Where I’m Coming From

7 Responses to “Where I’m Coming From”

1. 

   Charlie A. Roy Reply February 24, 2008 at 5:23 pm

   I recently attended a conference on authentic assessment. What struck me was the quantity of examples given that applied directly to math.

   A traditional math class room when studying surface area and volume probably features a numerous array of practice problems followed with memorization of the formulas for each. After a few days of working problems it is quiz / test time which usually means a few problems to work for a grade or worse a multiple choice assessment.

   Compare the above to this example of authentic assessment.

   Dear Students,

   I’ve recently been promoted to the head of the womens’ clothing department at Gimble’s. Christmas time is around the corner and I need to make the wrapping paper order. Our Christmas season runs for six weeks and during that time we sell on average twenty five blouses, fifty pairs of slacks, and twenty pairs of gloves a day. The boxes for the blouses and slacks are the same. Each box needs 15% more paper than surface area. Our store is open seven days a week. Wrapping paper is sold by square foot. Please help! How much should I order.

   Granted the above question doesn’t give all the info. Students have to work to find the rest. How big of a box do they need etc. But this problem could easily implement a small group of students using technology to find the answer. They could pull out their phone to call a department store and ask the dimensions of a usual box. Real learning using real math.

2. 

   Jason Dyer Reply February 24, 2008 at 9:54 pm

   For the record here, doing interesting projects isn’t really the bone of contention here, it’s applying all the “Technology 2.0″ things. Pulling out real world data has certainly been in the math teacher’s bag of tricks for a while, and seems like one of those things easily adaptable to modern tech.

   I do a lesson on depreciation rates, for example, where students look up different used cars in newspapers and use the prices to make an exponential decay model. Note however I’m using physical newspapers; the pragmatic math teacher then has to ask: what gain will there be in pulling the same things off of a computer? (From experience: you’ll get more data, but double the time the lesson takes.)

   In your example, calling department stores is the bit I haven’t heard before. I worry about the logistics (especially when using cell phones in class causes warning sirens in most schools; one district in this town just started a policy of mandatory detention for cell phones) but it’s still good thinking. Likely for simplicity I’d just have actual department store boxes in class (my similar lesson has students making their own boxes). Which unfortunately deflates any potentional social tech app, but there still might be an angle.

   Also, there are two caveats on project-based curriculum. 1: All the interesting stuff is on the “easy lessons” — probability, statistics, et. al. Combining like terms? Not so many good plans. Not saying it isn’t possible. I tend to build off a historical angle. 2: This sort of lesson needs a build up of the abstract technique behind it; really the problems need to be pared down to their simplest form. Surface area of rectangular prisms can get particularly rough and I have a very systematic method of teaching it, which doesn’t involve anything whiz-bang. And really the throes of *that* difficulty is what I’d really like to see augmented, but I have yet to see anyone do in a practical way, other than sticking to the basics and doing it really well.

   Thanks for the comment!

3. 

   Roland O'Daniel Reply February 25, 2008 at 9:48 am

   I think it’s a very interesting point to make, “…what gain will there be in pulling the same things off of a computer?…” I work with teachers who are implementing more technology into their classroom and the first question I ask them is, “What do you want to accomplish? and will technology do that better than another approach? Secondly, What does technology bring to the table that other modes don’t? and how will you build that into your instructional plan?”
   Most teachers don’t realize that they need to start with global type questions. They want to start with what cool thing can I do now. If they start there without asking those more global questions, teachers will often bog down with time constraints, technology ‘issues’ and a lack of results.

   I think the real power is in how a teacher chooses to embed technology into their class, make it an essential piece of what they and students do, enable students to add to class thinking, and (a really important piece) how the teacher enables feedback to students to improve/deepen their thinking. Notice I didn’t say give feedback, but enable feedback. Formative assessment is critical to students when they are learning, and one of the most important things that teachers can do in the classroom; just ask Grant Wiggins. Creating opportunities to get feedback on their writing, their thinking, their learning that causes the students to learn about how well or poorly they have communicated their ideas. I’ve learned to encourage teachers to find mentors for their students, pair up with other classes to share thinking about topics, and have their students publish their thinking/work so that they are forced find out how well they express their ideas. It’s social networking to a certain extent, because the teacher has to create an environment where ideas can be exchanged before they will see results. I think there are some great examples beginning to surface and I’m glad you’re bringing it up here too!

   I’m working with a young seventh grade teacher right now to integrate the usage of the new Smartboard that’s in her classroom. We started our conversation off globally and are now discussing the first baby steps that she can integrate now that will enable her to learn about the technology without diving head first into the fray. She’s using fooplots, and posting her notes on slideshare. I’m excited by your thoughts Jason because I see so many math teachers who don’t understand that communication is critical to mathematics and therefore don’t understand how these tools can be powerful. I look forward to reading your next post!!!

4. 

   Dave Reply February 25, 2008 at 11:55 am

   I think you have to be careful not to misinterpret “I don’t see a useful application yet” as “I don’t understand it” or “I just don’t want to use it”.

   For me, math was a more private learning experience. I listened to the teacher, I did the homework practice problems, and things stuck enough that I passed the assessments. I love social networking, I love Web 2.0 tools, and there are definitely some great ways for some technology tools to be applied in teaching math. But I have yet to think of or hear of any way that the core ideas of social networking could have been applied to my math education in a beneficial way.

   …and then as I write this, I thought that maybe some sort of competitive points system would have gotten me pretty interested, even if it was just a way for me to compete against myself rather than other students. My friends play a Scrabble clone Facebook app with each other…what if K-12 students competed as a school against other schools with real-time scores? Sort of like yearly testing (cringe) but it’s always running.

5. 

   Jason Reply February 25, 2008 at 1:40 pm

   Roland, as a caveat on my “what gain will there be in pulling the same things off of a computer?” comment, while I agree the question should also be asked globally, I did mean in that very specific case. Having a determination to use technology is one thing, but getting down to the specifics requires answering, yes, what do I do right now, and sometimes answering that question is much harder than you’d think.

6. 

   Scott Woelber Reply February 27, 2008 at 12:13 pm

   Here are two specific ideas for using blogs in mathematics. I am by no means an expert, so I welcome comments as to how to improve these activities. My junior/senior precalculus class includes a 3 week unit on formal logic. The students all read a short story by Isaac Asimov that included the Three Laws of Robotics. They had to create a story, as a class, with characters and robots that included a legitimate logical conflict involving the Three Laws of Robotics. The students used a blog where only invited participants could post comments but anybody could read. Different students were assigned to add to the collective story on different days of the week. The first students had the opportunity to create and introduce characters; the next students had the opportunity to create the conflict; and the third group had to resolve the conflict. Each day the contributions of the following days students were read. It was a fun activity that enriched the core content, but it was not a replacement to the regular classroom instruction.

   Also in the precalculus class, I included this year a 3 day extension unit about prime numbers that included the RSA algorithm for public key encryption. I wanted to include a component where students wrote encrypted messages to each other publicly with the blog, but there wasn’t time this year. I will include it next year because it will make the experience of public enryption more authentic.

7. 

   Jason Dyer Reply February 27, 2008 at 1:30 pm

   Scott, would it be possible to link to that blog, or is it private?

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