This blog is the fifth part of a multi-part series titled “Creating Centers in the Classroom.” If you’ve missed the previous installments, you can read part 1 HERE, part 2 HERE, part 3 HERE, and part 4 HERE.
Through our experiences with children here at the AIMS Center, based on the research of Dr. Les Steffe, we have seen 2nd-grade classrooms with children at many levels of readiness when teaching addition. The following is a simple summary of the five different types of understanding we might see in a 2nd-grade classroom and adjusted content for children in each group:
Counting All-Perceptual: The student needs to work with the actual material that they see, hear, touch, etc. The amounts need to be small, and students count from 1. If given five items and four more items, the student may count the five items (1, 2, 3, 4, 5), and then count the other four items (6, 7, 8, 9) to find the total. The teacher could begin allowing students to count one set and then hide it, using dice or finger patterns as suggestions to help the student have something to count. Having the student count items before hiding taps into their short-term memory as a tool and can eventually help them develop these patterns and tools in their long-term learning. Teachers could begin to increase totals beyond ten as the students are ready.
Counting All-Figurative: The student can begin to use their imagination to substitute for the material they are trying to count so that you can hide some of the material. They may visualize the material, use their fingers, or use patterns to count as substitutes. These students are still counting everything from 1. If given 12 items under a cloth, and 6 more items exposed, the student may point at the cloth and count 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and then continue to count the exposed items 13, 14, 15, 16, 17, 18, to find the total.
Counting On-By Ones: These students can “count on,” meaning that if they are joining 17 items with 4 items, they may say 17…18, 19, 20, 21. Both sets of objects can be hidden, and the numbers in each set can continue to increase.
Counting On-Coordinating Composites by Ones: These students are counting on, but one difference for these students is that they can now count on to solve a Change Unknown situation. It is also a great time to begin to work with increasing by 10’s. For instance 23 objects and 20 more. Teachers can have the students use material and make or stacks of ten blocks themselves. This step will increase the likelihood that counting by tens, or adding multiples of ten will develop with a deep understanding. As this understanding develops, the teacher can then begin to have the students work in situations where there is a multiple of 10 added on as well as some more ones. For instance, 20 and 3 ones joined with 43.
Counting On-Strategic Reasoning: Lastly, these are students who can count on, but who can reason strategically to join two sets. They may be the first students who are truly understanding addition as a concept. Given 58 + 45 they may increase 58 by 40 then add two more to get 100 and finally add three more to get 103. Teachers can give these students experiences that will develop more strategies and can begin to increase their ability to apply this to 100’s and 1000’s etc. Relating their understanding to the standard algorithm can come once this understanding is solidified.
There is so much more detail than I can address in one post, but if a teacher ran stations which were homogeneously grouped, he/she could address the needs of each child by modifying some simple details in the presentation of situations while still addressing the same concept at the level appropriate to each child. Feel free to share your ideas for using centers to meet the needs of all students in the comments below.