Archive for February, 2010
Watching for the Tricky Parts
Math can be tricky. Students make common errors, referred to as “math bugs” in the research literature (Ginsburg, 1987). One of the things that we can do is have a focused discussion each week about the tricky parts of problems that students make. These have to do more with conceptual understanding and procedural fluency. “Slips” (Ginsburg, 1987) are the silly mistakes that students make that can easily be corrected.
As a guided math strategy, the teacher actually has an in depth discussion about the tricky parts of whatever the students are currently studying. Let’s take a look at a Math Bug vignette done during a guided math group:
Mrs. Kay: Okay, everybody, today we are going to talk about Measurement Math Bugs. Our 4th grade standard says that you all will know how to make conversions within the Standard Unit of Measurement. This means that you will be able to convert inches, feet and yards. So let’s look at a typical problem and the common bugs that pop up when solving this problem.
Problem: Susie is going to make a dress. She bought 2 ft. 5 inches of material. She has to pay for the material by the inch. How much of the material does she have in inches?
Math Bug Answer 1: 10 inches
Math Bug Answer 2: 7 inches
Mrs. Kay: Who can tell me what the error is in Math Bug 1?
Tom: They multiplied the 2 by the 5.
Mrs. Kay: Who agrees? Thumbs up if you agree, thumbs down if you don’t and sideways if you’re not sure. [Most students agree and a few aren’t sure.] Ok, yes they multiplied here. What is the math bug in example 2?
Maria: They added, but you’re not supposed to add. You’re supposed to first change the 2 ft to inches. Then add that to the five inches and that gives you the total in inches.
Mrs. Kay: Who agrees? Thumbs up if you agree, thumbs down if you don’t and sideways if you’re not sure. [Everyone agrees] Ok, so if we were to write the steps for doing conversion problems, what would we write. Let’s chart it and then you write the steps in your own words in your math journal.
(Mrs. Kay Charts it and the students note it in their journals).
Ginsburg, H. P. (1987). How to assess number facts, calculation, and understanding. In D. D. Hammill (Ed.), Assessing the abilities and instructional needs of students (pp. 483503). Austin, TX: PROED.Read Full Post | Make a Comment ( 1 so far )
Several studies have shown that vocabulary is a big part of all math tests. Students don’t know the words and so they can’t solve the problems because they don’t know what they are being asked to do. So, a very focused, concentrated effort on building and using mathematical vocabulary is an essential part of any ongoing math program. Every Friday, I encourage teachers to play games to build vocabulary. Here is a list of vocabulary games: Jeopardy, Bingo, Charades, Crossword Puzzles, Word Find and Define. We use a mix of vocabulary from the current unit of study as well as vocabulary from past units.
Create great crosswords and wordfinds on www.puzzlemaker.com. Edhelper.com also has a way to create crossword puzzles. Crossword puzzles are great because students have to really think about the definition to get the word. Also, when I have them do word finds, they must define the words they find at the bottom of the page.
Interactive Math Crossword Puzzles: http://www.mathgoodies.com/puzzles/Read Full Post | Make a Comment ( None so far )
Recently in a conversation with my friend Christine Mulgrave-King, she talked about “stretching our pedagogy.” I like this term because it brilliantly provides a metaphor for what we do when we differentiate instruction. We must continually “stretch our pedagogy” if we want to reach all of our learners. We must “stretch our pedagogy” if we want to make sure that students are learning in their zone of the proximal development. We must “stretch our pedagogy” if we want to move all of our students to their next level of learning. Guided math provides us the perfect platform for “stretching our pedagogy,” requiring that we (the teachers) reach way down and come up with different ways (research based instructional strategies) to teach the concepts so that the ones who aren’t getting it finally do and the ones who are getting it, get something new!Read Full Post | Make a Comment ( None so far )