This has been a busy week, but I can finally sit down to write about day 2 of our Math Rocks class. (In case you missed the post about day 1, here it is.)
One thing that has kept me busy is reading and responding to all of the blog posts that our group has generated this week. Here are a few you should check out if you have a few minutes:
- Leilani wrote about how one simple sentence led to rich problem solving and discussion last year.
- Kari shared a story that sounds like it’s straight out of a teacher nightmare, but it really happened to her!
- Carrie’s post is short and sweet, but I love that she chose to write about Counting Circles in her very first blog post.
- Brittany shared an honest and touching reflection of an experience in Math Rocks this week.
I’m so impressed by the stories, reflections, and ideas already being shared. It makes me so excited to see what else we have in store this year!
We started Day 2 with some math. This is actually a problem we posed at the end of Day 1, but we never had time to discuss it because setting up everyone’s WordPress and Twitter accounts took quite a while!
This problem actually came from Steve Leinwand’s keynote at Twitter Math Camp 2014. The numbers involved are small, but I chose this problem because the relational thinking involved would likely stretch many of the educators in our group. This is the problem Brittany refers to in her blog post.
After giving everyone 5-10 minutes to solve the problem, I had them go around their tables to share their current thinking. I let them know before they started working that it was okay if they hadn’t finished solved the problem yet. The purpose of the discussion was to give them a chance to share either their solution *or* their current thinking about the problem. Both are perfectly acceptable. I wanted to model this specifically because it’s a teaching move I would like for them to try out in their classrooms. I got the idea from this Teaching Channel video. You’re welcome to watch the whole thing – it’s about introducing fraction multiplication – or you can skip to the 3:30 mark.
After sharing, most everyone was ready to jump into creating a solution together. I had them share their agreed upon solution on a blank piece of paper. Then they had to take a picture of it and tweet it out to our hashtag for the course, #rrmathrocks. As they worked, I walked around and talked to them about how their solution had to be convincing because anyone on Twitter would be able to see it, so the solution has to stand on its own.
I did this intentionally because after they tweeted out their work, I shared with them how they could do something similar in their classrooms by participating in the Global Math Task Twitter Exchange. Each week a class signs up to pose a problem to their grade level hashtag. Other classes from around the world solve the problem and tweet out their solutions. It can be very motivating to students because you’ve provided them a global audience for talking about and doing math. I wrote a post related to this a few weeks ago.
We didn’t talk about their solutions…yet. I have plans for them down the road.
After everyone tweeted out their solutions, we revisited our norms:
- Share and take turns
- Give each other time to think
- Be open minded
- Share far and wide
- Be respectful of each other
- Take risks
- Always do your best
I’m especially proud of how much they’ve embraced being open minded and taking risks already.
We quickly moved on to reviewing first drafts of our new district common assessments. Our department has to write them, but we try to involve teachers as much as possible in the review process in order to get feedback and to be as transparent as possible. We want to assure teachers our goal is not to trick them or their students.
Since we had a group of educators from grades K-5, and our assessments are for grades 3-5, we paired up the primary teachers with intermediate teachers. The intermediate teachers were responsible for ensuring the primary teachers understood the standard correlated with each question.
Some wonderful discussions ensued. I talked to a few teachers about a question that they felt was one step too difficult for the students. They convinced me to make a change to the question so that it will be clearer from students’ work and answers whether students can truly do what the correlated standard says they should be able to do. Another group had questions about multiplication algorithms. We had a great conversation about the distributive property and the area model, and how these two things can support students up into middle and high school.
After they were done reviewing assessment items, we came back together to discuss ambitious math instruction. I love the phrase “ambitious math instruction.” I didn’t coin it of course. This came from Teacher Education By Design, a project out of the College of Education at the University of Washington. It’s one of my favorite places on the internet.
You should probably check out their page on ambitious math instruction for yourself, but here’s a snippet:
Developing a vision of ambitious teaching and putting it into practice is complex work. The instructional activities, tools, and resources offered by this project are designed to support teachers to learn about and take up practices of ambitious teaching and engage children in rich mathematics. The routine structure of the activities bounds the range of complexity teachers might encounter while creating space for them to learn about the principles, practices, and mathematics knowledge needed for teaching while engaging in the practice of teaching.
