? really enjoyed this video and it's well worth watching. Here are my thoughts on why each point is important. But . . . watch the video first :)
1) Start with a question.
This reminds me of a point Jo Boaler makes in her MOOC quoting a six-year-old student, "Math is too much answer time and not enough learning time." Learning requires wonder and thinking. Questions can set up a situation beautifully to encourage both wonder and thinking, especially when we can get students to pose the questions that they are interested in.
Here are a couple of resources to activities that invite student questions and/or begin with interesting questions.
101 Questions--this site uses video and images to suggest interesting mathematical questions. Once you create a free account you can see and use lessons/ideas that other teachers have made for a variety of different grade levels. You can also post your own ideas and get some feedback before trying things with your students.
Yummymath--interesting, engaging, and mathematically rich lessons for all grade levels.
Which One Doesn't Belong--From here you start all discussions with the question "Which one doesn't belong?" Students then look at the image to decide their answer and that's where the fun begins because there are good arguments for anyone of the 4. It is in these discussions that the math happens.
2) Students need time to struggle.
Again (see above) to answer a good question students need time to think and try things out, get feedback (not answers and not grades), keep trying. They may need support and encouragement to keep going, but if we start with a good question they will want to keep going to figure things out.
3) You are not the answer key.
As soon as the answer is given (especially if step 2 is skipped) then the struggle ends. On the other hand if students are struggling with an interesting question they will likely come up with multiple valid answers. The discussions of these answers are fantastic in developing mathematical understanding and identities. Hopefully these discussions will also lead to more questions that are worth struggling with!
4) Say yes to your students ideas.
When we've started with a good question and a student gives us a serious answer we owe it to them to take their ideas seriously, to hear them out, and to probe for more. Saying yes also encourages students to keep going and to keep thinking.
Math class should be fun, it can be hard fun, but still fun.
Of course all of this assumes that thinking and reasoning are your goals and not just following a procedure to arrive at an answer. What did you think of the video? or of my thoughts?
I spent Friday and Saturday this week at the Utah Council of Teachers of Mathematics (UCTM) conference. It was a great opportunity to learn about and be inspired about mathematics education. And I got to reconnect with some of my past students who are now also mathematics teachers!
I attended several great session, but one that stood out was on 3 Acts Math by Jessica Patterson. I've already referenced the 3 Acts math that Dan Meyer's does in a previous post. Part of what Jessica did was to compare 3 Acts problems to typical textbook word problems. Now, especially in secondary math, typical word problems are ridiculous. As Jo Boaler explains they answer questions that no one is asking. Dan Meyer's refers to the them as "pseudocontext" which meet two criteria 1) it asks a question that most people would not ask and 2) uses a method that most people would not use.
Another problem that Jessica brought out is that most textbook word problems identify the variables and (at least implicitly) the mathematical model (or equation, algorithm, etc.) that students should be using. In other words the meaningful thinking has been taken away from the students. This aligns well with something Jo Boaler explains in Mathematical Mindsets, "Mathematics has four stages: 1) Posting a question, 2) going from the real world to a mathematical model, 3) performing a calculation, and 4) going from the model back to the real world" (p. 27). Done properly 3 Acts problems do all of these while textbook problems do 2 (2 and 3) sometimes and usually just require calculation.
Dan Meyer's Blog-- Dan Meyer's posts regularly and in thought provoking ways about teaching practices and ways to improve. He is humorous and highlights other comments and views as well.
Dan Meyer's 3 Acts-- So Dan Meyers gets two spots here, because his stuff is great. This site has video prompted math lessons in three acts. They pose an engaging, visual question to be answered.
Questioning My Metacognition--Similar to Dan Meyer's 3 acts, for elementary.
Mathematics Assessment Project--Fantastically detailed, task-based lesson plans for grades 6th-High School