With the advent of the Common Core and the changes that have already been made to the teaching of mathematics, I thought it important to list the standards for practice here. The first of these are the NCTM process standards of problem solving, reasoning and PROOF, communication, representation and connections. Thinking about just those pieces, it would be hard to pick one out that would be "more valuable" than the others. Add to these: adaptive reasoning, strategic competence, conceptual understanding, procedural fluency and productive disposition (habitual inclination to see mathematics as sensible, useful and worthwhile and belief in one's own efficacy and we are looking at a the teaching of mathematics in a whole new way.
The Common Core forces us to dig deeper and to probe for clearer, stronger and richer understandings in the concepts we are teaching and we must build on those foundational understandings that allow our students to effectively use and apply what they know, emphasizing the process and the inquiry that leads to an even greater understanding.
The first of these Mathematical Standards is Make sense of problems and persevere in solving them...
Here is the explanation" Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Mathematically proficient students check their answers and can explain correspondences between equations, verbal descriptions, tables or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Students continually ask themselves, "Does this make sense?" They can understand the different approaches of others to solving problems and can identify similarities between those approaches.
Think about this in relation to your students (all grades) and their math learning. This is just the first standard of practice. What does this look like in your classroom. What changes may have to be made in order to keep to this standard? Can you see how this connects to our journey with Accountable Talk and Inquiry Circles?? Please share your thoughts!
I will continue to post every few days with another standard. There are eight in all.
I am including a link that will take you to an Arizona site. Arizona has also adopted the Common Core and they have created a document that breaks down the power standards included in the core. The only piece that is not included are the MA only standards. It is user friendly and definitely worth looking at!
To access, just plug in the URL and click on the word doc or PDF for your grade.
http://www.ade.az.gov/standards/math/2010MathStandards/
Thanks Diane for breaking these down for us. It is a lot to swallow all at once. This first standard seems like a goal we have been trying to reach for years. I think it will be more attainable for our proficient math students more so than our struggling ones. It's difficult for a student to think critically when they don't know a math fact or can't read the problem. I guess starting on day 1 will give us the most time in accomplishing this goal.
ReplyDeleteI agree that problem solving is difficult for many, if not most of our kids... to me this is a perfect reason to use inquiry based learning where students, investigate, question, make mistakes and find solutions together. I also agree that we need to start day one with this kind of practice. Problem solving shouldn't be thought of as a separate piece, but as a normal way to investigate and learn.... Getting our kids to look at their work and ask themselves does this make sense, has always been a goal that is difficult to attain, but... perhaps if it is part of the group process, just one of many steps, we can make some success in that area...
ReplyDeleteAs I read your explanation of the Mathematical Practices, I immediately think of the Comprehension and Collaboration book. They tie in together perfectly. The students need to be able to talk through math problems in order for them to make sense of them. In time, this process will be internalized, and like most adults, our students will be able to become more independent.
ReplyDeleteAs Harvey and Daniels say in Comprehension and Collaboration, more and more workplaces are looking for people who can work collaboratively with co-workers. Our focus on group inquiry can really prepare our students with the skills needed to work cooperatively with others.
Kristin, are you sure you can't just show up at Mittineague in the fall? I can't tell you how much I will miss you. On the flip side, if you have to go anywhere, I am glad that it is Coburn. You will fall in love with the school, the staff but mostly the kids... :)
ReplyDelete