Video Blog #3

The videos on V-shape formations, beams and hair and nails had similarities. Each discussed patterns and formulas they could be created so that one could find the answer to a question with a high number. For example: If you went to the 100th V-pattern how many birds would be flying. Students can use the formula they came up with and tested with smaller numbers to determine this larger number. Connections to Standards of Mathematical Practice: The teacher introduced V-structure by inquiring about geese and their migration pattern in the sky. By relating it to this common site, children could easily use the manipulatives to form the shape with confidence. They also understood the real-life connection to the problem. (This also connects with the Process Standards of connections and representation). The progressive formalization structure was explained by a teacher within the video. Informal, pre-formal and formal stages are how students learn and participate. Informal is using pictures and manipulatives to solve, as in this example. Using these manipulatives, students could reason quantativley by counting and placing birds in a v-shape formation. During the lesson, students worked talked with eachother while constructing their formula, and it was evident that as soon as one student thought they had figured it out, they were defensive and tried to justify their answer so others understood it. This is also connected to the Process Standards of problem solving, reasoning and proof and communication. The teacher asked for participants to use the board manipulatives to model the v-shape and the addition of birds, so students could understand that well enough to then figure out the formula.
As all Process Standards and Standards of Mathematical Practice were apparent in the V-Shape lesson, they were in the beams and hair& nails lesson. In both, the teacher asked for prior knowledge or personal experiences about the topic (connecting and making sense of the problem--beams--asked if students noticed any building being built around town. H&N--asked student with short and student with long hair how long it took to grow etc). Both of these problems didn’t have manipulatives like the V-Shape, ones they could move around, but in beams they had the triangular pattern set-up they could add to and in the hair one they had a ruler to measure. I liked that both problems emphasized estimation because although it can make students feel uneasy that their answer isn’t correct, it comes into play when justifying an answer. Before they estimate they need to ask themselves if that number makes sense based on prior knowledge and other factors.
I saw the connection between the activity we did in our class on 3/30 with the excel spreadsheet and box dimensions. Technology can be introduced and used in the classroom when testing and using formulas to show the structure, accuracy and repetitive aspect of them.