Have you ever had one of those “aha!” moments when the light bulb goes off, and you come to understand something that makes your whole life easier? Or better yet as a teacher, you witness your students have one of those “aha!” moments. For us, at the AIMS Center for Math and Science, we have found in students understanding of number that one “aha!” moment for them is when they realize they can reuse their fingers to count past ten. This realization is a vital step in a student’s understanding of the concept of number.
In the following video, you will get to witness a student have one of these moments. Abby (pseudonym) is a kindergarten student, and the video was taken February of 2018, so it’s the middle of the school year.
There are two cloths in front of Abby, the teacher presents a problem by saying, “There are six M & M cookies under here.” (pretends to put cookies under the cloth) “Then we put three more under here.” (pretend to put cookies under the other cloth) The teacher reminds Abby of how many cookies are under each cloth and then asks, “How many cookies are there altogether?” You can see Abby start to move her fingers sequentially as she softly counts from one: “1, 2, 3… “ She answers “10”. The teacher remarks, “I like how you were using your fingers. Could you show me what you were doing on your fingers or maybe say out loud?” Abby shows the teacher how she used her fingers, holding them up high and uses her fingers sequentially to count up to 9. The teacher says “9, hmm” and Abby replies “I think it’s 9.” Notice how a little teacher prompting helps the student reflect on their counting and self-correct.
Next, there is some fun conversation about being full from eating too many cookies (it’s too cute!) then we get to the next problem. The two cloths are still in front of Abby, the teacher asks her, “What if we put eight cookies under here?” (pretends to put some cookies under the first cloth). “And then we put five more under there,” (pretends to put some more cookies under the next cloth). He then asks, “Now how many cookies would there be altogether?” Abby put her elbows up on the table and starts counting sequentially on her fingers “1, 2, 3, 4, 5, 6, 7, 8…“ looking a little perplexed. She counts “1, 2, 3…” on left-hand pulls her fingers in and starts over again “1, 2, 3, 4, 5, 6, 7, 8” pulls fingers in and (ta-da!) continues her count on her left hand “9, 10, 11, 12, 13?” (Seems unsure) The teacher asks “How many?” Abby runs through her fingers again gets “12” The teachers asks, “12 or 13?” The video ends there. As you can see the exciting moment is when she realizes that she can reuse her fingers to continue her count! As a teacher have you ever observed this “aha!” moment with your students? We would love to hear from you!