Apr

30

Teaching math using real world examples may not facilitate learning

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icon for podpress  Teaching math using real world examples may be counter-productive [3:16m]: Play Now | Play in Popup | Download (204)

Teaching math to students using real world examples may be counter productive. Wow, that goes against everything that I was taught and believe about teaching math.

Dr. Jennifer Kaminski, a research scientist at the Center for Cognitive Science at Ohio State, evaluated the efficay of teaching math using real world examples by subjecting the practice to scientific scrutiny. After conducting randomized, controlled experiments Dr. Kaminski and her colleagues, Valdamir Sloutsky and Andrew Heckler, concluded that the findings did not support the belief.

Surprisingly, at least to me, their research concluded that real-world examples “obscured the underlying math, and students were not able to transfer their knowledge to new problems”. This study which included 11 year old students as well as college students will be published in the May 2, 2008 issue of the Science Journal.

Dr. Kaminski even questions the efficacy of using concrete materials like blocks and other manipulatives to help preschool and kindergarten students better understand number concepts. She notes that there is no rigorous scientific research to support this practice. Dr. Kaminski and her team have begun to look into that now.

What do other experts in the field think about all this? Douglas Clements, a professor of learning and mathematics at the University of Buffalo allows that there’s no denying what the research has shown, but he cautions that we shouldn’t over generalize because “one size can’t fit all”.

That makes some sense to me given that different people have different learning style preferences. One style works well for some, but doesn’t for others. it all depends on the individual. Dr. Clements suggests that using manipulatives is a good idea for kids when they are beginning to learn the basics, just as a starting point.

My own experience as a teacher supports the use of manipulatives to facilitate learning. Besides, students know when using manipulatives is appropriate for them. They’re quick to tell me that they don’t need them any more or quick to ask for the them to help make sense of things. I don’t know. I didn’t do the research, so maybe the most I can say is that I believe that using manipulatives facilitates learning.

I’ve just had a thought here. Maybe the actual manipulatives don’t facilitate learning. Maybe it’s the students’ belief that using manipulatives facilitates learning. Maybe there’s a placebo effect happening here- they believe it, so it does.Now that’s an interesting thought.

It would be interesting to hear what other math teachers have to say on the matter. What’s your experience using manipulatives? Does the use of manipulatives facilitate learning in your classroom? How can you tell?

Apr

27

There’s a lot of math in them there socks!

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I love taking a strand of yarn and creating a three dimensional object. Here’s a picture of my latest creation.

My socks

It just dawned on me recently knitting socks involves a lot of math. I don’t know why I didn’t see the connection before. But, knitting socks involves

  • rate -the number of stitches per inch or gauge,
  • increasing and decreasing the number of stitches as needed for different parts of foot
  • ratio and proportion - creating the pattern using different colours of yarn
  • fractions and circumference- the heel flap is 1/2 the circumference of the leg
  • multiplication- the number of stitches per inch x circumference of your foot and leg
  • addition and subtraction of stitches to create the fit
  • data management- keeping track of where you are in the project and where you have to go

I think there’s a math lesson in this somewhere for those times when kids ask when are we ever going to use whatever it is I’m teaching at the moment. Even if they don’t knit socks themselves, they can appreciate the fact that math makes it happen.

I guess I should tell you, I cheated a bit here. The Opal yarn people have the colour and pattern all calculated in the yarn so that all I have to do is knit and the pattern appears. Talk about instant gratification and I don’t have to do a lot of number crunching- the kids would like that. Cool- eh!

Apr

27

What are the esssential qualities of a good math teacher?

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icon for podpress  What are the esssential qualities of a good math teacher? [9:32m]: Play Now | Play in Popup | Download (190)

I’ve been teaching math on and off now for more than 20 years and I really like it, but for some reason I still don’t think of myself as a math teacher but a teacher who teaches math. I don’t know why that is. I mean, I have my intermediate math qualifications which here in Ontario qualifies me to teach math up to grade 10, and I have attended countless PD sessions over the years to try to stay on top of things. So why don’t I think of myself as a math teacher?

I’m starting to think I feel that way because I don’t have a university degree in math. I mean you can’t take everything at university. You have to make a choice. I chose to major in Philosophy and minor in Sociology with a lot of English courses thrown in for good measure - I tried to do it all. Maybe it’s a self-esteem issue. Maybe at some level I think that because I don’t have a degree in math, I’m not really entitled to call myself a math teacher no matter what my teacher qualification certificate says. It’s not that I don’t think that I’m doing a good job teaching math. I know I am because my students tell me that they like the way I teach because they can understand it, and my students go on to to do well in the next grade- well most of them do.

You know, I’m beginning to think it must be a self-esteem issue or why else would I feel like that about not having a degree in math. I’m quite comfortable teaching intermediate math. In fact, I really enjoy it. I guess I think that having a math degree would give me those essential qualities, those elusive qualities whatever they are, that math teachers have and I guess that I still think I need to get. Was I ever surprised when I found Sean Cavanagh’s article about the essential qualities of math teaching. (I’m always looking.) Cavanagh says research has shown that the essential qualities of math teaching remain unknown. “How can that be”, I asked myself. It’s not like we’ve just stated teaching math and no one has had a chance to figure it out yet. Cavanagh notes that

Research does not show conclusively which professional credentials demonstrate whether math teachers are effective in the classroom…It does not show what college math content and coursework are most essential for teachers. Nor does it show what kinds of pre-service, professional-development, or alternative education programs best prepare them to teach.

