"All of us are smarter than one of us." Graham Fletcher

Since I can remember, I have loved math. I am unsure when this started but I have never once been 'turned off' math for any reason. When I see students who struggle with a connection to learning math, I see it as a challenge and, although not always successful, strive to spark and ignite a flame that leads to intrinsic interest with math learning.

This year, I decided to learn more about the methods and approaches taken to solve problems and gain conceptual understanding. The incredibly talented Robert Kaplinsky and Graham Fletcher were in the right place at the right time for me, with Kaplinsky offering his 'Empowered Problem Solving' online course and Fletcher paying a valuable visit to FISO. As a result, I have completely revamped my math teaching approach, becoming more specialised in how learners approach problem solving. I would encourage anyone out there who is wanting to become more equipped at preparing students to solve problems independently to look into Graham Fletcher's and Robert Kaplinsky's professional developments, resources, open middle problems and 3-Act tasks. 

By incorporating what I have learned from this course with what I have learned works best for math learners in the past, I am finding a nice blend of directed problem-solving, time spent on skill acquisition, collaborative hands-on and stimulating provocations with concrete materials, and applying the skills and knowledge they have conceptually. This biggest change in approach, however, comes in the LANGUAGE I use when interacting with learners. Posing questions 'what makes you say that', using turn and talks as a part of all discussions, being PRECISE and ACCOUNTABLE with my own mathematical language, and noting the STUDENT language down are all imperative in ALL math sessions. 
My take-aways from this new learning:

• being precise
• estimating on a line with low at one end and high at the other
• use turn and talk more than whole class discussions
• note down EVERYTHING in front of the class when students contribute to 'what do you notice' and 'what do you wonder'
• formative assessments can be short, deliberate and valuable as exit tickets

If you have any feedback or would like to connect, please do reach out!
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An example of what I am talking about with this 'blending':

Firstly, students opened up their packs of Cuisenaire Rods, given time to play with their 'new' materials prior to starting the learning process. 
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​The aim of this mini session was to explore how we can represent basic fractions. That is, showing themselves and one-another representations of a half, a third, and a quarter. Once they were able to do this effectively, convincing their 'skeptic' partner who needed convincing, they then devised a way of showing this in notation form. 
​Next, students were shown a street sign as per Robert Kaplinksy's task 'How Far Apart Are the Freeway Exits?' I posed the questions:

• How can you tell which exit is closest to you?
• How can you tell which exit is farthest from you?
• How would you show how far apart the freeway exits are on a map?
• Which exits are closest together?
• How far apart are the freeway exits?

Then, I asked students to blend their skills by asking them to represent the road and the exits using Cuisenaire Rods, explaining their reasoning to their skeptical partners, using their skills from Jo Boaler's 'Prove it to Me' approach (attached below). Next step is to ask students to represent these in different ways. I will also pose the question 'What if a different color was equal to one kilometer?' 

Thank you for reading and please do leave comments/suggestions/feedback - would love to connect!

One constant question I have heard (proudly) from my five year old son is ‘why not?’ Especially when it involves the great outdoors, watching a movie, or an edible treat. When he uses the phrase 'why not?', it is one of those rare moments when I am actually happy my offspring sounds like me…!!! I have been contemplating blogging and publishing a website for some time now and after years of journalling and collaborating with some amazing professionals, I am saying why not?! I mean first publishing a public website and blog in my forties? Why not?! 

It always seems impossible until it's done.
Nelson Mandela

Carol Dwek inspired many of us with the simplicity of writing 'not yet' on the report cards of those students who 'failed' on their report cards. For me, this had nothing to do with report cards but everything to do with a classroom culture that encourages students to look forward, set goals, and take ownership over their own learning journeys. Using ''not yet' opens gateways as opposed to hitting a dead end. A feeling I get that resonates with that of which I get from Albie's response of 'why not?' is when my seven year old daughter makes a statement that she cannot do something, pauses, looks at me, and then says '...yet'. In these moments, I feel like I am doing something right with their upbringing. So everything after this moment has not been done.....yet. So why not?

Do not get me wrong. I am not saying we should say yes to every idea put on the table. Why not does not mean yes. I repeat, why not does not mean yes. I have learned this the hard way. As a young teacher, I formed a habit early of saying yes to every opportunity, including extra responsibilities, thrown my way. At one stage in my first five years of teaching, I took on the roles of transition coordinator, camps and excursions coordinator, first aid coordinator, head of sports, alongside being a full time classroom teacher of wonderful Grade 6 students. Although I did not burn out, I was on the verge of not having enough minutes in the day to complete the required tasks successfully and therefore learned the hard way how to say no. This does not mean I did not use the whole 'why not' approach. Instead of saying yes immediately, I learned to figure out the reasons why not. When there were valid and reasonable answers to that particular question, I simply said no.

There are those who look at things the way they are, and ask why... I dream of things that never were, and ask why not?
Robert Kennedy
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There are unlimited options for how, when, why, and in particular, what to teach and learn. The criteria for each of these depends on where and who the teaching and learning taking place. However, from my own experiences over the years, the biggest hurdle when planning collaboratively is the 'blocker syndrome'. This is where ideas, often involving change, at times bizarre and occasionally outrageous, are immediately shut down. The reaction that I have most commonly heard and even said myself is somewhere along the lines of 'that is not how we have done it in the past'. Although at times this can be a valid argument against new ideas, more often than not it simply blocks ideas that may become something bigger and better than what already exists. I am unsure of whether us educators are inherently afraid of change, whether we feel like it is a personal attack due to the ideas being brought forward challenging those ideas that were historically decided upon as being the best, whether we feel like just because it involves change it means we have to work harder/longer, or if it is another reason, but I do know there is something within team structures and cultures that almost encourages 'blocker syndrome'. I have been completely guilty of this in the past individually. So much so that I consciously listen to every idea put on the table and even look from a balcony view, where I step outside of being a stakeholder and vision what an 'outsider' would see, think, and recommend. Blocker syndrome revolves around the collaborative cultures seeing what is and asking why. What we all need to get in the habit of doing is seeing what could be and asking why not (thank you Robert Kennedy!). 

So... from this day forward when I question myself about why I am blogging, why I am teaching, why I am learning, when I get to a hurdle that seems insurmountable and I feel overwhelmed that I will be failing some time in the near future, I am going to put Albie's figurative shoes on and simply say to myself: why not?

May our impossible become yet and our could be become why not.  
Me!

Who is this blog for? Anyone interested in reading. And my future self. 

Thank you so much for reading and I would very much appreciate your feedback.  Feel free to reach out to me if you have any questions/comments/feedback you are not willing to share on this forum.