Category Archives: Teaching

Parallels 2 – An ELA and Mathematics Pondering

I’m a math coach, but I love the opportunity to sit in on English language arts (ELA) trainings because it gets the mind turning about parallels between the two content areas. Math and ELA are different in a lot of ways, but I’m curious about how they are alike.

A couple weeks ago I sat in on Independent Reading Level Assessment (IRLA) training. Our trainer strongly advised against coaching an early reader to chunk text because she said it was developmentally inappropriate. She said the appropriate scaffold would be to coach the student to use the initial consonant sound and use context clues. She made this assertion strongly and nonchalantly, confident that it was the right move in the given situation. She went on to say that we need to take into consideration what students CAN do and build from there. She warned against instructing above where they were, saying that the students development in literacy can look like Swiss cheese, with major holes in underlying concepts.

I wanted to jump up and cheer.

It was great to hear her say this and gave me more confidence when giving the same advice to teachers who are dealing with struggling students in mathematics. So, a fourth-grade student can’t add and subtract using the standard algorithm… Do they understand the bundling of 10 ones into a 10? Ten 10s into 100?… And so on? How about decomposing? Can they skip count by 10s and 100s? Did they ever make sense of counting on or the importance of “making a ten?”

Let’s take the time to figure out what students CAN do and build on it to move them forward to where they need to be.

Don’t Be Afraid of “I Don’t Know”

I’ve found that some of my best learning experiences have come after thinking or saying the phrase “I don’t know.” This phrase is required if learning is to take place. If you already know, you’re not really learning. Often though, we have an aversion to this phrase. It’s a phrase that always involves discomfort of varying degrees.

There’s the “Where are my keys?” variety of “I don’t know.” The level of discomfort isn’t too bad, depending on the situation: late or on time.

There’s the “What really makes a rhombus a rhombus?” variety of “I don’t know.” This one can cause a moderate level of discomfort, depending on your familiarity with the content, but can provide a great opportunity for learning.

There’s the “What should three tiers of support really look like in mathematics?” variety. To me these are the best types of questions to which a response of “I don’t know” is awesome. They provide an opportunity to dig into a topic that is not usually discussed openly, or with enough honest conversation about barriers and specific ways to overcome them.

Of course, there’s also the “Where is the report I asked you for last week?” variety of “I don’t know.” This one kind of stinks because it usually indicates some sort of miscommunication or that someone dropped the ball.

I think we should be less apologetic about using the phrase when it’s used to create a sincere learning opportunity. So, throughout your day look for opportunities to think or say the phrase “I don’t know” (the productive middle varieties) and look forward to the mild discomfort and the learning that is to come.

Multiplicative Comparison Lesson Study – Part 1

MyLesson

I love lesson study. It provides a structure for slowing down and digging into specific standards and practices, then examining how they affect student learning. This week I was fortunate to have the opportunity to facilitate lesson study with our fourth grade team.

If you’re not familiar with lesson study you can learn more here. Essentially it involves developing a research theme and goals, conducting background research (including formative assessment data), creating and implementing a research lesson, and a post-lesson debrief (driven by data collection during the research lesson). Also, it’s common to revise the research lesson after the first implementation, teach the lesson again, and have a final debrief. Our lesson study schedule was crafted from a timeline embedded within the busy nature of teaching. We carved out a 2 hour after school planning (thanks to strong principal $upport) and a 40 minute PLC. Also, we have a half-day TDE which will allow us to implement the research lesson twice, with a debrief and time to revise in between the two implementations. Altogether, we will have about 6-7 hours for this cycle of lesson study. In my past experiences I’ve always had 12-18 hours, so this is a tight schedule.

The driving question behind our lesson study is, “How do we incorporate what’s working in our intervention block into core instruction?” The idea is that, if we can support students in similar ways during core instruction, we’ll have less students in need of intervening. I selected a few standards that have been challenging this year and presented them to the team. After a little back and forth we settled on CC.4.OA.2 (aka MAFS.4.OA.1.2 in Florida):

Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Prior to Meeting

I put together a pre-assessment that would support our study of how students were approaching problems that involve multiplicative comparison. The assessment included three compare problems, each having the unknown in a different position (see Table 2 on p. 89 of the CCSSM document). Each teacher gave the assessment and brought the student work to our first meeting.

The Planning

We took about 15 minutes to orient to lesson study by going over the nuts and bolts of the process, then read chapter 8 of Lesson Study: A Handbook of Teacher-Led Instructional Change by Catherine Lewis which details some common misconceptions of lesson study. Next, we spent some time discussing what it is about the intervention block that is working and came up with this list:

Assessment driven, small group, novelty of a new person, non-routine, exposure, “spiraling” effect, idea of a 2nd chance, research-based resource, differentiated

After this, we dove into the student work, analyzing it item by item. We found that the majority of students could find a solution on the result unknown problems, but struggled with the measurement and partitive division problems that involved comparison. Also, we noticed that a lot of students just took both numbers and multiplied them. Students who were successful typically utilized a number line. We hypothesized that they saw the word “times” and chose to multiply, not really making sense of the problem. Based on this data, we decided to use a partitive division compare problem as the main task of the lesson.

Next, we dug into the available research about comparison problem types. I knew we were time-crunched, so I pulled short chunks of research that would inform us on compare problems and what we may include in the research lesson. We used pg. 29 from K-5 Progression on Counting and Cardinality and Operations and Algebraic Thinking, A short text from Cognitively Guided Instruction on multiplicative comparison problems, and the rubric for Throwing Footballs (a formative assessment task on this standard, complete with detailed rubric). After reading the research, we decided to focus on using visual representations throughout the lesson to support students explanations of problems involving multiplicative comparison.

The Lesson

We embedded opportunities for student discourse about the visuals and the main task throughout the lesson. Here’s the general flow of the lesson:

1) Warm-up – We started by showing students a bar model visual (see below) and prompting with “What do you notice? What do you wonder?” The idea was to use the visual to get students comfortable with the language of multiplicative comparison. This idea came from the first level of the rubric for the Throwing Footballs task.

2) We really liked the football theme with Super Bowl 50 this weekend, so we modified the formative assessment task to be the main task for the lesson:

Two students were trying to see how far they could throw a football. Sadie threw the football 24 yards which was 4 times the distance William threw the football. How many yards did William throw the football?

We anticipated what students would do with the task and planned to focus on encouraging students to make a visual model that matches the problem to encourage sense-making.

3) In the wrap-up (or summary) portion of the lesson we planned on displaying student work, specifically a bar model (or number line) that matches the context of the problem and having students justify which equation (4 x 6 = 24 or 4 x 24) matches the visual model. We planned on addressing 4 x 24 since this is the error we saw most often in the pre-assessment.

What’s Next

This week we will implement the research lesson with two classes. We’ll collect data on what visual models students use and how they’re able to describe problems involving multiplicative comparison. We’re hopeful that the visual representations will support students in making sense of these types of problems. Next week I’ll post a follow-up with samples of student work and how students responded to the research lesson.