I just interviewed for a job teaching 3 sections of Algebra I to students I assume have already tried it at least once.
The principal of the school asked me how I would attack teaching all 38 per class enough Algebra to get them through this.
For one thing, if they've already flunked once, it is a real disservice to stick 38 of them in one class. Imagine have 3 sections of Algebra I in 9th and 10th grade, What does that say about the teaching?
Anyway, I started talking about Reasoning and Sense Making - and his eye brows shot way up - which I commented on.
The man must believe that drill and kill (which obviously didn't work before) is going to get these kids through Algebra I (and the state exit exam, too.)
I have had great difficulty finding teachers who actually practice other than procedures and drill.
If you do, please tell me about your experience with it. It seems like the only way to go. Why isn't it being done?
How Students Learn: Mathematics in the Classroom http://www.nap.edu/catalog/11101.html also corroborates it, as well as all the material at www.nctm.org.
I 100% agree that drill and practice is not at all what mathematics should be about. Like you, I believe that mathematics needs to be about problem-solving and reasoning. I think the reason that we don't see our vision for school mathematics implemented in practice is honestly because change is hard. It is so much easier to revert back to things that come easier to us than to go out on a limb and try new things. So, since most of us were the "survivors" who successfully learned the "traditional" way, it is much more comfortable for us to teach that way too. In my experience, I have found that I have to push myself and make gradual changes every year to push my practice so that it aligns with my true beliefs. Each year, I try to experiment with new problems or new teaching methods and slowly adapt my lessons. I think it's the whole idea that change doesn't happen overnight, you know?
One thing I have used as a step towards change is through the daily starters I use to start class. I have five categories: warm-ups, explorations, operation math, puzzlers, and spiral review. Explorations have been a successful way to get students to engage in the concept I want them to learn by exploring and brainstorming using a small problem task rather than diving into direct instruction with them. For example, in my Algebra I class, I may have students look at a series of graphs of linear equations and have them explore similarities and differences as a way to introduce slope-intercept form. Or I may give a basic direct variation situation (without calling it that), such as buying 3 loaves of bread for $12, as a way for my 8th grade math students to talk about proportional relationships and get a contextual understanding of unit rate.
I think it's also important to realize that change is hard for students too. They will fight you and want to be "told" exactly what to do all the time because that is what they think school mathematics is all about. So, there's a learning curve as you get your students to understand that the classroom environment you create is different from what they are used to, but that it is okay and even a good thing!
Anyway, I hope things went well and you got the job. Good luck with the new school year!
Thank you, Traci, for your well thought-ought reply. It sounds to me that you really are getting a reasoning and sense-making classroom.
I just attended the NCTM Summer High School Institute (the first!) on Reasoning and Sense Making - in Orlando. There were over 700 high school math teachers there from all over the country - including the Virgin Islands!
You can find a lot of information here: http://www.nctm.org/standards/content.aspx?id=23749
When I get my bags unpacked, I'll find the link the the Institute materials and presenter hand-outs.
We have to spread the word - get administrators to join the movement, and get PD locally to encourage colleague to use it.
Hopefully the textbooks for the new standards will make it all easier. The ones we are working with now are procedure, drill and kill all the way.
BTW no job yet. Sigh.
I'd love to be able to start with the school year!
The link to the High School Institute on RSM handouts is: http://nctm.org/profdev/content.aspx?id=30496
There is a link from there to a Forum as well, which is just starting. You have to be logged in as an NCTM member to participate.
Thank you so much for sending the link for the NCTM Institute resources. I was planning on attending that conference but had to stay home to help with a local conference/workshop related to graphing calculators. [I am working on my PhD part-time while staying a full-time teacher, and I am doing research with a group of teachers who were at that workshop.] I can't wait to explore the handouts from the conference - thank you!
The president of NCTM has written up his final remarks at the institute here:
I've been inspired to write a few blog posts about the topic, too:
I believe that problem solving, which involves reasoning and sense making, is a key component of any mathematics class. I teach at the middle school level and part of my curriculum is having students complete a Problem of the Week each week. It requires them to solve a math problem, but the main credit in the assessment is given for their explanation of what they tried and why, and how they eventually got the answer they did.
I looked at the first website you listed, Bonnie, which seems to be more focused on the high school level; I would be interested in learning about resources that address the Reasoning and Sense Making concept focused on middle school curriculum.
The link for K-8 on the NCTM website is http://nctm.org/standards/content.aspx?id=270.
There are lots of materials there for anything you could wish for.
Check out Lessons and Resources http://nctm.org/resources/default.aspx?id=230
Are you a member? It's not that expensive, and they have great materials, conferences and other PD.