There's a Pattern to It

Last month, while an associate sub, I walked out of a middle school math class thinking, "Wow! That was fun!" The students spent the first part of the period using the Percent Of activity on this website - http://www.mathsisfun.com/numbers/estimation-game.php - to hone their estimation skills and increase their number sense. Some of those with higher scores explained their thought processes to others. They all enjoyed trying to improve their outcomes, and most succeeded.

Previously, the class had worked to determine which of three restaurant patrons was the most generous tipper, so the next activity expanded on that. The teacher projected a chart with several dollar amounts across the top and percentages (1%, 5%, 10%, 15%, 20%) down the side. Students worked in pairs to complete the chart. Listening to their conversations was great fun. Most pairs were diligently calculating each result, but I started to hear a few talk about the relationships between the percentages. The most exciting moment for me was when one boy looked up at me with a grin and exclaimed, "There's a pattern to it, isn't there?"

I applaud the teacher for this example of math being taught and learned the way it was meant to be - with a combination of cooperation, collaboration, communication, creativity, and critical thinking.  

The Power of Positive Thinking

Since March, I have had the opportunity to chat several times with the 5th grader from the homework group. (See From Can't to Can) Each time she mentions something positive about math class. I subbed in that class yesterday while the students worked on the final test. Before they got started, I told them that any can'ts in their heads would keep them from thinking and asked her to tell them what they needed to believe. She grinned and said, "I think I can!" After school today, she and I worked on some strategies to help her learn and remember some of the addition and multiplication facts that give her trouble. Although I am a volunteer after school, I was richly rewarded when she said, "Ever since I've been working with you, I am really liking math." She now believes in herself, and it has made a big difference in her attitude and her accomplishments.

Tonight I rediscovered a poem I had forgotten about and am making a copy for her - "It Couldn't Be Done" by Edgar Guest.

Thanks for Asking

Lately, I've had several experiences with the one kid in a class who will speak up and ask the question most of the others are wondering about. I love it!

While subbing in the computer lab, one 2nd grader came up to tell me that the teacher lets them have the lights turned off on Fridays. Having discovered in the past that there may be disagreements about such things, I asked the class how many would object if I turned the lights off. About half the hands shot up. Then I heard a small voice say, "What does object mean?" I explained that it means you wouldn't like it, and all of the hands quickly went down.

Near the end of another 2nd grade day, an intercom message told one little boy that his dad would pick him up tonight. Later, I noticed that he was looking confused and not getting ready to go. Finally he said, "How long is it until tonight?" I knew the secretary meant after school, but he did not. This got me to thinking about how hard kids must work every day to figure out the meaning of things they hear. I told my 91-year-old mom, who struggles with hearing, that it must be similar to how she pieces together conversations when she doesn't quite hear all of the words.

Three cheers for the kids who will ask for an explanation!

From Can't to Can

Some of my most rewarding experiences this year have taken place after school, while volunteering with the middle school homework group. This week was no exception. I enjoyed teaching K-4 music, although I sing off-key. Then I headed next door to see who needed help. I found a 5th grade girl struggling with a math test review. She was really down; the can'ts in her head were shutting down all possibility of real thinking. I smiled, encouraged, explained, asked questions, and listened. She was working with fractions, so I gave her one of my dry erase cards I made to help her rename and/or reduce fractions. (See Equivalent Fractions) I watched her eyes slowly light up, and we had a great hour of math. She left saying, "I can!" We met again the next day and she dug in to finish the review with a positive attitude. She will take the test today, and my fingers are crossed that she will stay calm and think things through.

My Expanding Digital Footprint

Recently, I read a blog post requesting submissions for the next issue of Math Teachers at Play, so I decided to submit my equivalent fractions post. It was accepted and published - http://letsplaymath.net

While searching my own digital footprint at http://pipl.com, I came across a mention of that submission at http://www.mathteacherctk.com

It is exciting to see how my digital footprint quickly extends beyond the original source of my posts. It is also a constant reminder to think carefully about what I make available to the world.

Successful Cure not Symptom Relief

While responding to another post regarding reward systems, I thought about a paper I wrote for my Educational Psychology and Human Development course in 2007. My experiences in classrooms since that time have greatly reinforced the beliefs I expressed in that paper. What do you think?
    
http://tinyurl.com/46eo5tz

Does Your Answer Make Sense

The more time I spend subbing in classrooms, the more I am discovering that I had some pretty amazing elementary math teachers in the 1960s. They taught us the whys and the hows. They also taught us to check the reasonableness of each answer. In fact, I remember learning to look at a problem to determine about what the answer would be before solving it.

I think the focus of math instruction in some classrooms is more on accurate calculation and less about understanding numbers, the procedures, and the processes. Last week, I tried using logic to help a 4th grader understand why his answer was not correct. The problem: 258 - 199. His answer: 159. He knew that 199 was only 1 less than 200 and that 258 - 200 = 58, yet he could not understand how that affected his answer. I've also tried to help students think logically about multiplication facts. If they know that 5 x 8 = 40, they should realize that 3 x 8 can't be 36.

While working on equivalent fractions with middle schoolers, they told me that to find equivalent fractions you do the same thing to the top as you do to the bottom. I asked them why I could do that without changing the value of the fraction. Not one of them knew, so I taught them what I had been taught about equivalent fractions. I could see the lightbulbs go on. They understood that when you multiply both the numerator and denominator of a fraction by the same number, you are really multiplying by 1, so the resulting fraction is equivalent to the original fraction. In my own class, I would take the time to write 4/9 x 4/4 = 16/36, and let them talk about it to see if they would discover for themselves that 4/4 = 1.

After watching Conrad Wolfram's TED talk, I believe he is 100% correct - "Stop teaching calculating, start teaching maths."



Computers can do the calculations. Students need to be able to ask the right question, turn it into a math problem, and check the reasonableness of the computer's answer. If we must use multiple choice assessments, perhaps we could check for understanding by posing questions like this:

I have a garden that is almost 38 feet by just less than 32 feet. About how much planting area do I have?
a) 120 ft    b) 1,200 sq ft    c) 120 sq ft    d) 1,200 ft