Math Anxiety

http://math.about.com/od/reference/a/anxiety.htm

Many of the students I've encountered with math anxiety have demonstrated an over reliance on procedures in math as opposed to actually understanding the math. When one tries to memorize procedures, rules and routines without much understanding, the math is quickly forgotten and panic soons sets in. Think about your experiences with one concept - the division of fractions. You probably learned about reciprocals and inverses. In other words, 'It's not yours to reason why, just invert and multiply'. Well, you memorized the rule and it works. Why does it work? Do you really understand why it works? Did anyone every use pizzas or math manipulatives to show you why it works? If not, you simply memorized the procedure and that was that. Think of math as memorizing all the procedures - what if you forget a few? Therefore, with this type of strategy, a good memory will help, but, what if you dont' have a good memory. Understanding the math is critical. Once students realize they can do the math, the whole notion of math anxiety can be overcome."

When Students Fail...

I just read this article about when students fail math.  It was very insightful.

http://www.slate.com/articles/health_and_science/science/2013/04/math_teacher_explains_math_anxiety_and_defensiveness_it_hurts_to_feel_stupid.html

Guard Your Goals

A quick TED talk about how to achieve your dreams and goals.

Derek Sivers

Teaching Creativity

A TED talk about teaching creativity through beating back fear of failure with small successes.

Dave Kelley's TED

Wheel of Theodorus

Hello.  I stumbled on a neat art project for math today, called the Wheel of Theodorus.  Hopefully we can get that going in class.  The link for instructions on how to teach it is here.  It's for 8th grade and beyond, however, as it has to deal with Pythagorean theorem.

http://www.ldlewis.com/Teaching-Mathematics-with-Art/documents/MTMS2007-04-442a.pdf

Book Review: Brain Rules by John Medina

Brain Rules, subtitled 12 Principles for Surviving and Thriving at Work, Home, and School, by John Medina, deals with the above topic through the author's use of anecdotes, examples, and simple explanations of the science that make the stories relevant.  The book is a fairly quick read, although slow because of the breadth of the topic at hand.  Medina breaks the topic into 12 rules: exercise, survival, wiring, attention, short-term memory, long-term memory, sleep, stress, sensory integration, vision, gender, and exploration.

John Medina is uniquely qualified to discuss this topic, given that he researches the molecular basis of psychiatric disorders.  He writes that he "occasionally would run across articles and books that made startling claims based on 'recent advances' in brain science about how to change the way we teach people and do business. And [he] would panic, wondering if the authors were reading some literature totally off [his] radar screen." But there was no need for panic, as the science cannot yet tell us how the brain knew how to pick up a glass of water.  Instead, Medina wishes more research would be done.

In this way, he does not ever demand that we follow these rules, merely points to the results of going with or against them.  With exercise, he pointed to sharp intellectuals still active in their nineties vs "couch potatoes" who were fading or already gone by seventy.

This book is helpful to us as teachers in that it shows some of the science behind why our students behave the way they do, perform the way they do, and ultimately need our help in the areas they seem to be weak at.  Using these rules can help us as educators adjust our teaching to fit our many different learners.

Open Ended Math Problems

Group work can be an excellent source of exploration and learning, but sometimes it can be difficult to tap into in the subject of mathematics.  One of the reasons why is because many mathematics questions are set up to be closed ended.  You find the one right answer and you check it and you're finished.  Here's an example of changing closed ended to open ended.

Which of the following numbers are prime? 7, 57, 67, 117

Fred thinks that 57 and 67 are prime because they both end in 7, which is a prime number. Dick says he is wrong. Who is correct and why?

Source: http://books.heinemann.com/math/construct.cfm

As you can see with the open ended question, the restraint to one answer is removed.  Also, more information can be given and more critical thinking can be asked by using the question on the right.  I could say 77 is not prime, but it ends in 7, therefore Fred is wrong.  Or I could say 57 can be divided by 3 evenly so it's not prime.  These are not the only rational answers to the question on the right.

Further opening it up could be a question like "What prime numbers end in 7?"  By asking this question, I removed another limitation, this time I removed the upper bound on prime numbers.  Daring students could find primes that are beyond our usual scope of 1-100.

Product Review: Kuta Software: Infinite Pre-Algebra

Mr. V. here.  I purchased a product called Kuta Software's Infinite Pre-Algebra to help me generate content during summer school.  After using it all through the past few weeks, I thought I would give it a review for their information if they ever stumble over my blog, and for any fellow teachers out there.

The options on Kuta's website are Pre-Algebra, Algebra, Geometry, Algebra 2, and Calculus.  All of these options would load in the same program if ordered together.  As a teacher of middle school math, I limited my purchase to Pre-Algebra.  Any Elementary teachers should do the same, as the content will quickly become more and more limited to the specific subject, and Pre-Algebra had the broadest set of concepts.

Kuta is strong at reinforcing the mechanics of calculation, as you have near complete control over difficulty of problems through slider bars and can "regenerate" them as needed (the software will swap out one problem for another).  You could also use it to try to build teaching worksheets, that move from easier problems and concepts to more difficult ones or ones that use the previous information.  I found this style to be a bit more successful, as it reminded students of what they needed to keep track of when they were doing more complicated questions.

Where I found Kuta falling down a bit, and this may be just the package that I bought, was in measurement of shapes and solids.  It seemed like the program's idea of difficulty was to include decimals in measurement.  Basically this challenges students who's foundation of multiplying decimals is weak, and that's it.  There were no Integers only check boxes for measurement, and the number slider did not seem to adjust the shapes in the same way it did other problems like fractions and order of operations.

Another area that I wasn't quite pleased with was Kuta's attempt at creating word problems.  While some seemed interesting to the students, they seemed to lack that STAAR craziness quality that the students hate.  It was usually very clear what the student was supposed to do.  This is a strange complaint, I know, but one of my goals is STAAR readiness, and these word problems do not come as close as I'd like.  While there is a way to write custom questions, this somewhat defeats the purpose of buying this software as an aid.

Overall, I would give Kuta's Pre-Algebra package an 8 of 10 and would recommend it to late elementary school teachers onward.