Last week I continued to work with two teachers at Betty Huff who teach Grade 3 and 3/4. On Monday, I popped by their classes to assist in introducing patterning. Inspired by Kristen's Gray's blogpost on Talking Points, which she used as a pre-assessment, we decided to try this strategy with the Grades 3/4 class to see what the students knew about patterns, as well as reveal any misconceptions they may have. We reviewed the revised curriculum for Grades 2-4, in particular the learning standards for patterning to determine the talking points to use. I've added the word doc file for the patterning talking points below the post, should you wish to adapt these and try it with your class.
Since "Talking Points" was new to the students, we decided to adapt it from its original version. For those of you who have never heard of Talking Points, you'll want to read either Kristen Gray's blog post or the one on Cheesemonkey Wonders site. Instead of using Talking Points in small groups, which we will do one day, it was decided to begin by using it with the whole class so the students could see how the activity works.
Prior to coming to the carpet area, we had the students read each of the five Talking Points and where it said "Round One" they marked whether they agreed, disagreed, or were unsure of the point. Next we gathered at the carpet and each student was asked to share aloud what they wrote and give a reason why. The other students listened to each of their peers but did not add any comments. As we went around the circle in the first round, the teacher and I quickly realized that although many students agreed "Patterns are predictable," they really had very little understanding of increasing or decreasing patterns, positional patterns, using numbers to describe patterns, and whether or not patterns could help us solve problems. Most students explained that they "couldn't remember doing that last year" or "I've never tried that". This was really important formative assessment. The teacher and I realized that we needed to spend some time revisiting repeating patterns and exploring positional patterns before we could investigate increasing and decreasing patterns. We wondered whether what the children knew was representative of their knowledge or perhaps indicative of lack of experiences with these types of patterns? In speaking with another Grade 3 teacher, she mentioned that they had only worked with pattern in September and not since.
Being responsive to what we were hearing, we knew that moving ahead into Round Two wouldn't necessarily cause any new thinking, as so many were unsure. We decided to tweak our plans and had the students return to their tables and engage with creating patterns. We had set up materials prior to the class and in retrospect, I wish we had of provided a table area where all the materials were the same (e.g., same size and colour) such as beige toothpicks for the students to explore creating patterns using one item in creative ways such as positional patterns. There were opportunities for students to build increasing/decreasing patterns. We hoped these experiences might activate more prior knowledge and/or cause students to shift some of their thinking.
After about 30 minutes we had the students stop what they were doing and do a gallery walk. Then we cleaned up and met back at the carpet. The students recorded their thoughts in Round Two and we went around the circle and shared again. This time, the students had more to say. Their rationales were stronger, as they could connect with an experience. We stopped after the second round because we wanted the students to have time to write in their Math Journals. We asked the students to write:
Here are a few of their responses:
I was pleased to see how some students used examples to explain their thinking.
The next time the teachers have the students reflect in their Math Journals, they will highlight examples like this, so students are able to see how using examples can strengthen their arguments.
Additionally, when reading their reflections, it became evident that students did not have some of the mathematical vocabulary around patterns. For example, in the last journal below, the student wrote "...patterns are predictable because you can always know what comes next when you do 3 or 2 shapes". I wonder whether she understands the term elements or what a pattern core is? These are important for clear communication.
I am excited to continue to use Talking Points to explore students' understanding. We will revisit these points again upon completion of this unit (and likely there will be a blogpost!). Although the teachers will wrap up the patterning unit at some point, the teachers realize that this does NOT mean they are done patterning for the year. As we know from the First Peoples Principles of Learning, "Learning takes time and patience". We need to remember that learning is recursive. Patterning WILL be revisited throughout the year. These teachers intentionally will include patterning in their daily number routines (e.g., an image of pattern is presented and students guess the rule, predict the fifth term, etc.), including patterning activities daily math investigations and weekly rich problems, and whenever it makes sense to do so.
I am a Numeracy Helping Teacher with the Surrey Schools District. Each day I am thankful for being able to work with amazing students and teachers in an area I am passionate about ~ Mathematics!
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