Week 3: A Thinking Classroom

This week in class we discussed the article Building Thinking Classrooms. The article defines a "Thinking Classroom" as a space inhabited by thinking individuals, where students are working collectively, learning together, constructing knowledge and understanding through activity and discussion. (Liljedahl, 2016) A thinking classroom is one based on inquiry, where the teacher is not only delivering content and transmitting knowledge, but students have questions and use problem solving skills and collaboration to work through problems. A thinking classroom also deals with a good amount of struggles. If students are working together and thinking out loud about problems they are discussing how to work through them, through this students meet struggle. Struggle takes on a new term though, in allowing struggle and mistakes happen when problem solving helps to make your brain grow (Mistakes and Research, 2016). This weeks forum video Mistakes and Research discussed how mistakes allow for synapses in the brain to fire and growth is made, but getting an answer correct, no growth is made. It is because struggle and hard thinking is when the brain grows the most (Mistakes and Research, 2016). A thinking classroom is therefore a critical environment to cultivate that would allow students to work together, make mistakes and practice tasks to develop their learning.

In class we had our own example of a thinking classroom. We were given a variety of problems to work out with our table groups such as Tax Man or the Collatz Conjecture. During these tasks we did reach some struggles, or at least I did. But working collectively allowed for different perspectives to be encountered, and problem solving to become less difficult. The teacher walked around as a facilitator of discussion and when we thought we were done with beating the Tax Man, asked us to see if we could beat him in a better way. With more thought, we were able to beat the Tax Man better. We also used vertical non-permanent surfaces (whiteboard) to show our work. The benefit of using white boards or other non-permanent surfaces is that it gives students an opportunity to show their work to an audience. It also allows students to look around the room and visibly compare the problem solving strategies done by their peers. It allows students to get out of their seat and actively participate and be contributors of knowledge.

EDBE 8P54 Week 3 Slideshow. Teaching Mathematics for all learners.

These types of implementations in the classroom not only successfully build knowledge, but they are ways to trigger engagement. A thinking classroom is a meaningful experience that gives students responsibility to contribute to learning. A thinking classroom also allows for multimodal problem solving, activity, and collaboration which varies drastically from a traditional classroom. Just even these few simple differences make all the difference in engaging students and diverse learners. Diverse learners have so much more to benefit from this type of environment; they are able to collect strategies from their peers, visualize problems, ask questions openly and build confidence in their math skills while being a part of a solution team. In a thinking classroom worry over making mistakes does not exist so much, since it is an open environment to discuss strategies and work through problems collectively.

Sources:
Lesson 3a 360p. (2016). Retrieved September 23, 2016, from https://www.youtube.com/watch?v=kGV0HQujmKs

Liljedahl, P. Building Thinking Classrooms: Conditions for Problem Solving. Simon Fraser University (June 2016). Retrieved: September 23, 2016

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

Week 1: Establishing Confidence

This week's online activities really established a mindset that teachers and students should have prior to engaging in mathematics. By addressing stereotypes, reflecting on myths we have heard about math, and looking for instances where stereotypes are broken allows us to confront and reflect upon our own math experiences, successful or unsuccessful, and uncover those experiences.

Being aware of how math is portrayed through media, fashion etc. shows us as teachers why young people may be so hesitant towards the subject. The overall big idea we uncovered this week was that

everybody can do math.

So, knowing this as teachers, why should we not have our students know this as well? In my forum post I addressed the myth that some people are left-brained (logical) and some are right-brained (creative) and there is no crossover. This means that if you are good at math you cannot do well in the arts, or if you excelled in arts, you could not do well in math. This seems as though a heavy weight excuse for those who do not want to try at the "opposing" discipline. If anything it allows students to give up much more easily because they are going in with the mindset that they cannot accomplish much because it is not their strength. And as students go further into their education they follow their strengths. As educators, especially in junior intermediate, where students are becoming more eager to identify themselves, we should be showing and encouraging students to see disciplines as integrated subjects that make up our world. Because they are. We should be insisting that you are whole-brained and as said in the video The Brain science on Growth Mindset mistakes help to grow your brain.

EpilepsyUni. August 16 2013. epilepsyu.com

It is absolutely crucial to establish an environment that encourages students to have an open mind, mistakes are welcome, and have them know they are capable of being successful at math. Doing this will be a stepping stone towards confidence and student success. 

Starting in September we have the opportunity to debunk any stereotypes in our classroom. We could have students do the exact thing we are doing in class. We could be asking them about their personal math story and have them address stereotypes and myths they may have, and smash the stereotypes for them. We could show students Hollywood Hates Math  (appropriate clips) and challenge students to become aware of any time math negatively comes up when they are watching television or movies, and have them bring those instances to the classroom.

We could also have them look for instances where stereotypes are being altered. One particular scene that came to mind for this was from the movie Stand and Deliver:

In this scene the teacher, Escalante, shatters his students' own ideas of what they can accomplish in math. He challenges them with something new and difficult, algebra, and proves to them that math is in their blood. You can see after the student correctly answers 0 the look of satisfaction on his face. It takes a teacher to come in and drive confidence into students. Establishing confidence from the start will put students on a pathway to success.

Sources:

Jo Boaler: The Brain Science On Growth Mindset. (2015). Retrieved September 23, 2016, from https://www.youtube.com/watch?v=s4xqzgBy-lM 

Stand and Deliver (1988) scene. (2013). Retrieved September 23, 2016, from https://www.youtube.com/watch?v=Q3a-bXXN9Xc