Comments on: Planning problem-based lessons

By: Dominique Hodgin

Dominique Hodgin — Sat, 05 Dec 2009 20:01:30 +0000

During my last three weeks of soloing, I taught many lessons for fifth grade from the Investigations curriculum. Although this curriculum is not designed in a Launch, Explore, Summary (LES) format, after some experience I found it was not all that difficult to put each lesson into that format for teaching.
I have been primarily teaching out of the Between Never and Always Investigations unit and the lessons all build on one another. During much of my teaching, I have learned that activating prior knowledge and increasing the engagement of the students with interesting openings helps make for a more successful lesson where student’s learning is heightened. One lesson in particular is worth discussing; the lesson was on graphing probability. After a couple of lessons on previous days introducing the concept of plotting information on a line plot, the students participated in an activity using a colored spinner with four different colors on it, each having a probability of 1 out of 4. Students guessed which color the spinner would land on prior to spinning it. I spun the spinner just after each student recorded their guess. We did this 20 times and then as a class, we plotted each student’s results. The students discovered that the middle of the data plotted on the line plot centered on and around the number 5 (exactly 1/4 of 20).
To launch the activity and to activate the student’s prior knowledge I placed the line plot that we did together on the visualizer. Students talked to one another about what they noticed on our class’ line plot from the 1 out of 4 colored spinner activity we did together. They noticed that the data centered around 5, that there were some gaps in the data, that no one got 1 or 20, but that there were a few outliers at 10 and 13. We also discussed the shape of the line plot.
For the explore part of the lesson, I placed a sheet with several line plots onto the visualizer and in groups of 4 the students had to discuss how likely it was that the line plot was actual data or inaccurate data (made up). As students discussed each characteristic of the different line plots, I roamed the room listening to the conversations the students were having and selecting a few students to bring up their reasoning during the summary.
For the summary part of the lesson, the students came back to the floor in front of the visualizer with their results of their discussion within their groups. We discussed each of the line plots and what characteristics of each line plot the students used to decide if it was likely that it was actual data. Only one of the line plots was unlikely to be actual data but was selected by the students as likely to be actual data. We discussed in depth the characteristics of this line plot and how some of those characteristics made it less likely to be actual data.
Using the LES strategy to teach math, I believe is very effective. It gives a map for teachers to follow so students are more engaged in the lesson. Activating prior knowledge really increased student’s interest level. Allowing students to problem solve on their own stretches their learning and the summary allows an opportunity for the teacher to reiterate the teaching point of the lesson and to confirm and discuss their understandings.

Actually, Dominique, the Investigations IS designed with launch/explore/summary format in mind. In the second edition, I believe they actually broke the lesson down into this format to be more explicit. In this first edition, it is hard to find it on your own, especially when you are new to using the materials.
I am familiar with this lesson and find that it is interesting to discuss the outliers and other terminology when going over the summary and deciding which graph(s) is unreal. I know that you have struggled to keep using the Investigations throughout your intership, and I applaud you for using it as much as you could. When you are out in the field actually in a classroom of your own, remember that the planning sheet and ideas discussed in “Orchestrating the Discussion ” article are helpful to review and use. Carol

By: Susan Jakob

Susan Jakob — Thu, 03 Dec 2009 21:23:51 +0000

I did a first grade math launch on measurements on longer and shorter. It really helps to review all parts of the lesson ahead of time so I put together baskets of items for the students to measure. I found that a good opener is the key to getting the students excited about the lesson. I started by telling them I had a problem and that I have some curtains to put on my window but was sure which way they went. I knew one side was longer. I followed the examples from the Investigations by holding up a bottle and the students would tell me which was the longer side and how they knew. We practiced this with a few more items. The student task was to measure items against their pencil. It was important to demonstrate the importance of measuring both objects from the bottom. To do this I had one student stand on a stool next to a student on the floor and asked if it was fair to say student A was “longer” than student B. They said yes until I told student A to step down on the floor. Seeing the demonstration helped them understand the importance of measuring from the same starting point. I also set my expectations that the students measure at least 3 items and record their answers before going to specials. Next time I would incorporate more pictures to the activity sheet as the students are not able to read words like pencil and longer.
I am glad that you took note of the words that kids struggled with. It is usually not the math so much as the vocabulary. Under the launch section called Understanding the Task,there are several ways to handle this…one is to ask students to read the directions and tell their neighbors what it says..another is up front to note the words that students may struggle with…another is to put the words on chart paper and read over the words together before starting the task.
I like the way you launched with asking what was fair/unfair. The demonstration helped by solving a simplier problem. Keep practicing! Carol

