Week 2: Adaptive Reasoning

In this past weeks class we participated in a variety of highly engaging activities.

The first warm up activity asked us to find out how many owls were laid out throughout the blocks. Most students had to visualize this in a different way and went to take the snap cubes to start building a 3d model of the image, while some students drew out the image from a surface view.

Image from: In Class Activities Slideshow. EDBE 8N54 J/I Mathematics II Retrieved: September 19, 2016 

Another activity we participated in was the finger counting problem. We were asked which finger we would land on if counting to 1,000 and then again if we were counting to 12,345,789. Students were very engaged at this point and were up at the board problem solving and writing down their strategies that proved their answer. There were agreements and disagreements, but there was also a ton of communication involved while retrieving a general consensus. 

Chamberlain, 2016.

Chamberlain, 2016.

The reason I chose to discuss these activities was because they embody the building blocks to mathematical proficiency. According to the article The 4 Strands of Mathematical Proficiency, proficiency develops over time. Students need enough time to engage in specific mathematical activities in order to develop that skill. Only one or two experiences with a procedure will likely not help them succeed, but practicing over sustained periods will help make connections between previous knowledge and new knowledge. (137)

Practice with mathematical concepts is hidden within these brain teaser activities. Students want to solve the problem and without being told begin to find resources to solve that problem (i.e. snap blocks, visual pictures). They get up and start to explain the justification of their strategies and communicate with others around them and form adaptive reasoning. They start to think logically about the relationships among concepts and situations, justify their procedures and give sufficient reasoning. (130) 

Adaptive reasoning is the overarching goal for mathematics, it is the last step towards mathematical proficiency. It goes back to the video we watching for our online modules Messages about Math, when students are praised for giving the correct solution they are more likely to choose easier paths that do not challenge them, where students who are praised for their hard work will continue to challenge themselves and be more confident in mathematics. Students need to be acknowledge for the effort they put into deriving the answer, for their ability to get up and explain their thinking, regardless if it is right or wrong, if they can express what they are trying to do and we can correct it together. Students minds need to shift from the end answer as the goal and the classroom should practice the pathway to adaptive reasoning. A shift in focus will allow for students to be more engaged, more confident in themselves, less worried about making mistakes, and more literate in math.

Sources:
Kilpatrick, J., Swafford, J., & Findell, B. (2001). Chapter 4: The 4 strands of Mathematical Proficiency in Adding it up: Helping children learn mathematics. [pp. 115-135] Washington, DC: National Academy Press.

Lesson 2c 360p. (2016). Retrieved September 23, 2016, from https://www.youtube.com/watch?v=_9q0paQoZa8