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Wednesday, October 12, 2016

Humpty Dumpty: Using inquiry-based math tasks in grade 1 to teach addition/problem solving

This week I had the pleasure of demoing/co-teaching a 3-Act math task, created by Graham Fletcher, in a 1st grade classroom in my district. I have always been a big fan of making math relevant to my students, and incorporating open-ended tasks that they can relate to, so when I first learned of Graham Fletcher's 3-Acts for primary age students (inquiry-based math tasks), I was hooked. I am sharing these like crazy at my math trainings, to encourage more inquiry-based math and student-driven problem solving in classrooms, and teachers' interests are piqued!

A reflection on our "Humpty Dumpty" 3-Act lesson in grade 1--

Prepping the Lesson
A common request from the teachers I support is for ideas on how to customize and differentiate our current math curriculum, Eureka Math/EngageNY. With that in mind, the first part of prepping this lesson involved finding the specific grade 1 lessons and math standards that the lesson aligned with. I also identified alignment with specific tasks in the upcoming mid-module assessment, and attached the annotated lessons and assessment to the end of the lesson slide deck for teachers to use with their unit planning.

I also decided to take the original task and embed it into a slide deck. For teaching purposes, I found it easier to have each step laid out for me in the deck with discussions/task prompts. The first time I taught a 3-Act last year, I missed a couple of steps that I wished I hadn't. Teaching from the slide deck kept me better organized and allowed me to embed a few additional language supports. The format worked really well for the classroom teacher and I!

(Click to view the lesson slide deck)

Supports for ELL & Language
The classroom we taught this math lesson in has a high population of English language learners (ELL), so extra language supports were imperative (and a good opportunity to model language supports in general for Eureka Math).

I printed the Act 2 images in Fletcher's lesson to tape to our Notice/Wonder chart, included images to support the text in the slide deck, and used TPR (total physical response) along with academic vocabulary (example: when talking about part/whole and number bonds, I usually open up my arms at my sides like I'm holding up two "parts" and then bring them together and clasp my hands when saying/modeling the "whole").

Vocabulary on charts was also accompanied by sketches to help with meaning, and sentence stems were provided to support students with speaking and writing about math.

Other Scaffolding & Differentiation
One of my favorite elements of 3-Act tasks is the low-prep/no-prep differentiation possible within the tasks. For example, early finishers were simply asked to show another strategy (and potentially a third way), or another model, they could use to solve the problem. And while early finishers were getting creative with their math, the classroom teacher had time to support students that were struggling with the task.

Printing the Act 1/Act 2 visuals and taping them to lesson charts served as scaffolding for students, as well. As students got stuck on parts of the problem, we directed them up to the lesson chart, notes, and slide deck to access their resources for help first; our goal was not only to teach content in context, but also to help students learn how to learn and find answers.

Teaching the Lesson
I love using 3-Act lessons to bring a little mystery into math instruction! I started by telling students that I needed their help solving a problem, that a friend of mine sent me a video of something that happened at his house last night, and that I needed their help. Students were immediately hooked-- a math mystery?? "Yes, we want to help!" was the overwhelming response. Throughout, all students were engaged in the mystery and in our task. Aside from the typical fidgetiness of 1st graders, students were excited to work on the problem for a full hour!

I mentioned above that one of the reasons I like using these open-ended tasks in math is that the model shifts the math lesson to more student-centered instruction. In a 3-Act, we open the lesson with a hook/problem/mystery to be solved and then ask students what questions they have, and center instruction around the student questions. This process is a great opportunity to teach students how to ask questions, and how to become more curious about math. The first time students work through this process takes some support-- although we validate all questions as good questions during this process, the teacher also guides students to ask the relevant questions that will help us solve our problem.

Once we get a set of student questions recorded, we use those questions to determine next steps. Again, students are asked how they think we should solve the problem. The whole activity is focused on students driving the work.

Student Work
It doesn't necessarily take a set of 20 math questions for a student to clearly demonstrate their understanding of a math concept. In this case, it took just one math problem for students to demonstrate both their conceptual and procedural understandings and gaps in math.

While the main learning goal was for students to use information to be able to solve a missing addend problem, we also learned, through observation and conversations with students, which students understand the relationship between addition and subtraction, which students need some reteaching in counting and cardinality, and which students fully comprehend the meaning of an equal sign (when a seemingly advanced math student disagreed with one student's 4+5=9 equation and said the answer could only be 9=5+4).

The Closing
We ended up closing our lesson with a modified, hands-on number talk focused on the misunderstanding around equations and equal signs. We asked students to prove (or disprove) whether 5+4=9 and 9=5+4 have the same meaning or not. Students pulled out rekenreks, counting chips, linking cubes, and place value cards, and drew math pictures, to defend their reasoning.

It was an important conceptual misunderstanding that may not have been spotted on a fill in the blank worksheet, but that we were able to diagnose in this student-guided, open task, and during the in-depth math conversations that students engaged in during the problem solving process.

Both the classroom teacher and I were really happy overall with the lesson. Students learned new problem-solving strategies, learned to ask questions in math, were engaged in mathematical conversations, used academic vocabulary in context, practiced counting and addition skills, and defended and modeled their thinking. The language supports that we used for our English language learners were successful, and students needing extensions were appropriately challenged to push their thinking.

In reflecting with the classroom teacher, one change that I plan to make is to add a visual of the original 9 eggs to accompany the Act 2 clue about how many eggs there were to start. A handful of students got caught up with the idea that an egg carton has 12 spaces so there must have been 12 eggs to start, whereas the problem stated that the carton only had 9 eggs in it to start. The next time that I teach this lesson, I plan to provide students with an image of the 9 eggs in the carton. I'd also love to have an actual egg carton with the surviving 5 eggs in it to use as a model for students.

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