teachers in complementing classroom efforts. Parents and teachers must keep a constant eye on the tools they deploy, ensuring they stay positive and work well with encouraging cognitive tasks while being specific to the motivators of each student.

While these tools can be used to activate, or re-activate, a learner, regardless of level, in any subject area, the focus on math is because of its criticality for other subject learning, the long-term usefulness of education in life and careers, and the history of math in being a source of challenges. Not learning the state capitals has few long-term effects, but not knowing your multiplication tables can trip you up for life.

The astronomer Galileo Galilei observed in 1623 that “[the entire universe] is written in the language of mathematics” and that science and society are governed by mathematical principles and ideas. From counting and sets to systems theory and practice, understanding mathematics helps us, as humans, overcome our genetic programming, and function better as a society.

Postscript and Thanks to …
In writing this article, I did a little self-reflection on my own mathematics learning journey. I was lucky to have parents, teachers, and colleagues who gave me many of the above items. Here are a few key people that I could remember who helped me on that journey:

• 2nd Grade – Ms ??? for letting me compete with Wally P. to finish that workbook first.
• 3rd Grade – Scott S. for being a worthy, nearly unbeatable competitor in “around the world”.
• 7th Grade – for Ms.??? for working with me 1:1, and encouraging me to compete in and study for the county math exam.
• 9th Grade – Dr. Zalewski – For allowing me to earn my first C in math [15] and teaching me to work hard at math again. I also remember waking up in class after being hit by chalk. I guess I knew he cared and knew I could do better.
• 10th Grade – Mr. Philips – For “bet A points”, “minus B”, and more contagious enthusiasm contained in one teacher than I thought was possible.
• 11th Grade – Ms. Potrikus – For 3/11 day, having purple as my favorite color again and an understanding of how Newton got to inventing calculus.
• 12th Grade – To the ‘ov people’. I took the AIME exam that year and got clobbered by all these people whose last names ended in ‘ov’ (e.g. Kasparov) from the New York City area. I began to think about how a whole culture can bring about an accomplishment.
• High School – Dr. Swanson for encouraging my efforts at leadership on the math team. We really managed to get kids excited about math and make it a team sport.
• The entire MAA/AIME/Mathematics Olympiad team that created the tests every year that I would get excited about. Yeah… I was that kid and still have a stack of the old tests.
• Stevens Institute of Technology – Dr. Roger Pinkham – For introducing me to Apostle’s Calculus book, deep mathematical thinking and an appreciation for how math describes the universe. Ohh.. and to Vivek and Henry L. who showed me what real math-smart people could accomplish.

References:

1. https://www.edutopia.org/article/growth-mindset-resources
2. Silvia, P. J. (2005). What is interesting? Exploring the appraisal structure of interest. Emotion, 5, 89-102.
3. http://illuminations.nctm.org/uploadedfiles/activities_home/familyguide_fulltext.pdf
4. Some favorite paradoxes, fallacies, and amazing results:
5. http://www.bloomberg.com/news/videos/b/92966fc7-c54d-4405-8fa6-cbefd05bbd6f
6. https://www.math.toronto.edu/mathnet/falseProofs/fallacies.html
7. https://www.youtube.com/watch?v=w-I6XTVZXww
8. E.g. http://www.eduplace.com/kids/mhm/brain/gr6/index.html
9. http://community.homedepot.com/howto/DiscussionDetail/Marshmallow-Cannon-9065000000008MO
10. This was used by the founder to teach his son calculus
11. https://www.edutopia.org/blog/strategies-helping-students-motivate-themselves-larry-ferlazzo
12. James A. Middleton, “A Study of Intrinsic Motivation in the Mathematics Classroom: A Personal Constructs Approach,” Journal for Research in Mathematics Education, Vol. 26, No. 3, pages 255-257.
13. https://www.lynda.com/Higher-Education-tutorials/Gamification-Learning/173211-2.html
14. https://www.edutopia.org/project-based-learning-guide-importance
15. This sentence initially read “..gave me my first C..”. My teacher wife corrected it. 🙂

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