Archive for May, 2010
1. Enjoy it. Find the fun in numbers. Because if you Don’t, your students NEVER will:)
2. Learn it. (Study, buy the algebra book or the geometry book….by it in cartoons, buy it in the “for dummies” series,but it in the “painless” series, buy it in the middle school version, however you can get through it…but by a content strand at a time and master it).
4. Go to a math conference (local, regional, state, or national) http://www.nctm.org/meetings/
5. Commit to “stretching your own pedagogy,” –often.
See some of the books:Read Full Post | Make a Comment ( 1 so far )
Today I was talking with a friend about a really rowdy class. We both try to help the teacher. We were discussing strategies to help her given the context of her classroom. She has some rough customers. She has some great kids with some really bad habits. She is a new teacher and her response has been to be very stern. She never cracks a smile and she uses her voice in harsh tones alot. So, we were talking about the ideas of classroom environment–Madeline Hunter’s famous notion of “Feeling tone” (A way of being and knowing and learning in the classroom environment). Classrooms can’t be a free for all. There have to be rules and consequences so we can all learn together in civilized fashion. It’s not Disneyland. It’s school. But, at the same time, there should be some “Disney” in the land (classroom). By Disney, I mean fun. School should be fun and exciting and something children look forward to. They should want to come to school and when they get there, there should be magic. They should feel the magic of learning! When we are doing whole group work, they should enjoy it. We should use picture books and songs and videos and you tube clips that “catch and hold” their attention. They should look forward to being pulled in small groups and working the math out with each other. They deserve it. We all deserve it. We all need to enjoy learning and teaching with each other, everyday, in this place called School:)Read Full Post | Make a Comment ( None so far )
It ‘s really important what students think about themselves, about us and about each other. Students should think they can. Really. Just like the choo choo train did. The research shows that if they they can, they’ll keep trying until they do. Resnick (1999)wrote a great article about the conceptualization of “smartness” in America (see reference below). If our students really believed they could, with the correct instruction and encouragement, they would.
Furthermore, the recent National Math Report (2008) states that what children believe about what they can do matters. It matters in a big way. It discusses how when children believe in themselves, they try harder, they put more effort into learning math and that effort increases their engagement, which in turn raises performance.
They would be able to do so much more than we can even imagine. Moreover, if they thought that we were really on their side, batting for them, cheering them on, searching every kind of way to help them learn it (whatever “it” might be); if they were truly convinced that we were there to teach them until we reach them, they’d try harder too. Finally, if they became cheerleaders for each other as well, really concerned about the learning of each other– helping each other and encouraging each other…they’d do better. I really believe they’d do much, much much better:)
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This is the beginning of an extended conversation on regrouping. I will be posting student work in the next few days.
Regrouping is one of the hardest concepts for students to understand. They struggle with it when it is introduced and often times even when they gain procedural fluency, they never get the conceptual understanding. We have to give students many opportunities to see it in context. Here are a few ideas. I like to start out by acting out scenarios where the students get to make meaning of what it means to regroup. Here is one I have been using lately.
Mrs. Martinez has some cookies. There are ten in a baggie. There are 3 baggies. She wants to give 5 cookies away. What can she do? [Here the students begin to give suggestions. We decided that she has to zip open one of the baggies so those cookies are loose]. We then discuss how she can take 5 away from that group of ten that is now ten ones. We actually act this story out.
We do several problems like these with different scenarios before I ever show them the regrouping algorithm. The next step is that they work in partners with manipulatives that are in groups of tens and ones and they act out the stories as I tell them and then volunteers take turns telling the class stories to act out with their partners.
After several days, we move on to base ten blocks. After using the base ten blocks I show the traditional paper and pencil algorithm with pictures drawn beside it. Eventually, the students do just the paper and pencil algorithm as one strategy.
We then go on to talk about other algorithms (ways of doing something). We talk about how different strategies work with different numbers and how people have favorite ways of doing things. We discuss “elegant solutions” and “quick” or “efficient” ways of doing something. We work in groups to make strategy posters and display them around the room.
Some strategies we discuss: Compensation
So, to do compensation we look at the number and try to find a friendly number (one with a ten). Here we see that 29 can easily be rounded to 30 so we decide to add 1 to both numbers and we get 76-30 (which we inevitably agree is much easier to think about) and we get 46. We look for lucky 9’s and 8’s so we can use this strategy whenever possible.
Let’s look at a lucky 8 example. 62-48. We add 2 to 48 to get to 50 and we add 2 to 62 which makes 64. Now 64 -50 is much easier on the brain (we talk about it like this) and we can quickly get the answer of 14.
Compensation makes thinking easier. Another way to think about this is “Find a Friendly Number”:
I could change 74 to 75 by adding 1. That would give me 75-25 which is pretty friendly. Now, I can’t just keep that 1 I added, I have to take it away once I get my answer. So 75-25 =50. Now, 50-1 =49. That was pretty easy.
Another strategy that we talk about is Jumping Tens. So we look for Jumper Numbers and then we begin to hop back on the number line in our minds. For example, 65-27. We say that 27 is the Jumper Number. There are two jumps of ten in this number. We start at 65 and we hop back to 55 and then to 45. Now we have 7 more to go. We decide to break the seven into 2+5 and then we hop back 5—which gets us to 40. Now we only have 2 more hops and that gets us to 38.
Counting up is a 3rd Strategy.
We look at a problem like 51-27. We say “Well, mmmm, 3 more gets me to 30 and then 21 more to 51 so 24 is the answer.” We just counted up to count back ….we counted up to see how far back 27 really was….
Another Strategy is Splitting Numbers:
Here it helps if the students write it in expanded form.
70 + 0
-30 + 3
So here if subtract 3 from 0 we will get a negative number, which isn’t exactly friendly, so we’ll do something else.
Let’s break a ten into ones. We’ll rename 70 as 60+10 Now, we can continue.
– 30 +3
30 + 7
http://www.youtube.com/watch?v=CqOsj2JWbyE&feature=relatedhttp://www.eduplace.com/math/mw/models/overview/2_12_3.html (don’t use peanuts…use something else…cheerios, unifix cubes, cotton balls)Read Full Post | Make a Comment ( None so far )