Conference by Sue and Randy Pippen
What makes a good problem?
- Multiple answers with justification
- Correctness lies in the mathematical argument
- Don't stop with just an answer
- Multiple entry points
- We're not questioning the student's answer, we're questioning the thinking behind it
- Ask "Is that the only way?"
- If you tell the answer first, students quit caring about the understanding.
- Richer, requires more reasoning, a directed solution instead of just a single answer
Student yellow pages- students write down a problem they missed and the correct solution, making a note of where they went wrong or what they didn't know how to do; write down new strategies they observe from others during class
Teaching isn't telling- it's listening. (Be Less Talkative...yeah!)
When students ask for help and we stand and watch them work, we are sending the message that we don't think they can do it right on their own. Offer a suggestion and then walk away.
The mantra of Common Core is fewer, higher, more focused. It's a 3-legged stool: understanding, applications, and skills. It's highly visual and connected with multiple representations. Three shifts: focus, coherence, and rigor.
Common Core is about different representations: fractions will focus on equivalent fractions, so three-fourths is just as good as sixth-eighths. You won't see simplest form in the Common Core.
Fluency means fast and accurate- not memorize.
- Single answer multiple choice
- Multiple answer multiple choice
- Extended response
- Short answer
- Drag and drop
- Fill in the blank
- Constructed response
In error analysis, we focus on the mistake. Force students to decide if it is right or wrong, always asking for justification.
The goal is to prevent guessing.
Create problems where students find data from words, graphs, pictures combined- not a paragraph. Break up reading into bullets.
Focus on structure rather than procedure.
Rather than teaching in pieces, delve into multiple parts at once, especially through multiple answer multiple choice questions.
Can you take the numbers away and focus on how to do it? (Problems Without Figures, Gillan, 1909)
CC starts visually and graphically. (Noticing and wondering. Yay Max!) When graphical methods don't work, then there is a hook for teaching the algebraic method. Is one method better than another depending on what you're given? Explain. Graph first every time so you can see if you need a different method.
Give the problem and the answer so students have to justify/explain/prove. Take the focus off of the end result.
New testing starts in spring 2015.
Teach conceptually- don't teach rules!
Algebra I takes Algebra II concepts and introduces them graphically, asking for differences in order to make connections.
Give specific problems that lead students to the strategy and listen to other students' strategies.
Mathematical power and mathematical strategies through reasonable problems that are properly structured. (Makes me thinks of Exeter!)
Standards now include the verb 'understand' which was never used before because it couldn't easily be assessed through a multiple choice test.
Each standard is not a new event, but an extension of previous learning. Use previous standards to launch later standards and build coherence.
If you value mental math, you can't force students to show work on every problem. It doesn't have to be all or nothing.
More in-depth mastery of a smaller set of things pay off. If our students were problem solvers, we could give them anything and they could attack it. Exposure doesn't work in math.
Mastery doesn't mean memorize- its knowing because you have worked with it SO MUCH.
Teach context first to create curiosity. Make sense of situations.
Standards with plus signs are not for ALL students. Consumer statistics would be more useful for students who are not STEM-career bound. A star means it is a modeling standard.
Look for ways to use previous mathematics in service of new ideas rather than re-teaching.
Use application problems to introduce a topic.
Our books give pieces and then ask them to put it together at the end. The brain works opposite- need to see the big picture in order to make connections. Learning is making connections to what you already know
Wrong answers are part of the process too. What was the student thinking?
What Math Do All Students Need?
- Understanding math
- Doing math
- Using math
CC constantly makes us go back to number sense to understand that algebra works because numbers work.
Write answers to word problems as a sentence so students think about their answers in context.
Let students choose the tools they need rather than handing it to them.
Use precise mathematical vocabulary, symbols, and notation. Constantly connect to properties. The language comes after the concept. Use it enough so that it needs to be named. Stop trying too make it easy- make it accurate. You have to accept student language in the development of their ideas and thinking. But then go back and refine with precise vocabulary in order to make their ideas mathematically accurate.
Be ready to extend problems. When you have scaffolded questions prepared, give the next extension as students are ready- that's differentiation. Not a new problem, not more problems, but an extension of the problem they are already working on.
3 Part Lesson Plan
- Discussion and Processing- Notes may be created as a result of discussion, practice may result from methods presented
Also I have a handout of links with REALLY good resources, I tweeted two of them earlier but I just can't sum up the will to retype all of them. So, here's a pdf that I scanned in. It's worth it to go through and save the links, and maybe I will type them up. Or maybe not.
I was really happy to see that a lot of things mentioned in this conference were things that we all have been blogging and tweeting about and doing in our own classroom. I actually left feeling less overwhelmed even though I had about 1000 things going through my mind. I felt like this helped me to focus on what I'm doing right and how to do more of it. It made Common Core seem more accessible to me and that's thanks to all of you.
P.S. Thanks to @Fouss for helping me embed my box documents into my post. Aren't they cute?