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."

Planning

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If you don't understand the problem, creating a solution can be nearly impossible.

Word problems can be especially tricky, especially when they don't have accurate diagrams attached.

If you see a word problem that has to do with 2D or 3D shapes, one of the first things you should do is to draw a diagram using the information given.  That's why it's important to pay attention when Mr. V explains how to draw the shapes, especially 3D ones.  That's coming up in a video for next week.  Also watch out when a word problem starts slinging around a variable, as they might not always want to know what the variable stands for.  All of this has to do with understanding the problem.



Once you've done that, you can make a plan of what to do about it.  Perhaps your plan might include drawing the shape being described, or if the shape is on it's side, redrawing it so that it is on the base.  Or finding what the variable stands for so that you can test each answer choice.



Then you need to be extra careful about working your plan.  If your drawing is missing some information, you might need to adjust it.  Or if you aren't careful in finding the variable, your tests might say all answer choices were wrong.



In those cases, the reasonableness (meaning is it likely that the answer you got is the correct one) comes into question.  So you may need to look at the answer choices to see if you're close or way off.  Again, be careful about this, as there may be one close to yours intentionally placed there by the test giver.


At any rate, knowing what plans to use is a skill that can be practiced, and I intend for us to do that.



So, now that you've read the post, either put in your journal or take a sheet of paper and let me know where you think you might run into trouble when trying to solve word problems.

Venn Diagrams

A Venn Diagram is a set of circles that overlap.  It is useful in explaining similarities and differences.  I will create part of it and you recreate it and then finish it.

Other things you could put in there for me are reading, science, technology, art, classical music, and I may add a few extra tomorrow in class.

I didn't include them in the example because if we both like one of those, it should go in the middle with SASIC.

We'll do something similar with your classmates during class tomorrow.

Estimation or Using the Test Against Itself

Hello everyone.  I'd like to discuss using estimation as a test taking strategy.  This is one of my favorites, but one some students that I encountered did not willingly embrace.  Some of the complaints were that it was extra work, or that they were not careful enough with the estimation.  I believe they may have had bad experiences in the past with estimation and rounding, as it has a few arbitrary rules that they may have been caught up in.

Estimation is a vital skill that we use every day whether we know it or not.  When we're out shopping, we estimate prices all the time.  19.95 becomes 20 very quickly.  This in turn, helps us calculate and budget how much should be spent on each item.  It also helps us compare prices, especially when the stores don't want to give out cost per unit.  3.99 for 10 apples for example versus 0.67 for 1 apple.

Where students seem to be falling down is that they don't understand when to estimate, or what information the estimate gives us, thus why it's useful.  Estimation is especially useful on problems that involve measurement, as they nearly all include multiplication, sometimes multiple step multiplication.  Thus, having an easier set of multiplication to do can eliminate answers, perhaps even enough answers that the correct one is left alone.

Estimation gives us minimums and maximums.  In my example above, the maximum it will be is $20.  Then estimating tax of 10% gives us tax of $2, so we should have $22 ready to spend at the register for our item that costs $21.64 exactly.  Thus, we got a maximum price, exceeded it so that we would get change back instead of having to leave without the item.

Likewise with measurement.  We should estimate close to the measurements given but make sure we always round down to get our minimum, then always round up to get our maximum.  This strategy can help students who are not careful with decimals when they multiply.  Students who know their multiplication facts will also find that estimation is much faster than multiplying the decimals out.  Other things to point out would be when a number is very close to an easy multiplication fact, like 2, 5, or 10.

The problem with this strategy, when the test is really mean, is that it is possible that it will not eliminate enough answers and a guess or the long multiplication is still required.  In that case, remind students that their exact answer will fall between their minimums and maximums.  Looking at the entire question including the answers would be the best idea to determine if they should estimate or not.  If the numbers vary greater than 3-4, estimation will eliminate 1-2 answer choices and possibly all 3 of the wrong ones.