Math and technology…
So the question came up of using technology to teach math at Dangerously Irrelevant: Mathematics En Masse when guest blogger, Jason Dyer, brought up the two schools of thought on this subject (should we let them use calculators). Frankly, that argument is as old as, well, so old I remember dear dad (BA Mathematics and a computer programmer back in the day) yelling about not needing a calculator because he could add and subtract just fine. Of course he ran out for a TI when they could do math in HEX because it helped with him doing programming (don’t ask me, I have NO idea why or how he needed to do that). Dad discovered that routine but large figures could be better handled by a calculator, and leave him to do the heavy grunt work figuring out whether the logic of the program was correct (his specialty I’m told, people would avoid bringing code to him for correction unless they were desperate, because he could find most problems and correct them, but he would also read you riot act about how lousy your coding was). Enough of my eccentric family life…
Jason then looked at how collaboration, and discussion could be used with Web 2.0 tools to teach mathematics, which is usually about one correct answer. I shared some of my experience using blogs to have kids talk about how they came to answers.
One problem I think we have with mathematics education is that we assume it’s all about numbers. No, you can’t use a calculator because you should be able to compute, and here is another one, language learners do okay at math because it doesn’t use words. WRONG! via Larry Ferlazzo, Teaching Math to English Language Learners: Can Research Help? Development of vocabulary, and having kids (all kinds, not just language learners) explain their work is really almost a necessity. This calls on oral and written language skills, but it really helps students build their foundational knowledge in mathematics.
Here are some examples from my classroom last year of how I would question students about Math problems, Ms. Mercer’s Class Website » Mathematics
This is based on a method I learned at SCOE (Sacramento County Office of Education) that they used for test analysis. They would give students release test questions, and have them give a reason why answers were correct, or not correct. Then you would have a class discussion, so that students would learn what to look for like, “Hey, the answer to 40 x 20 can’t be 80 because they are being multiplied and it has to be greater than 100, but 1,000,000 is way too big.” I’m usually loathe to teach the kids test monkey routines, but I liked this one because it helps them develop number sense, critical thinking, and lastly, test taking skills.
Now, what am I doing? Well, I don’t have my own class, and the emphasis is really on Language Arts standards, so I’ve been concentrating on that. The text book adoption is California for math at elementary was just ugly. The math standards are some of the highest in the country. Let me prove my point. California adopted the Saxon Math series (and Scott Forsman) for elementary. To make it “align” they bumped the books up one level for each grade, here:
| Book | Grade level in the rest of U.S. | Grade level in California |
| Math 54 | Low fifth graders and regular fourth graders | Third graders |
| Math 65 | Low sixth graders and regular fifth graders | Fourth graders |
| Math 76 | Low seventh graders and regular sixth graders | Fifth graders |
| Math 87 | Low eighth graders and regular seventh graders | Sixth graders |
Now, it still doesn’t adequately cover the standards. In particular, the standard on coordinate graphing, and linear equation in fifth grade (yes, this is a fifth grade standard) which is in Geometry and Algebra and Functions is handled at the end of Math 76, usually after testing. So, here is this complicated concept involving multiple skills, calculations, and choices. Frankly, I’ve tried this one a lot of ways…
1. Making sure they understand how to graph xy coordinates. When I returned to teaching I couldn’t remember what came first the vertical or horizontal (hint, its the second one), so I do some review on this as seen here.
After that, practice, practice, practice…
My entry in this effort this year is…
[kml_flashembed movie="http://voicethread.com/book.swf?b=85785" width="480" height="360" wmode="transparent" /]
Which I’m sure will get a laugh, what the heck is she doing, trying to hack a math lesson onto VoiceThread? First, let me assure you gentle reader, the concepts of teaching coordinate graphing came before the idea of sticking it on VoiceThread. Its’ a lesson where you don’t run into the notation issues that Jason Dyer (and Dan Meyer) have discussed as keeping math lessons “offline”. It just requires drawing, and the doodle tool is good enough for the job. It still may fail. My other option is to do a stop action movie with the dry erase Cartesian grid that I have (one of my favorite teacher tools). The technology would largely be a documentary tool, and not “the” tool in that.
2. Input tables are usually next for the fifth graders. I started a lesson in GoogleDocs with input output tables, but that went nowhere rapidly as I had all the students accessing a single document at once. I have to figure out how to make this work in a lab environment. doing it separately in Excel may be better.
3. Finally, taking the input/output results, and using the two numbers as coordinate pairs, and graphing them. I’m thinking the dry erase grid, and some photos will be about as techie as I get on that one.
So there is the math unit I’m planning, why I’m teaching it, the technology I’m using, and the parts where I’m not.
Computers work in binary, base 2. Thus, multiples of two are big news. A bit is one single switch, 01. A byte is 8 bits. The actual size of megabytes, gigabytes, etc. that get used for hard drives and the like come out of that.
4 bits is enough to make the numbers 0->15, hence, hexadecimal. It was (is still?) used for assembly language. I remember writing assembly code in the 80s where I kept having to convert between base 10 and base 16.
Thanks for the followup on my posts!
Yep, my dad’s FAVORITE language was assembly language! Smirked when mom took a class in COBOL. I’ve never gotten beyond 4th generation (dBASE, Paradox, Access) myself.
I think for the time being the biggest thing that can be done with tech (discussions, podcasts) are going to be around how you come to answers. I’m going to see how spreadsheets and graphics can be used for certain specific areas, but we’ll see how that goes.
Thanks for the post. I agree with you that math is more than numbers. I read the article on Teaching Math to ELL. I think that can apply to all learners. I have found success working with students in both small group and whole class instruction. As part of an intervention program we did, I found that students in small groups with similar abilities were able to express what they did and did not understand. They took risks, explained their thinking and when they were in their regular math class, you could see the progress they made.
The difference that the article points out is in the vocabulary, which uses common words, but they have slightly different meanings, which ELLs may not grasp at first. I think also that teachers think about scaffolding, and building schema when it involves language and words, but may “forget” with Mathematics instruction.
Your point about small heterogeneous groups is good. I’ll be starting a group like this soon to work on neighborhood maps.