By: mclaurin gillette

mclaurin gillette — Wed, 02 Dec 2009 17:19:44 +0000

During a LES lesson i implemented on ways to make $.25, I opened the launch by asking students what coins they know about and how much they are worth. Students were able to make approximations about coins through pair share and discussion. Once we all agreed, i showed students a blown up sheet that had pictures and text for each coin amount and picture. I created a chart to keep track of the ways we would make $.25. I then asked students to Think-Pair-Share and tell tehir partner what they think is the easiest way to make $.25? Once students approximated an answer, i asked students to share: most knew the easiest way to make $.25 was by having 1quarter. A few students thought that the easiest way to make $.25 is 25 pennies. This was an informal way for me to quickly assess which students see the bigger numbers and which students see adding 1’s together to be the easiest way to count. As a class, we came to the consensus that 1quarter is the easiest way to make $.25; i recorded that information on the chart and then asked students to go back to their tables and record all the ways they came up with to make $.25. NOTE: students had previously on different days this week practiced recording different ways to record coins….students also had an abundance of fake coins on their tables for exploration. At this point, students returned to their tables and explored the various ways to make $.25. I monitored student work while informally monitoring the ways students were making $.25. At teh end of the exploration time of the LES lesson, I asked students to bring their journals to the meeting area. I turned on teh dot cam and also had a bowl of change for students to use when sharing their work to their classmates. One by one, i had students show their work-how they recorded the change when making $.25 as well as use the coins to count out making $.25 so all teh class could see. I though this was an effective way to play out the summary portion of this LES lesson. Students recorded the coins in a variety of ways and through the sharing of their classmates, students discovered new and more effective ways that they now understood, when recording coins in mathematical activities. Students were also able to make connections to their fellow classmates by listening to their reasoning and understanding of why and how those coins made $.25. overall this was a meaningul LES lesson where students were engaged and immerse in crucial mathematical content.
Mclauren, you did not say how you selected who would share out, but I am sure you had a plan. It is interesting that some 2nd graders think counting out 25 coins is easier than using the quarter. Doing this sort of combination making for different numbers is also a very good independent activity for your students. I often used the Investigation lesson as a jumping off place for station ideas. You mentioned at seminar that you are amazed at the materials your CT has at hand for stations. Just being aware all the time of where extra practice can fit in, as well as studying deeper the K.R. brown teaching books, will help you there as you get into your own classroom practice. Carol

By: Kayla Shea

Kayla Shea — Wed, 02 Dec 2009 02:52:48 +0000

I found the orchestrating discussions article to be particularly useful to me because it gave me the sense of knowing more about instructing a math lesson. I have stuggled with relating math to a way students think about math. To me, math is a set of processes one does to find an answer. I don’t understand why but I can do it. I think in order for me to be able to teach math, I need to understand “why” math works. If I understand it, I think I would be able to teach to students better. This article allows me to see structure in teaching math and gives me things to think about when planning a lesson. For example, it is important to consider how the problem is phrased and how a child might interpret it.
Kayla, Have you tried out a launch yet? I am eager to hear what your experience with that part of the three part lesson has been. Carol

