In my travels so far as an IL I have found that teachers I have observed or worked with have a much stronger grasp of how to form guided groups in reading then they do in math. It is an area that we are working on this year in the schools I work at and as board. How well do we know our learners? Are we planning instruction that is responsive to our students needs? In this post I am going show some work I have been doing with Mrs. K in regards to her journey to be responsive to her students needs in math and the building of her own content knowledge.
A little background to what you will see in the series of videos and pictures. At her school we have been focusing on operational sense, more precisely her students journey from direct modelling addition and subtraction problems to proficiency at solving addition and subtraction problems. We are using Alex Lawson’s book “What To Look For: Understanding and Developing Student Thinking in early Numeracy” as our mentor text to help build content knowledge and for the continuum on numeracy development for addition and subtraction that is provided in the book. Below are two pictures, the one on the right is the cover of the book and the left is the continuum for addition and subtraction.
After you have completed diagnostic interviews with your students by asking them a simple story problem you can then analyze what strategy they are using and then place them on the continuum. Once you have the strategy they are using you can use the resource to help you understand what key ideas the student has developed and what key ideas they still need to develop to move towards proficiency (automaticity for fact combinations/efficient methods for 2 digit by 2 digit problems and beyond). Once you have a class profile of where your students are based on your data, the continuum helps you to group your students into guided groups based on the key idea they need to move towards proficiency. The continuum is divided into four main sections. Direct Modelling and Counting, Counting more Efficiently and Tracking, Working with Numbers and Proficiency. The series of videos I have below show the process from the initial interview to working in a guided group for one student in Mrs. K’s class. I have provided her data chart that shows where everyone is at on the continuum. The reason this guided group only has one student is because he was the only student using this strategy at this time.
Here is the initial interview problem:
With this interview Mrs. K determined this boy is using the strategy of counting on. All of her students were assessed and then placed on the continuum. Here is a pic of her data chart that she uses to track the student’s progress. She uses this chart to group her students into guided groups. As you can see there was only one student using counting on at this point.
Using the interview observations Mrs. K and I chatted about what key idea this student needed to develop in order to move along the continuum to counting on from the larger number. We decided that he had not yet developed the key idea of the commutative property in addition (the idea that the numbers can be flipped: 5+7=7+5). Mrs. K then brought this student into a guided group. It happened to be only one student this time but as you can see by her data she would have a few groups at counting three times, near doubles and up and over ten .
I had to break up the guided group video into parts because of the length of the video.The next series of video’s is of Mrs. K working with this student. This was his second time in a guided group for this key idea. I wasn’t there for the first guided group session so he has moved in development from the first session
As you can see in the video’s this student has now started to develop the key idea of the commutative property and is recognizing that he can switch the numbers in order to count on from the larger number. He shows this understanding by stating, “Makes it faster to count on” and by reversing the rods to show his understanding. He doesn’t say it’s faster because there are less numbers to count up from 7 than there would be from counting up from 5 but he is clearly understanding that it is more efficient. Mrs. K is now having him practice using counting on from the larger number independently with similar story problems and with math games. She will then add him to the group that is working on hierarchical inclusion (which means there are smaller number inside of numbers that increase by 1 or the easier way to say it “decomposing numbers”) in order to help him start using strategies that are in the working with numbers part of the continuum, for example: Using 5 and 10 Anchor, Up and Over Ten, Doubles Near Doubles.
While Mrs. K works with her guided groups the other students are playing math games where they are grouped based on what strategy they are using. This helps them get more efficient using that strategy and helps move them further along the continuum to proficiency. There are many math games out there to use for these strategies but some excellent ones are provided in the teacher kit chapter of the What to Look For resource. Mrs. K also has them work independently answering story problems that use the different problem types (joining, separating, part-part and compare) as research shows this is one of the most effective ways to help them develop more efficient strategies.
This blog is an example of how you can get to know your students well in the area of operations and then be responsive to their needs. The example holds true for all concepts or cluster of concepts. Diagnose, look at your data and then plan instruction with quality math tasks based on your students needs using guided math, shared math, independent math.