Could it be that the roots of math anxiety lie not with math itself but with the way math is taught? In this episode I am extremely fortunate to speak with Dr. Eugene Geist, Associate Professor at Ohio University – Athens, Ohio and specialist in early childhood education. We talk about math anxiety – how it develops and what can be done to help kids overcome it. So if you have math anxiety, are a parent of a child with math anxiety or are a teacher of math you’ll want to hear what Dr. Geist has to say about this topic. Don’t let your kids say “I hate math!” Children are, as Dr. Geist will point out, natural born mathematicians and you can help them with their math homework and in the process help them overcome math anxiety.
Summary of Dr. Geist’s ideas as to what causes math anxiety
- Understand that, developmentally, young people hate to be wrong. We all don’t like being wrong, but it is especially embarrassing and painful to the developing child.
- Don’t Create Embarrassing situations: Asking students to “come to the front of the class and work out a problem on the board” contains the potential for a publicly embarrassing situation for a child. Use this approach (if at all) very carefully.
- Don’t focus on right and wrong: Math learning is difficult if it occurs in an atmosphere (either school or home) in which there is pressure to use one method to find the right answer. Allow some room for exploration and for the child to find one or more ways to find the best answer.
- Focus on Concepts instead of Math Facts and Processes. Focus math on applications and uses in daily life. When teachers focus on teaching only the processes or procedures of solving math problems and not on helping students understand conceptually why we do those procedures, then students will focus on learning processes (ex: “invert and multiply”) and not on seeing how those processes make sense. Fluency with the multiplication table can come later – first make sure students understand what is going on and why.
- Let Students Work On Their Own. Let students try to figure math problems out first on their own and let them debate with each other about the right answer. You’ll find that they enjoy learning math this way and are more likely to understand it better.
- Don’t Let Math be a Mystery: It is no wonder that math can seem like a mystery and create anxiety in many children when it is taught in the ways described above.
- Don’t Give The Right Answer. Give a try doing what Dr. Geist mentioned in the podcast: give students a problem, but don’t give them the answer right away. Let them think about it until next class when you give an answer – but tell them that it may not be the right answer. Let them tell you if it’s right or wrong and why.
What to do if Your Math/Statistics Teacher’s approach Isn’t Working For You
- Study in Groups: work with other students in your class to see how they are coping with the situation. Students can be great at explaining things to other students.
- Look online for help. Search YouTube – there’s lots of tutorials there on math made by other teachers. Also, iTunesU may have a lecture from a teacher on the topic you’re stuck on.
- Rewrite Your Notes After Class. I know – this one sounds dull, but I did it when I was taking a class and was really confused. Re-writing your class notes – immediately after class – can really help clarify things for you.
- Use Your Textbook. Most textbook authors bend over backwards to explain things clearly. You paid for it – use it. And don’t forget to use the website that accompanies most textbooks.
Ideas on What Teachers and Parents Can Do to Avoid Fostering Math Anxiety in Children
- Have the right attitude toward math: math is not inherently “hard”. Math is about puzzles and kids love puzzles.
- Work together with the child when working on math problems. Don’t stand over the child holding onto the “right” answer, ready to judge the child if he/she doesn’t get it right. Work collaboratively with the child to solve the puzzle.
- Model problem solving with the child. “Now let’s see, what should we do…?”, “How about if we try this…?”, “You know, I think I may be wrong here – let’s try a different approach.”
- Take a constructive approach to wrong answers: “Gee, that seems like a really big number. Do you think that’s right? I mean, how could….lead to….?” and, “I’m not sure about that one. Can you show me how you got that answer?”
- Get kids to work with each other to solve a problem. When they come up with different answers, have them work together to see who has the right answer.
- Make math learning not about long pages of worksheets, but rather an adventure in puzzle-solving.
Resources on Math Anxiety
- Dr. Geist has written and spoken widely about the topic of math anxiety as well as about the teaching of math and about constructivism. Here is just a sample of some of his publications:
- Geist, E.A. (2008 In Review) Because I SAID So: Power Relationships in Teaching Mathematics
- Geist, E.A. (2008 In Review) What Is The Self-Fulfilling Prophesy and What Does It Have To Do With Learning Mathematics?
- Geist, E.A. (2008 In Review) Dealing with Math Anxiety in Early Childhood Teachers and Students
- Geist E.A & Geist K. (2007 in press) Do Re Mi:That’s how easy math can be: Music interventions to support mathematics concepts in infants, toddlers and preschoolers. Young Children
- Geist E.A. & Janson G. (2007 in Review) Timed Tests and the Effects of Anxiety of Learning Mathematics.
- Phillips, S.K., Duffrin, M.W. and Geist, E.A. (2004). Scientific salad and apple analysis: Take food out of the kitchen and into the classroom to teach mathematics, science, and more. Science and Children, 41(4), 24-29.
- Geist, E.A. (2002) Annual Editions – Early Childhood Education 03/04 Children are Born Mathematicians: Encouraging and Promoting Early Mathematical Concepts in Children Under Five. p.174-179 McGraw-Hill; Guilford CT
- 1993 Jacksonville State University – Jacksonville, Alabama – What is Constructivism: Beyond Just a Buzz Word.
- 2000 Research Council on Mathematics Learning – Las Vegas, NV – Constructivist VS Traditional Methods of Teaching Mathematics.