By: Carly Stenseth

Carly Stenseth — Sun, 22 Nov 2009 22:27:28 +0000

This past week I did a lesson on ordering fractions with respects to landmarks. For the launch of this lesson students were reintroduced to the concept of what a landmark number was. This went rather smoothly as they had previously learned about landmarks earlier in the year. After that I displayed some fraction as well as a table of landmark numbers 0,1/2, 1 and 2. With respect to the landmarks as a whole group we decided where 3 of the fraction cards we made the previous day would go and put them under the correct landmark. Before returning to their desk to continue on into the explore I encouraged kids to look at the pictures they drew of the fractions in order to help them order their fraction independently. Students seemed to get the concept and so I sent them back to their seats to continue onto the explore. During the explore many students struggled with ordering the fractions correctly. I found that the pictures they drew of fraction were not all that helpful. Students comparing 1/8 to 1/4 were confused because they had drawn their rectangle the same size and broke the parts up unevenly so they were unable to tell which had more pieces and which didn’t. After noticing that a significant amount of the students were struggling I decided to regroup them and move onto a summary where we would do the activity together. Overall the summary went well and I felt like students were starting to get the idea. However, I noticed that their was not enough room to place all the fractions underneath the visulazor so students could see. In addition, I needed to dig deeper with the students whose answer were correct on where the fraction go and ask them “How do you know?” so that they could explain their thinking to the whole class. In looking back at this lesson overall it went okay, next time I might be more supportive in the launch, and hopefully that in turn would allow students to do most of the talking during the summary.
Carly, remember about the levels of support and try the ” I do, We do, You do” strategy when you are demonsrating. In the “I do “portion, you need to be metacognative about what you were thinking, so that children can see how you figured it out….example might be: ” I know that 1/8 must be smaller than 1/4 because if I make fair shares of this rectangle ( model on board) than 1 piece of brownie out of 8 pieces is much smaller than 1 piece of brownie out of 4″ Then, ask partners to decide which is bigger 1/5 or 1/4 and explain why in their notebook…right there in the launch). This is the “We do” part of the launch. By having a writtine record of how to record thinking( and checking this before releasing to seats), each student now has a model of how to answer the question when they are on their own. Carol

By: Jeanie Brown

Jeanie Brown — Sun, 15 Nov 2009 20:55:23 +0000

Hi Carol,
I just wanted to leave a brief comment about the Explore Monitoring Sheet. . . When I take time to use the sheet in my planning, I find that my Launch is more focused, the children seem to have a better idea of what they are expected to do during the Explore time of the lesson, and it makes me take the time to mentally rehearse the Summary before I present anything to the kids. All in all, I have found that maintaining a tight focus and appropriate timing are my two biggest challenges during my 5913 Internship. If I use the Explore Monitoring Sheet, I seem to be more focused on only one big idea which keeps me on track and helps tremendously in the timing of the lesson.
Thanks,
Jeanie Brown
Jeanie, It does take time to fill this form out, but I often “chicken scratched” ideas before leaving school and then brainstormed more ways as I drove home. I am glad you are finding it a help. The top coaches in the US are using this as an engagement tool during summary, as I have seen at national conferences, so you are on the “cutting edge” with this tool. When children share their ideas during summary, it builds confidence and reinforces the multiple ways to solve a problem. Carol

By: Lauren Sottnik

Lauren Sottnik — Tue, 27 Oct 2009 01:39:05 +0000

Well all, I’ve been working on my LES this past week and it’s not as difficult as I thought. I did not make a list or anything, but I searched my classroom for various methods. I’m having a hard time figuring out the different entry points students will use for problem solving, and that’s why I haven’t used a chart to figure out who should be presenting during summary. I’m finding that there are various ways though, and it’s upsetting to feel like I keep having the same people present because they’re the ones who are finished and have somewhat of an idea of what they’re doing. Anyways, I’ll obviously get better at this once I’m soloing and doing this daily! Hope you all feel the same way!!! :oD

Lauren, reading the “teacher notes” that are near the lesson you are teaching will give you some ideas of the various ways that students will begin working to solve the problem. Also DOING THE PROBLEM YOURSELF will give you an idea of how some students will approach the problem…remember to keep in mind how manipulatives will be useful to some students. Carol

By: clwilson

clwilson — Mon, 27 Apr 2009 20:23:14 +0000

\Thank you for responding. I will answer each commented posted. Your experience with this 3 part lesson format is fine information for all of us to read and think about.