Integrating Peer Feedback

Sometimes my students surprise me.

We're studying the Measurement and Data standards right now in math, and we were struggling a bit with 4.MD.2 - the measurement word problems standard. We've been using some of the free math units from Engage NY (a resource I highly recommend), and we were on day 3 of working through word problems, and I knew I had to mix it up a bit. Here's what we did.

First, students worked through 6 word problems from module 2. The word problems were multi-step and used many different types of metric measurement. They completed these problems independently, but they could consult other students if they got stuck. Once everyone at the table finished, they checked their work with each other to make sure they agreed on the same answer.

Next, I assigned each table a different focus problem from the 6 that they solved. They had about 10-15 minutes to work together to design a poster that explained the problem and solution. They could represent their work any way they wanted, but the work had to speak for itself -- they wouldn't be there to explain the poster to anyone else.

Once the posters were completed, I gathered the students together on the carpet, and we reviewed the Standards for Mathematical Practice using these posters I've made:

We talked about using these standards as opportunities to give feedback. We also discussed how effective feedback needs to be specific and constructive. If you like something, say what, specifically, you liked and how it helped communicate an idea. If something needed to be improved, explain what and how that could be done.

Once I felt like the students had some ideas for ways to give good feedback, I had the students do a gallery walk around the classroom to look at the other posters. In a gallery walk, students use sticky notes to comment on other people's work. They can leave positive and/or constructive feedback. I let the students comment anonymously if they wanted, and they were able to reference the SMP posters if they needed ideas (I gave them access to a digital copy on their iPads). I used a timer, and they spent 5 minutes studying and commenting on each poster before rotating.

Once they'd rotated through all of the posters, the returned to the poster their group had made, and they took a few minutes to read the feedback. I had them work together to sort the feedback into the categories "helpful" and "not helpful."

We shared a few examples of helpful comments with the whole class:

• "I like how the team drew pictures to represent the problem, but I think the team could have explained what each picture represented from the problem."
• "The pictures aren't in proportion to one another. The drawing of 1,500 mL is much larger than 3 L, but really the 3 L should be larger."
• "Something I really like about your poster is that it has pictures to represent the problems. One thing that you could have done differently is represent the subtraction and addition with a tape diagram."
• "You could have represented the answer in mixed units to make your answer clearer."

We then talked about unhelpful comments -- one word comments or feedback that focused more on style than substance.

Overall, this lesson was very helpful in getting the students to think about the Standards for Mathematical Practice and how to give effective feedback. Each group had ideas for things they wanted to change on their posters based on peer comments, and some groups even asked to work on it more during recess! It was also a good reminder for me that students can give each other powerful feedback, and I need to provide them with more opportunities to do this across the subject areas.

If you'd like to get a copy of my student-friendly Standards for Mathematical Practice posters, they're available in my TpT store by clicking the image below.

What are some ways you incorporate peer feedback in your classroom? I'd love to hear more ideas in the comments section!

Back to School - Math Edition

It might be time to think about renaming my blog, because I'm really excited about teaching math this year! It all started when I read the book Number Talks over the summer.

I've always understood the importance of mental math and computation strategies, but I'd never really understood how to teach it. It felt like something kids either had or they didn't. This year, however, I decided that we'd start doing number talks from day #1, and I'm already blown away by how my students are developing as mathematical thinkers. They're able to solve complicated addition problems in their heads -- no paper allowed -- and they're articulating their strategies well. I've been introducing a new strategy every 2-3 days, and it's been awesome. We'll be moving on to subtraction strategies in a few days, and I have high expectations for that to.

To help students with the mental math strategies, I made a set of posters that describe each strategy with an example of how it works. There are 20 posters in all -- one for each strategy described in the book.

The complete set is available in my TpT store, and they'll be on sale for 28% off this weekend as part of the Teachers Pay Teachers back to school sale if you use the code BTS13.

As I've been working on order of operations and number sense with my fourth graders, I also introduced the four fours problem. The premise of the problem is this:

Using some arithmetic combination of four 4's, can you write an equation for each of the numbers from 1-100? Here are the rules:

• You may use any combination of addition, subtraction, multiplication, and/or division
• You may combine numbers, e.g., use 2 of the fours to make the number 44
• You may insert decimal points
• You may use a four as an exponent
• You may use square roots
• You may use factorials, e.g., 4! is equivalent to 4 x 3 x 2 x 1 = 24
• You may use overbars to make a decimal repeat
• You may NOT use any digit other than a four
• You MUST use all four 4's in each solution

Before I go on, let me give two caveats. 1) I didn't expect all of my students to be able to handle all of these rules. Square roots, exponents, and factorials are WAY above my fourth graders heads generally, but I did have a handful that could handle it. And there are plenty of solutions to be found that don't require those operations. 2) This problem freaked out the parents more than it scared the kids, I think. I had a few panicked parents that I had to talk down while we were working on this, but in the end, it was well worth it. My students were so excited about math and problem solving as we worked through this problem. It was homework each night to try to find a few more solutions, and then we'd add to a chart during math class. Look at all that my students accomplished after just two days!

We've filled in a bunch more solutions since then, but of course I left my camera at school this weekend...

Finally, in honor of the big back to school sale on TpT, I've bundled four of my favorite math resources into a back to school math pack for this weekend only. 

Sold separately, this is $17 worth of products that I'm selling this weekend for $10, but after Monday, the bundle will no longer be available in my store. So if you've had any of these on your wish list...

Hope everyone had a great week! I'm still learning how to juggle grad school with teaching, but I'm hopeful that I'll still be posting at least once a week.

Off to start catching up on blog reading and filling my cart for the TpT sale! Have a great weekend!

New Teacher Tip #3

Continued from "Things I wish someone had told me before I started teaching (or maybe they did and I just didn't listen)"

Tip #3: Trust Your Instincts.

In my first year of teaching, I was assigned two classes of fifth-grade math. One was a section of the average students at the grade level, and the other was the bottom 20 students. Georgia has an annual standardized test that is administered in all grades and fifth graders are required to pass the math and reading sections to be promoted to middle school. It's high stakes testing at its worst. You can only imagine the pressure that I felt with a class of the lowest performing students. Many of them were years behind grade-level, unable to do things like subtract with regrouping or multiply and divide with one or two digit numbers. It was unfathomable to me how I was going to teach the fifth grade standards such as multiplying and dividing fractions and decimals. Whenever I discussed this with my administrators, I received the same response over and over: "You have to teach the standards."

The dirty secret about standards is that even with pacing guides, you have a lot of flexibility about how much time you allot to different topics. During my unit on measurement, for example, I was able to spend weeks covering one- and two-digit multiplication. The actual time spent applying that to finding the area of quadrilaterals was small in comparison to the amount of time developing a conceptual understanding of multiplication, but in the end they got it. My lesson plans consistently reflected that I was teaching the standards relating to area – and I was – but maybe not in the way that I imagine the state or district envisioned. Be crafty, reach out for help, and remember that you know your students best. If you identify fundamental weaknesses that need to be remedied before moving on, do it. It's far better to teach fundamentals and build understanding than add to confusion.