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,

Adding to the Growth Mindset Conversation

There are 2 points in this article sent to me from a colleague that made me reflect. The first is the notion that Growth Mindset is more than praising students for hard work. A Growth Mindset "involves reflecting on and changing our strategies so we become more and more effective learners over time".  The second is the mistake matrix that is presented to help students understand the difference between "sloppy" mistakes and mistakes that "stretch" their learning. Have a look.  

http://ww2.kqed.org/mindshift/2015/11/16/growth-mindset-clearing-up-some-common-confusions/

Growth Mindset: Clearing up Some Common Confusions Carol Dweck's work has made growth mindset a hotly discussed topic in education. It has also spawned misunderstandings about growth mindset and what it means in education. Read more...

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The Impact of Information Access

Our students today have infinite resources at their fingertips with personal devices in their pockets and free wifi growing everywhere. Never before has it been more important for teachers to be able to convey why the content they are teaching is relevant and important because our students have become much better at filtering information. They are bombarded with data and are constantly categorizing incoming information as either relevant/important or irrelevant/unimportant. I believe that their predisposition to filter incoming information is why it's crucial for educators to connect learning to relevant situations. This article in Edutopia offers a great perspective on "Why Math?". Have a look.

Genius Hour...A Systematic Approach to Inquiry

This video below was shared with me by a colleague as a starting point for "Genius Hour" in a classroom. I like the layout that is described and the supporting links that are provided. I especially appreciated that post regarding students who aren't sure about where to begin. "Don't Blame the Student" really made me think about the lack opportunities for students to follow their interests and motivations within school. I like the idea of getting students who are "stuck" to help out with a personal project - I've used helping our local food bank as a topic. Once students realized that there are an infinite number of ways to help others, the ideas became quite diverse. 

http://ajjuliani.com/webinar/

What to do when Genius Hour fails....

The Active Student

Our students today are always "on". They multi-task much more than I ever did as a child - texting, gaming, Instagram, twitter, selfies, social media......they are in a constant state of heightened "stimulation".  Students have become acclimatized to this state and may actually learn better when active. I recently took a course on Mindfulness and just taking time to be aware of the present moment. I believe that our students need support with this as well. This post on Edutopia pertains to ADHD students in supporting concentration but what I like is the implication for all students that learning can occur within a non-traditional setting. Students should be given the opportunity to move and, as educators, we do whatever we can to keep our students engaged. Have a look.

The Power of Play

I recently watched this video and considered its implications for what we see in our classrooms on a daily basis. I agree with Dr. Gray that play fosters independence, self esteem and sense of capacity to solve problems. The way children play has changed. Many students play video games with friends online. Would this form of play elicit the same results? Or is there something more needed - like more sensory/tactile-kinesthetic opportunities, social context, etc to develop coping skills? Within a classroom, I believe we can foster a similar play context through the use inquiry-based learning, regardless of grade level. Have a look at Dr. Gray's video.

Rethinking Math Instruction

This video sent out by the Brant Haldimand Norfolk Catholic School Board highlights how we should be rethinking math instruction. Students should not be expected to simply follow a set of procedures to achieve a desired outcome. They need to be able to show that they understand. We often say that the best way to learn something is to have to teach it. By expecting students to justify and prove their response, it solidifies understanding. Have a look at the video.

Web Tools to Support Inquiry

As we continue to engage students' in their own learning through inquiry, there are a number of tools that can be of assistance. Have a look at this article from Education Technology and Mobile Learning about various web-based supports. Tools such as these are not device specific so teachers and students can used them regardless of their platform of choice.

http://www.educatorstechnology.com/2015/09/10-educational-web-tools-that-support-inquiry-based-learning.html?m=1

Creating Growth Mindset Classrooms

What I like about the linked Growth Mindset blog post from Matt Bromley is the list of ways teachers can create this atmosphere within their classroom. I especially emphasis the importance of feedback through small group instruction.  When teachers embed this structure within their programming, students will receive immediate, non threatening feedback with which they can shape new learning. Have a look at the article below. 

https://mjbromleyblog.wordpress.com/2014/05/17/growth-mindset/

The Ever Changing Brain

As an educator, I subscribe to the belief in Vygotsky's "zone of proximal development." We need to provide learning opportunities where concepts and skills are within reach for a student based on their current level of achievement. I have to admit though, that I have been guilty of categorizing a student based on assessment data and, perhaps, have limited my expectations. The idea that we can alter neurological pathways through programming is something we need to keep in mind as we develop programs for students. Planning must consider not only the zone of proximal development but also that, if given the right challenges, the neurological plasticity of the brain will alter pathways. We can increase IQ.... something that I need to keep in mind when examining student profiles. Have a look at this simple video. I believe that it's important for teachers to educate their students to be aware of this concept in order to foster more perseverance and resiliency in children.

Are there Learning Styles?

In education, we have discussed the notion of Learning Styles to ensure we are meeting the needs of every learner. This TedTalks video by Teisa Marshik is compelling in refuting the importance, or even existence, of Learning Styles. 

While I agree with the presenter in many ways, I don't think we can simply discard it. Historically, teaching was auditory...the teacher stood at the front of the class and talked or lectured to the larger group. This doesn't work for everyone. Teachers need to consider the modalities or preferences of learning and ensure that they tap into the various domains regardless of the content. One way to view the brain is as a filing cabinet and by ensuring each style (I am using style and preference interchangeably) is addressed, we can store data in more "files" to be accessed easier at a later date. It makes connection to prior knowledge easier, which is the critical point the presenter makes when discussing the importance of meaning. Like I said, I agree with the video but I feel the most important point made is not that Learning Styles do not exist, but that for learning to occur it must be meaningful to the student. That is why inquiry-based education is so important.