From: Suzanne A.
(for Teacher2Teacher Service)
Date: Oct 16, 2005 at 09:31:22
Subject: Re: Foundations of Math
Hi Michael, I agree that the nice thing is that you have the freedom to do anything! The other great thing is that you have 95 minutes together a day but I agree that that can be a very long time if you don't think of it in different stages. Let's see if I can explain a model that you might work from to break that time up into reasonable, interesting, and productive chunks. Here's one timetable you might consider: 1. Math Message - 10 minutes (an opening (written) activity at the beginning of class that is accessible to all of the students - usually lasts about 5 minutes and then another 5 minutes can be taken to debrief the work) 2. Introduction of material - 10 to 15 minutes (whatever the topic is for the day this is when you present it to the class) 3. Pairs or Group work - 20 minutes (working on the material that you've introduced) 4. Discussion - 10 - 15 minutes (bring the class back together to talk about what they've been working on) 5. Mental Math - 5 minutes (a short oral activity where the teacher gives a mental problem, the whole class responds in unison) 6. Focus Group and Independent Activities, Session 1 - 20 minutes (You work with 4 or 5 students on the math topic of the day. Meanwhile the other 12 or 13 students are working in pairs or groups on activities that they can do independently - I'll give an example of what that might be below.) 7. Focus Group and Independent Activities, Session 2 - 20 minutes (After Session 1, you work with a second group on the math topic of the day and the pairs or groups working independently change to a new activity to do independently. Using this model with 17 students, you can have focused time with small groups of students every other day.) This is about 95 minutes! Now let's see if I can give you an example of how it might work. So, you're probably wondering....what do I actually do for math topics, etc. If I were teaching this class I would use the Problems of the Week as the basis of what I do each week. I would probably use the Math Fundamentals Problem one week and the Pre-Algebra Problem the other week or I might use the problems that are in the Active Problem Library and choose problems that are not too text intensive and then I could vary the math topics as I would like. So, let's think about this using the current Pre-Algebra PoW as an example: http://mathforum.org/prealgpow/ 1. Math Message: The radius of a circle equals two times the diameter. Find the diameter if: 1. r = 4 inches 2. r = 17 feet 3. r = 2 meters Find the radius if: 4. d = 20 meters 5. d = 8 inches 6. d = 14 feet Note: This questions should be written so that all of the students will be successful. It's introducing a concept that will be needed to solve "How Fast Is a Minute?" in a way that's quite basic. As the class discusses the work, I would make sure that they fully verbalize the concepts of radius, diameter, circle, multiply, and divide. Because the students are ELL any time that you can encourage them to explain helps them both in the language development and also their mathematical thinking. 2. Introduction of Material: I would pass out a copy of How Fast Is a Minute? to each student having printed it using the Print This Problem link: http://mathforum.org/prealgpow/print_puzzler.ehtml?puzzle=270 I would give them a moment to read it independently and then either I or another student could read it aloud leaving the "Extra" for later. After reading I would use literacy techniques to check to see if the students comprehended the question. I'm not trying to get them to solve the problem at this point. I just want to make sure that they understand the context and the question (reading comprehension). 3. Pairs or Group work Now I have them work together to solve the problem. 4. Class Discussion I would have a class discussion as soon as I think the students are ready. Important at this point is not to acknowledge right or wrong answers. Important is to encourage students to explain why they did this or that and detail the steps that they took to solve the problem. In other words, at this point students are verbally "writing" their explanation of their solution. Depending on how that went, there might be time to have each student draft an explanation of their answer. 5. Mental Math Sometimes I would have this "break" activity relate directly to the math topic of the day and sometimes I might have it completely separate. At first as with any of these "parts of the class routine" it takes a little training time to get the students used to the activity. Some of my favorite Mental Math starting activities are extremely simple but still exercise the brain. Since you are dealing with an ELL population again realize that not only are they challenged because of the mathematics but also they are practicing listening, comprehension, and speaking skills! Idea #1: The teacher says, "When I say a number, you say the number that is one more than." Example: teacher: 4 ALL students when I give the signal: 5 They will think it is trivial at first but then as you use other variations and as you use larger numbers, it gets a bit more complicated. variations include: "one less than" "two more than" "two less than" "half of" "twice" "a third of" "the decimal equivalent"....etc. So, in effect they're practicing addition, subtraction, multiplication, division, fractions, percents, decimals, etc. Idea #2: The teacher says, "When I say the radius, you say the corresponding diameter including the units that I use." Example: teacher: 4 feet ALL students in unison: 8 feet 6. Focus Group and Independent Activities As the students are working on the problem you'll be able to assess who is "getting it" and who might be struggling. I would form the first focus group by selecting 4 or 5 students who seem to need the most 1:1 help on working the problem. While you are working with them, the other students can be playing Everyday Mathematics games like Top-It (a game played with cards and there are many variations of it) See general directions here: http://everydaymath.uchicago.edu/educators/samplegames.shtml Another idea for an "independent activity" could be that some of the groups can continue writing their explanation, read it to each other, revise and improve it, etc. without direct help from you. So, that's another option. 7. Session II - Change to work with another group and also have the students who were doing an "Independent Activity" change to another activity. If you have computers in your room, I have a lot of suggestions of independent activities that use Java applets, etc. that are available on the Web. Many of them are cataloged here: http://mathforum.org/mathtools/ I hope some of these ideas are helpful, Michael. If something resonates and you'd like to discuss it more, just let us know. Sincerely, -Suzanne A., for the T2T service
Math Forum Home || The Math Library || Quick Reference || Math Forum Search