- Here is the word problem Dr. Geist discusses in this class:
A man buys a horse for $20 and then he sells it again for $30. He then buys the horse back for $40 and sells it to somebody else for $50. Did he make money or lose money and how much did he make or lose?
- Here is the link to the web site called Project Construct. Here’s a blurb from their website telling what Project Construct is all about:
Project Construct is derived from constructivism — the theoretical view that learners construct knowledge through interaction with the physical and social environments. Through “hands-on, minds-on” experiences, students in Project Construct classrooms attain deep understandings in the core content areas, while they also learn to work collaboratively with adults and peers and to be lifelong problem solvers.
Books
- Dr. Geist highly recommends the books of Constance Kamii. Here is a link to one of her books on Amazon: Young Children Reinvent Arithmetic: Implications of Piaget’s Theory (Early Childhood Education Series (Teachers College Pr))
- Dr. Geist also recommends the work of Catherine Twomey Fosnot. She has a number of books on Amazon as well: Young Mathematicians at Work: Constructing Fractions, Decimals, and Percents
Fergus
April 13, 2008The reason for the discrepancy in the answers people get to this problem is down to the assumed value of the the horse in each transaction. You can argue that the man spends a total of $60 on the horse ($20 +$40), that he receives a total of $80 on the sale of the horse ($30 +$50), thereby ending up with $20 extra in his wallet. That looks like a profit of $20, no argument, but it assumes that the horse was always worth the $20 the man originally paid for it. But what if the horse he sold was always worth the $30 he sold it for? Or what if the value of the horse rose from $20 to $30 over the course of its purchase and sale? Or what if it proved to be the greatest steeplechaser ever to have lived, worth millions? How much did he lose then!
If you take the value of the horse to be always $20, here’s how it works:
Buys a horse worth $20 for $20. No loss or gain
Sells the horse worth $20 for $30. Gains $10
Buys the horse worth $20 for $40. Loses $20. Net loss of $10.
Sells the horse worth $20 for $50. Gains $30. Net gain $20
If you take the value of the horse to change over the course of the transactions, it becomes harder to say how much the man made or lost. We would have to ask him what it was worth to him!
Jamie
April 13, 2008I love math! This discussion makes me happy.
Jennifer
April 13, 2008If the horse is only $20.00 to begin with, there’s clearly a problem, and no-ones profiting…
David W.
April 13, 2008He profited $20.
If he starts with $50, then after buying the horse for $20, he has $30. After selling it for $30, he has $60. When he buys it back for $40, he has $20. After selling it again for $50, he has $70. He started with $50 and ended with $70. He profited $20.
I’m not sure how anyone thinks he broke even. It really does not matter if its the same horse each time or not.
Anne McLoughlin
April 13, 2008He started off with $30 in his wallet.
He paid out $20.Then got back $30 from selling horse.
$30+$10=$40
Now he spends entire $40 to buy back horse and sell it for $50.
Now he has $50 in his wallet. So profit of $20
Maura
April 13, 2008I think that the man made a profit of £20. If he began with £100 in his pocket spent it on the horse he is left with £80.Then he sells it for £30 so he now has £110 . Next he buys it back for £40.So now he has £70. Finally he sells it for £50 so he ends up with £120 which means he has made a profit of £20.
Nicholas Corwin
April 13, 2008One further note: when I said it is partially correct to assert that the buyer earned a $20 total profit, I meant the following: If you look at each transaction separately, you could say that he earned a $10 profit twice, for a total of $20, but that reasoning ignores the money he laid out. In any case, here, such is not the case, because it’s the same horse. This fact, I would argue, is significant: the problem states that he “buys the horse back.” If it were two entirely separate transactions, you could argue that he made a $20 “profit” in the aggregate.
Nicholas Corwin
April 13, 2008Well, now, it seems we’re straying from a purely mathematical problem into a kind of philosophical or semantic one. You can’t say “it doesn’t matter if it is the same horse or not,” because the facts of the problem state explicitly that he “buys the horse back.” Hence, with all due respect, Jim, supra, is at best only partially correct to assert that the buyer earned a $20 profit.
The first sale generated a profit of $10, it is true, and the second one appears to have generated a profit of $10. However, the second time around, the seller laid out $40 for the same item, erasing his previous $10 profit and costing him an additional $10. So at this point he has a loss (or money laid out) of $10. Then he sells it for $50, recouping his $10 loss, but earning no additional money. In short, he breaks even.
Jim
April 13, 2008Regarding the selling of the horse, I would look at each instance of buying and selling instead of adding them up to get zero.
In the first instance, he bought a horse for $20 and sold it for $30, a profit of $10.
He then bought it (it doesn’t matter if it is the same horse or not) for $40 and sold it for $50, a profit of $10. In total, he made a profit of $20.
In a spread sheet, he would have a total of $60 going out, and a total of $80 coming in, for a profit of $20.
If you look at his net worth (say $100 to start with) it would go down to $80, up to $110, down to $70, and then up to $120. Again, a profit of $20.
Michael
April 13, 2008Andy: I’ll send your solution to Dr. Geist to see if you’re right! Michael
Andy
April 13, 2008I think I know the answer to the question above about the horse. looking at the problems the man buy a horse for 20, then sell it to for 30 and buys it back for 40 and sells it again for 50. the person lost 20 for buying the horse, but he again 10 for selling it. Then he lost the 10 for buying it back and another ten for selling the horse.
So: -20 + 10 = -10,
-10 – 40 = -50
-50 + 50 = 0
The person break even>