What I really like about this is the use of routine activities as a way to allow teachers to try out new ideas and practices within clear boundaries. They go on to share their core practices of ambitious teaching in mathematics:
In Texas we have mathematical process standards that tell us what students should be doing to acquire and demonstrate understanding of mathematics. Now I have a set of practices I can share of what teachers can do to support their students in learning and using these processes.
We gave each table one of the core practices and asked them to create a semi-Frayer model that showed why the practice is important, example(s) of the practice, non-example(s) of the practice, and an illustration of the practice. Again, we had them take a quick photo and tweet them out to #rrmathrocks. This time we did pull their tweets up on the big screen and use them to talk through each practice.
Teacher Education By Design currently has 5 instructional activities on their site with more to come. Regina and I chose to share two of them – Quick Images and Choral Counting. Many of our teachers are already familiar with Quick Images, which is exactly what I wanted. Since they are already familiar with the routine, it meant they could focus on looking for the core practices in the videos we watched rather than trying to balance that with learning a new classroom routine. Choral counting was new for many of them, so we shared that activity second.
Before getting into either routine, I wanted to stop and think a bit about number sense. We did the Number Sense Trajectory Cut-N-Sort from Graham Fletcher.
As expected, there was a lot of interesting conversation about which concepts come first and why. I had wanted them to make posters and draw a quick sketch next to each concept, but we were pressed for time so I just had them do the matching and ordering. When they were done, I handed out the complete trajectory so they could self-check and discuss with the other members of their group. Because we ended up going through this activity more quickly than I had planned, I’m going to look for other ways to revisit the components of number sense at a later date. It’s a really rich topic, and I want to ensure our group has a good grasp of all it entails.
We finally went into the Quick Images activity. Regina modeled the activity with the group and did a little debrief before we watched two videos of Quick Images in action in a Kinder and 5th grade classroom. I think this routine is often considered a primary grades activity, so I purposefully showed both ends of the elementary spectrum to give them an idea of how robust it really is. When we discussed the videos, we specifically asked for examples of the core practices in action, and we talked about what math concepts can be explored through this activity.
I had wanted to end this activity by having everyone plan a sequence of 2-3 Quick Images that they could do in their classrooms at the start of school, but we were still trying to make up for some lost time. I’m sad that it didn’t happen because I wanted them to experience what it’s like to think through the planning of this activity. However, since this wasn’t a brand new activity for most of them, I felt like it was okay to let that go for now. Maybe we’ll revisit it in the future.
We then moved into Choral Counting. I led a count with them where we started at 80 and counted by 2s all the way up to 132. In the middle of the count, I stopped everyone and asked what the next number would be, and I asked how the person knew. In our debrief afterward, I admitted that I wasn’t intentional enough about where I chose to stop. I asked the group where I should have stopped, and they agreed that 98 or 100 would have been a better place to stop because students often have difficulty counting across landmarks.
I also asked whether we would say 216 if we continued the count. One person said yes, because all of the numbers are even and so is 216. I did my best to act like the surprised teacher: “Whoa! You just said all of these numbers are even. How in the world could you make that claim so quickly? There are 27 numbers up here!” She shared that the ones digit in each column was an even number. I told them it’s important to keep an ear out for grand claims like this. It’s easy to just accept the statement that all of these numbers are even, but to the untrained elementary school eye, that is not necessarily obvious nor do they necessarily understand why or how it’s true.
We watched a video of a 3rd grade class doing this activity, and again we debriefed with a focus on the core practices. I was so impressed with how intently they watched all the videos and all of the teacher moves they noticed. From conversations I had during the rest of the day, it sounds like some of them are inspired to be more intentional in their planning and carrying out of these types of activities.
