Marilyn Burns and More

One of the highlights of the NCTM Meeting for me was the presentation by Marilyn Burns on the topic of "Using Assessment to Guide Grades K-6 Mathematics Instruction: A Focus on Number and Operations." I have long used books by Marilyn Burns as a resource for my math teaching. She is a wonderful presenter, engaging with a warm sense of humor. Yes, she did use Powerpoint, which she noted was a recent change for her. But it was an outline which she fleshed out in her talk. She also incorporated some engaging video of the kind of assessment she was talking about. I particularly enjoyed seeing her use an assessment that I have used before, taking it from one of her books. Seeing the questions she asked, the way she encouraged the student to verbalize her thinking and reassured the student that the information would help Marlilyn be a better teacher, was quite helpful. All in all an inspriring, productive hour.

Later in the day I attended a session with a colleague of Marilyn Burns at Math Solutions, Lisa Rogers. She was addressing the development of number sense with primary students. By modelling some of the strategies she suggested and drawing in the audience with questions, she kept me alert and involved even though her session was late in the afternoon.
I also enjoyed a presentation on Singapore math, which is creating a buzz right now in this country. A lot of what was presented to us described a central focus on problem solving, the importance of helping students visualize math, and the laying of a foundation with informal experiences before introducing formal treatments. It is also a spiral curriculum that comes back around and revisits and reenforces topics. Other presentations I attended explored the development of algebraic thinking and the development of an understanding of base 10.

NCTM Meeting in Washington, DC

Pictures: Entrance to the NCTM Meeting Exhibits, Convention Center displays

I've recently returned from the National Council of Teachers of Mathematics Annual Meeting in Washington, D.C. I had thought I might be able to blog from the conference but ran into a couple of problems. The first was the limited free internet connectivity available to me, and the cost of the paid connectivity that was offered. As a result, blogging during the sessions did not work. The second problem was I had little time between sessions, as I tried to pack in as much as I could.

So here's my post today. It was a great conference. I had several sessions that were exciting, informative, and stimulating. Several more were interesting and gave me food for thought. A few were rather dull. When will people realize that simply showing a Powerpoint presentation (without pictures or video) and reading it to us with a little extra explanation does not make for an interesting session?

Fortunately most presentations had more zip, including an engaging delivery, thoughtfully posed questions, and for some, audience participation. Another post will detail some of the better sessions that I attended.

More Fractions

One fraction activity that I particularly love with this age is one I take from Marilyn Burn's About Teaching Mathematics: A K-8 Resource. In the activity, the students make fraction kits, cutting identically sized and multi-colored strips of paper up different ways. First they cut one in half and label each piece 1/2. The next strip is cut in 4 equal pieces and labeled appropriately. By the time we get to the fifth piece, the children have cut and written a lot. They are worried that they will need to cut this piece into 32 pieces, so they are relieved that this piece stays intact to represent 1 or 1/1.

Last week we made our fraction kits and learned the game Cover Up, in which they roll a fraction cube to get pieces to cover the whole piece. Later this week we will learn the game Uncover. We will also use the kits to explore how fractions add together and equivalent fractions. It is a great hands on activity.

Fractions

This week I pulled out several board games we have that use fractions. As we looked at them, we discussed what fractions actually are. Students often say they do not know what fractions are. Yet if you ask them to give you half of something they can do it. The gap is between the abstract idea of fractions and their experiential understanding of the world. So part of what we work on is bridging that gap, using manipulatives and talking about what they represent.

Today we used frog counters in two colors to represent fractional parts of groups of objects. If you have 6 frogs and half of them are red, what does that look like? Students made groupings that fit the fraction given and worked on writing the fraction. Can you show what it looks like if one third of them are a given color? Is there another fraction name that would represent the same amount? Some quickly came to 2/6, while others got help from a partner to figure it out.

Gone Fishin'

In S'math we are doing an activity from AIMS Education Foundation (Activities Integrating Math & Science) that helps show the effects of camouflage. Half the students have done the activity and the other half will do it next week.

Students "fish" for paper fish that are spread out on a construction paper ocean. There are equal numbers of four colors of fish: red, white, blue (the same color as the "ocean"), and black. Teams of students take turns fishing and record their results. Then the whole group meets together to share the class results. We put them on a big chart on the chalkboard so that we can easily compare the number of fish caught. Inevitably either the red or white fish are caught the most. Usually the blue is caught the least, though a few times black has come in last in number caught. I don't tell the students ahead of time that this is a camouflage activity. It prompts some "aha" moments as the students consider why we get the results we do.

I have learned to trust the activity and not get worried if one team's results are skewed because black or blue is a favorite color of some of the fishers. Though I tell the kids not to try to pick up certain colors, a few will do that. Fortunately the rest of the group balances them out. (Or maybe it's the kids who like white and red best!)

World Math Day

Wednesday, March 4, was World Math Day. Although we did not participate in any of the online competitions associated with Math Day, we found a fun way to celebrate the day. Lower School head teacher, Lisa, came to Sky Class and taught the students a math game based on some traditional Native American math games. After playing the game with a partner, students got to take the materials home so that they could play the game some more.

100 Equations

On our 100th day we began a chart to see if the class could come up with 100 equations that equal 100. There was a lot of initial effort and now it has ebbed somewhat. But slowly we are creeping up to 100. As of now we have 98, so just 2 more to go! We've got an interesting combination of addition, subtraction, multiplication, and division equations and some combos. It has been fun watching the kids work out equations. Some just think of one and then look to see if it's on the chart already. Others will take an equation already on the chart and vary it a little.