Developing "Thinkers"

Creating a Culture of Thinking - The 3 Part Math Lesson is a format that has been used for some time now but I feel there is still a part that is missing when describing an effective math lesson. Minds-on should involve more than reviewing what was covered the day before. Students have to be given opportunities to explore, inquire, manipulate, etc. Open-ended inquiry opportunities are essential in order to create a Culture of Thinking in our classrooms. By providing students less information and letting them determine what is needed in order to solve a problem, we are requiring them to think rather than simply work.  Have a look at this article which expands planning for math instruction to a more concise 4 Part Math Lesson. It provides a great description of each of the segments. Let's develop thinkers!

https://tapintoteenminds.com/4-part-math-lesson/ 

Visualizing Math

As I explore my own learning of mathematical foundations, I recognize more and more the importance of being able to visualize concepts and be able to communicate that representation to students. Where to begin and how best to represent a concept can be challenging though because it is not how I was taught math!  I like the 18x5 demonstration in the article below as a good starting point. The link to an algebra example towards the bottom of the article (starts at about the 5:20 mark) provides a great connection to more advanced math. If we can use these strategies, perhaps students won't "hit the wall" like I did in high school where memorization could only carry you so far. 

https://www.youcubed.org/think-it-up/visual-math-improves-math-performance/

The Importance of Patience in Teaching Problem Solving

We are often such a rush to cover curriculum or acquire grades for reporting purposes that we overlook the importance of patience in teaching problem solving. This article was interesting but the video by Dan Meyer really brought the concept together. We need to show patience in the short term if we are to see improved outcomes in the long term. This underscores the importance of recognizing multiple math strands in a single math activity in order to create time for patience. Have a look.

http://www.middleweb.com/33114/how-to-get-students-to-slow-down-and-think/

Connecting Math for Deeper Understanding

This article highlights the notion that students need to engage in tactile-kinesthetic mathematical learning and prompts me to consider how important it is to embed math across the curriculum. We should see math through the lens of various subject areas such as Drama and Dance, Music, Physical Education, Outdoor Education, etc. in order to further develop and solidify problem solving skills and strategies, as well as alleviate some of the negative attitudes towards math. I feel that the example of students acting out a math problem and subsequent improvement in scores emphasizes the point. Math concepts should not be addressed solely in math class if we are going to create a solid foundation in our learners - it is everywhere and we should treat it as such. Have a look at the article.
https://ww2.kqed.org/mindshift/2015/03/26/why-kids-need-to-move-touch-and-experience-to-learn/

The Importance of Mistakes

As we enter a new school year, many teachers are reinforcing the concept of a "Growth Mindset". While we recognize that making mistakes is important, I believe its important for students to learn to classify or categorize their errors as outlined in the article below. When I took a Mindfulness course, one of the strategies to redirect focus was to label any thought or distraction that entered my mind in order to move beyond the distraction. I believe that labeling errors can help students learn to deal with them more effectively. Have a look at the article.

http://ww2.kqed.org/mindshift/2015/11/23/why-understanding-these-four-types-of-mistakes-can-help-us-learn/

Smart Search to Develop Inquiry Skills

This is a great place to start with your students in order for them to search for information with a more critical eye. There is so much information available that we need to teach our students have to research differently than the way we... or should I say "I"... learned. I like how there are a variety of starting points for the lessons that are provided.
https://goo.gl/JipNpo

Rethinking Problem Solving

In an attempt to improve math scores, many schools have implemented school-wide problem solving models. The idea is that if students develop a routine for approaching, interpreting and planning solutions for a problem, they are more apt to be successful. Teachers are more able to identify where in the process a student has encountered difficulty.  The challenge has been finding a strategy that provides the necessary structure but works for everyone. What I like about this article on structured thinking routines is that the "model" for thinking is not specific to math. Students can use this model across the curriculum, making it more likely to be practiced and used successfully. Have a look at the article and video.

PZ Thinking Routines from Sue Borchardt on Vimeo.

Effective Questioning to Increase Thinking

Dr. Marion Small, a renowned author and Math Consultant,  was at Tecumseh Vista on Saturday for the Edcamp Conference today. She emphasized the point that our curriculum expectations are worded as "just do it" expectations - not thinking expectations.   A teacher can make a lesson thought-provoking or bland and would still meet the curriculum expectation as worded .... but the consensus is that we want to develop "thinkers". We can address this by altering the way we ask questions.  Even a rich task can go "dead" if it doesn't embed provocation for students' questions. Even struggling students need to be challenged to think rather than be given simple questions with simple answers. Have a look at the link below for her presentation and samples for the simple ways to alter our questioning tactics. 

http://www.onetwoinfinity.ca/wp-content/uploads/2016/04/EDCAMP-keynote.pdf

Harnessing the Power of "Interest"

When I read the article below, I drew parallels to the 3 part math lesson and the importance of the "Minds-on" stage - I've always viewed this stage as critical in my work with students who have self-regulatory issues. The introduction is what "hooks" the learners to help direct future learning and activates prior knowledge so that connections are more likely to be made. Learners are more apt to self regulate when the brain is actively engaged.

http://ww2.kqed.org/mindshift/2013/11/04/how-the-power-of-interest-drives-learning/

The article also addresses the importance of a guiding question .... the foundation of inquiry.  By taking the time to frame an engaging, guiding question, teachers can elicit curiosity and foster student interest. 

Promoting a Growth Mindset

This is an interesting comment from Carol Dweck during an Education Week conference keynote address -"We used to say kids don't have the ability. Now we're saying they don't have the mindset? I think it's protective. It's our way of saying 'It's not my fault that child isn't learning.'"

As educators, we need to ensure that labels are used to proactively assist us in strategy development rather than attribute blame to the individual (i.e. teachers need to approach student challenges with a Growth Mindset as well). Have a look at this article in which she identifies 6 "tips" to address Growth Mindset.

I also like this article on how teachers can promote a Growth Mindset in Math in the way they frame questions. For example,