Now that we had made up for lost time, I was able to have them practice recording some counts. One of the powerful pieces of choral counting is that how the count is recorded impacts the patterns students notice and the conversation that ensues. I had each person choose a count appropriate for their grade level and record it three different ways. This reinforced what some of them already noticed before about how intentional planning can make these activities that much more powerful.
At this point we were starting to run out of time, so all we were able to do with the remaining time is introduce the book Intentional Talk. We’re not going to read the whole book during this course. It offers so much, but I’d rather be selective and practice a few key strategies out of the book. We’re going to start with chapters 1 and 2 and add another one down the road if time permits. I really want to ensure everyone has the chance to process and practice the concepts from chapter 2 before trying to add more to their plate. If you’re wondering why, check out these posts I wrote about the first two chapters of Intentional Talk here and here.
After reading the first few pages of chapter 1, everyone tweeted out a key point that stood out to them.
We wrapped up our intense and amazing two days of learning by telling them about Math Rocks Mission #3. The gist of it is that they have to set goals for themselves and their students. They also have to anticipate the obstacles that might get in the way of meeting their goals. I’ve listed all of the Math Rocks blogs on the sidebar of the Math Rocks site. If you get a chance, you should take a look at their goal-setting posts. I’ve enjoyed reading about how excited they are for the upcoming school year as well as their thoughtfulness regarding their goals and potential obstacles. Not everyone has written yet, so you might wait until Tuesday which is their soft deadline because that’s when I launch Mission #4! We’ll be launching a mission per week up until school starts.
If you’ve made it this far, thank you for reading about our first two days together! It truly has been a privilege to spend 12 hours with this talented group of educators. I can’t believe this is just the beginning. We have 9 after-school sessions together throughout the school year and one half day session to wrap everything up in February. I’m looking forward to it!
I love what you are doing. We just finished a 3-day exploration of math teaching in a very intentional way, too, for HS. So many of the points you have made are also important for the secondary classroom. I love the deconstruction of the teacher actions through the Frayer model – I am going to share each of them next week with our teachers and district level coaches! I think teachers really need clear guidelines for what we are to do to support our kids in the mathematical practices- especially if our goal is a student choice, student voice centered classroom. My goal for my students is to enjoy learning, enjoy the process, and come away with a sense of accomplishment.
Thank you! I’d love to hear what your teachers and coaches have to say about the core teaching practices. I know they sound great in theory. My goal this year is to help the educators in my group find ways to bring them into their practice.
I will get back to you!
I accept the challenge! I am so ready to GO BIG this school year! Thank you for the inspiration!
I am having a serious problem with your first example, the suitcase problem. It is the words.
I thought it might just be you, but inspection via google of the use of the word “mass” in basic math shows otherwise.
Mass is a physical attribute of an object which is quite difficult to measure directly.
Weight is a simple attribute of an object when in a gravitational field.
When I weigh something, my suitcase, I get its weight. If I use a direct method like a spring balance then the weight I get depends on where I am. On the Moon my suitcase will have a much lower weight, but its mass will be the same. In space my suitcase will be weightless.
To measure its mass I have to push it along and measure its acceleration and the force applied.
So, to treat the terms weight and mass as interchangeable is going to create problems down the line for kids studying Physics or applied math.
Not only that, but in the outside world (known as the “real world” in the education business) NOBODY uses the word “mass” except in the new fangled fitness measure of “body mass index”.
I am in a state of despair over this, but I am pretty sure that teachers and textbook writers don’t give a damn about such “niceties”.
I would love to have your thoughts on this !
You’ve given this a lot more thought than I ever did. 🙂
I was trying to think of a problem to use with the educators in my group that would be a bit beyond the math that they usually teach. I quickly remembered this problem from Steve Leinwand’s keynote at Twitter Math Camp 2014, and that’s pretty much how it ended up in our class.
I checked the Common Core and they talk about finding masses of objects, and then in the examples they talk about the weights of a team of football players. There is so much of this sort of stuff in school math. My blog goes on and on about it. Check out my posts on “bad language” in math.
I do like the “chuck a problem at them and see what they come up with” approach. There are not many “problems” in elementary math which are so obscure that a “have a go” won’t get you anything.
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