Looking back over the quarter's math work, I've come out with a real appreciation for the merits of cooperative groupwork in math education (and all education). In fact, next week I'm going to introduce cooperative groupwork to my 4th graders (I'm using Elizabeth Cohen's Designing Groupwork) -- we'll be engaging in an activity called "Broken Circles." Each group member will have an envelope with circle sections, and each member of the group needs to finish with a complete circle in front of them. They can't talk or take pieces, they can only give pieces. I am very curious to see how this exercise goes. These kids work in partner stations during math right now, but I think the kids would benefit from strategies that foster deeper cooperation.
Our math class also highlighted for me the value of manipulatives (both traditional and online) in "higher order" math...such as algebra. I appreciated learning different strategies for exploring concepts in ways that allow kids to construct their own knowledge, as opposed to being forcefed rules and formulas via direct instruction. The Annenberg videos also gave me good ideas for how kids could construct their own knowledge, such as the video that showed kids developing a rule for calculating the volume and area of rods. Approaching math in this way also allows us to make it more engaging and interesting for kids. I was completely absorbed by the logic puzzle we worked on during our last class. The only danger is how absorbing some of these activities can be -- regrouping students could be challenging if everyone hasn't finished!
The last observation I'd like to make is the value I see in exploring our kids' mathematical identities. Finding ways in which kids can see themselves as mathematicians will help them approach math in a more positive way. As I mentioned in last week's math blog, I found the chart of mathematical activities to be particularly promising for exploring math in our everyday lives. The ideas in Complex Identities are fantastic for both students and teachers to explore their own preconceived ideas about math.
In all, this quarter's math class provided me with good information (via the readings, videos, and class discussion) about how to implement middle level mathematics curricula. The ideas, though, will also be useful to me in my 4th grade main placement class. Thanks to Robin for making math approachable, fun, and edifying!
Friday, March 11, 2011
Tuesday, March 8, 2011
Friday, March 4, 2011
final thoughts about the ipod touch
As the quarter draws to a close and I prepare my loaner Ipod Touch for the next student who will use it, finding something new or insightful to say about this project challenges me.
If the Ipod Touch has one significant power, it's its allure. Every kid seems to want to get their hands on one and see how it works. In this way, the Ipod Touch could really stimulate an apathetic kid's curiosity. A good app like the NASA app or the How Stuff Works app could inspire some students to want to learn new things -- if simply by virtue of offering a novel method of investigation. An ordinary vocabulary lesson with my fourth grade Juanita buddy became much more compelling once the Ipod was brought out for dictionary research! However, this kind of differentiation is something all kids will want to "qualify" for...
While I didn't get a chance to explore all of the uses I suggested in my initial blog post about the Ipod Touch, I do still think there is good potential for the apps I talked about to differentiate learning. For instance, Logic Box could provide great enrichment for more advanced math students and Pocket Phonics could help struggling readers learn to more successfully decode words.
In the end, the most use I made of the Ipod was as a recording device. Ulitmately, I think I see this as one of the best uses of the Ipod Touch for differentiating instruction. Supplementary notes could be recorded for students to refer to when working in their journals or completing their homework. Students could record lessons and listen to them again later. Instructors could record conferences and be able to easily track students' progress. ELL students could hear native speakers' pronunciation of English words in a recorded word list or listen to annotated narratives to foster fluency.
To be sure, if the Ipod fairy came by and said she was dropping off thirty free Ipods for my classroom, I could make good use of them. I just don't know whether they'd be on the top of my priority list if I had to buy them with real money.
If the Ipod Touch has one significant power, it's its allure. Every kid seems to want to get their hands on one and see how it works. In this way, the Ipod Touch could really stimulate an apathetic kid's curiosity. A good app like the NASA app or the How Stuff Works app could inspire some students to want to learn new things -- if simply by virtue of offering a novel method of investigation. An ordinary vocabulary lesson with my fourth grade Juanita buddy became much more compelling once the Ipod was brought out for dictionary research! However, this kind of differentiation is something all kids will want to "qualify" for...
While I didn't get a chance to explore all of the uses I suggested in my initial blog post about the Ipod Touch, I do still think there is good potential for the apps I talked about to differentiate learning. For instance, Logic Box could provide great enrichment for more advanced math students and Pocket Phonics could help struggling readers learn to more successfully decode words.
In the end, the most use I made of the Ipod was as a recording device. Ulitmately, I think I see this as one of the best uses of the Ipod Touch for differentiating instruction. Supplementary notes could be recorded for students to refer to when working in their journals or completing their homework. Students could record lessons and listen to them again later. Instructors could record conferences and be able to easily track students' progress. ELL students could hear native speakers' pronunciation of English words in a recorded word list or listen to annotated narratives to foster fluency.
To be sure, if the Ipod fairy came by and said she was dropping off thirty free Ipods for my classroom, I could make good use of them. I just don't know whether they'd be on the top of my priority list if I had to buy them with real money.
complex identities
We engaged in an activity found in the article Complex Identities in our math methods class last quarter -- we explored what adjectives we would apply to someone good at math or not good at math. However, this article was about more than just the activity we engaged in, and it really shed more light on how we and our students see ourselves in relation to math. I was particularly interested in the mathematical task chart, which listed a number of different activities. Students could be asked to identify which of the tasks, such as sending a text message or riding a skateboard, were mathematical in nature. The answer, of course, is that all of the tasks in some way involve math. I believe that this is a great activity which can help our students see that math is everywhere...not just in the memorization of math facts and rules and passing math tests.
A question I have is why this question of mathematical identity isn't given more emphasis in school. When I read about the honors math student who couldn't think of herself as good at math because great mathematicians are "brilliant" and she didn't see herself as brilliant, I had to wonder if a lesson exploring mathematical identity might have helped her bypass this conclusion.
I definitely see a place for exploring mathematical identities in the classroom. In fact, I'd like to explore ideas about what constitutes a mathematical task in my fourth grade classroom. I can envision applying the same strategy to an exploration of scientific tasks, too! How many things do we do everyday, without thinking, that involve either math or science. Yet many students see math and science as their weakest, and sometimes least enjoyable, subjects. It would be particularly nice to see those kinds of attitudes turned around!
A question I have is why this question of mathematical identity isn't given more emphasis in school. When I read about the honors math student who couldn't think of herself as good at math because great mathematicians are "brilliant" and she didn't see herself as brilliant, I had to wonder if a lesson exploring mathematical identity might have helped her bypass this conclusion.
I definitely see a place for exploring mathematical identities in the classroom. In fact, I'd like to explore ideas about what constitutes a mathematical task in my fourth grade classroom. I can envision applying the same strategy to an exploration of scientific tasks, too! How many things do we do everyday, without thinking, that involve either math or science. Yet many students see math and science as their weakest, and sometimes least enjoyable, subjects. It would be particularly nice to see those kinds of attitudes turned around!
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