What math programs or ideas have you used that have been effective? As school soon approaches for most of us, lets share those “tried but true” methods and program ideas. I am looking for ideas for students in grades 6-8 as I will be in charge of math for several of my students this coming year. I have extensive years in reading (25 years) but would like some new ideas in math as I have not served that many students with that need area.
I've got some online...
http://www.resourceroom.net - click on “math”
I work with college students now and it just reinforces what I suspected & read in research — so many kids do *not* connect the recipe for the symbols with anything real. No, the answer isn’t to abandon calculation for “problem solving” — but to really work with making that connection between the symbols and what they mean. A visual learner who doesnt’ understand subtraction needs to do more than look at 30 and 36 and “see” what is different about the numbers to help figure out that you add six to get from one to the other. POpsicle sticks are not out of the question for understanding numbers and place value, even in middle school — you just have to keep them from being cute :)
Re: Don't leave the "concrete" too quickly
Thanks — excellent ideas.
You’ll find you have a lot of UNteaching to do before you can apply those ideas — kids who have been told it’s wrong to use concrete materials, kids who have been told to throw out every scrap of work and present only answers (thus rewarding cheaters and punishing thinkers), kids who have been rewarded for neatness above mathematics, kids who have been told not to think and ask questions but just shove symbols around because that is the “right” way, kids who focus only on the marks and will not look at the math work to get those marks, and so on. Just getting the students to realize that the drawing of the rectangle is the real math lesson is hard — I have had one boy tell me “well, you’re not teaching anyway” because I was drawing and writing on the board, not readingout of a teacher’s manual, so he figured it was OK to be disruptive because it wasn’t a real lesson (and no, he wasn’t even officially special ed, a regular Grade 7 class).
Be patient and work for the long haul and try to avoid letting everyone (students, teachers, parents, principal) push you into a ritual of handing out worksheets and collecting and marking them just to keep everything quiet.
Once I have found the place in the sequence of instruction where the student has “broken down,” then I go back to re-introducing the concept with concretes like cuisineirre rods (sp?) or pattern blocks or counters or cut pieces of paper (if that is all I have) to demonstrate the concept. Allowing discovery with the manipulatives before using them for instruction is also helpful in knowing how he/she “sees” them used. After needed time using just concrete, I use symbols (numbers and process signs) *with* the manipulatives simultaneously. Then, I work toward removing the manipulatives when the student is firmly grounded in the concept. That varies by student. I try not to rush it. “As fast as I can, but as slow as I must.”
I do not allow independent practice of a concept until they can do at least 50% of guided practice correctly on several trials. IMHO, many math problems are caused by doing homework before one is ready for independent work.
I’m not especially trained at task analysis, but I try to be very careful about this so that I’m not “mixing” problems that require more tasks.
That’s not everything, but all I’m thinking about just this minute. I’m sure others have more…