How can that be? As I read on, I found that part of the reason seems to lie in the high standard for the type of research that the panel looking into this would be willing to accept. I don’t really understand this either. You mean after all this time, and all the bad press about math test scores, no one has come up with a high enough standard of research? The panel looking into this matter does allow that effective math teaches have an impact on student achievement- 12- 14% of variation in student’s math achievement in the elementary grades The panel concluded

1. It hard to determine what credentials and training have the strongest effect on preparing math teachers to teach, and teach well. Research has not provided “consistent or convincing” evidence, for instance that students of certified math teachers benefit more than those whose teachers do not have licenses.

2. A weak connection exists between teacher’s college math course taking and the achievement of their students at the elementary level, although there is a strong link between the educational background and high school achievement.

3. It is important for educators to have “solid grasp of mathematics for teaching- or an in depth knowledge of specific math needed for their classes and how to make it understandable to students.

What do people not on this panel have to say? Ms Ball, the Dean of education at the University of Michigan in Ann Arbor, says that schools of education need to provide courses and tests that provide instructionaly relevant content knowledge rather than just providing generic math content. Cathy L. Seely, a former president of the 100 000-member National Council of Teachers of Mathematics argues that teacher training especially for elementary grades should focus on training student teachers to be able to work with students and not just have them become more proficient at advanced math because math in the elementary grades is a different kind of math. I take this to mean that she’s wants aspiring teachers to get more training on how to be an effective teacher and not an expert on advanced math.

So what are the benefits of having math specialist teach in elementary schools? That isn’t clear either. I was surprized to read that some high math performing countries like China and Sweden have math specialists in elementary grades but many other high math performing countries don’t. So what’s the key to higher performance? Heidi Schweingruber says that although there is a lack of high-quality research on the topic, having math specialists teach math in the elementary schools is beneficial as an alternative to trying to raise the math skills of elementary teachers many of whom are subject-matter generalists and a have probably just taken one or two course of math at college. as a whole. Ultimately she say, that

I don’t care if you have math specialists or not- but I think you should guarantee you have someone teaching math who knows it and likes it.

She does say that that someone would probably be a math specialist. Well, maybe. I found the article very interesting on many levels. First, I found it interesting that there was no conclusive evidence regarding the essential qualities of math teaching. Who knew. I ‘m still puzzled by that. Why has no high quality research been done given the importance of the issue? That doesn’t make sense to me. After reading Cavanagh’s article, I’m not so up tight about not having a university math degree since the panel wouldn’t/couldn’t state conclusively what post secondary math courses an aspiring math teacher should take- at least at the level I teach. My intermediate math qualifications seem to serve me well.

After thinking about this for a while and talking about this topic to an intermediate math teacher at my school who has a masters degree in math, I ‘ve decided that yes, I am a math teacher and a teacher who teaches math. My colleague assured me that I am a math teacher because I know the subject matter that I’m expected to teach, and I’m also a teacher who teaches math because I know how to teach kids so that the subject matter is accessible to them. He felt that at the senior levels, teachers needed a math degree to be able to see the big picture so they could better prepare students for post-secondary math courses. He agreed with the panel that math teachers should know their stuff and know how to teach it so that students get it. Cavanagh’s article which was published on-line March 28, 2008 allowed readers to make comments about his article, and they did. I will share one comment with you because it really resonated with me. Cdheaston notes

I have been working with middle school students for 10 years, and I have seen how years of dependency on the calculator and rushing them through the text to get ready for high-stake testing have left many children bereft of basic skills and number sense…and not just students with disabilities. Students who do not know their multiplication facts or how to recognize patterns, therefore do not perceive the relationship between numbers, especially fractions…they can’t reduce to lowest terms, they don’t see the pattern in powers of ten, they don’t know how to read the ruler. Later on they struggle with one and two step equations, slope, ratios… and it goes on and on.

So true, so true. After reading this, I thought it would be a good idea for my grade nine students to learn their times tables. I talked to them about why knowing their times tables was so important and asked them if they would like to have another go at learning them . They said yes, and we talked about learning the times tables by listening to them as rap songs. I found a CD of multiplication rap songs on line, down loaded it and took it to school and played it as the kids came into class. We clapped and danced around the room for about 10 minutes to the six and seven times tables songs. It was great. They loved the songs. They loved the the beat. I told them they would be an expert on a specific times table- for example the 7 times table, the six times table etc. I would be the expert on the 2, 5 and 10 times table, and we would lead games and activities based on our number.

Is this going to work? Will my students be able to remember their times table. I guess we’ll have fun wile the beat goes on. I liked the rap beat so much that I played the Cd during my prep time. That put some smiles on a few faces. Here’s the link to the music. I’m not affiliated with Jack Hartman in any way but I love his CD. JackHartman- Multiplying By Music CD

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