We have noticed significant improvements in the following area’s.
Experimenting and estimating results
As students have come to better understand the influence of their disposition they will be better equipped to self regulate their learning (including how they work mathematically).
The time spent exploring and understanding not only the different dispositions but how they fit into working mathematically and how working mathematically fits within the syllabus has been invaluable and no doubt a worthwhile learning experience. Whilst it was a learning experience it also enabled me to assess the influence of working mathematically with my students. From this learning I’ve developed working mathematically learning intentions and success criteria, checklists to monitor how and when students use these skills, and finally assessable rubrics to assess properly the outcomes linked to these skills.
The measure of success, though academically, is based on the content of what we teach rather than the way students work. Working Mathematically helps students problem solve and reason their strategies when learning. Whilst it doesn’t link directly to the content of learning how to add and subtract 4-6 digit numbers, it does allow the students a framework. The framework gives them the pathway to create mathematical hypotheses, solve their own problems by testing what went right or wrong, and reason and communicated that reason for why it did or didn’t work.
Changing the mathematical disposition of students and the way they approach mathematical problems.
Changing the mathematical disposition of students is interesting. The youcubed framework provided students with opportunities not only to work with different challenges, but with a different mindset approach with each task. To consolidate this task we asked students to create a poster that displayed their mathematical disposition. Below are a few of the best examples taken from our classes.
By students creating their own growth mindset posters on what has changed in their own mathematical disposition it provided students with an authentic task to not only apply what they had learned, but also apply it visually (Make maths visible).
The Next Step
The next step whilst we could definitely attribute this to both content within the syllabus and the working mathematically outcomes, however we need to analyse exactly where this fits within the working mathematically framework and content strands to see if this really is measurable, and assessable.
How does a change in mathematical disposition and working mathematically work together?
To tackle this question it is necessary to completely strip down what working mathematically is and how it fits not only within the curriculum but also within the content. The statements and definitions of working mathematically can be stripped back to the most basic of elements. Working Mathematically is divided into 5 different areas.
To further understand exactly what is required when working mathematically and to understand what we are looking for in students the working mathematically detailed descriptions were used to build Learning intentions and Success Criteria for each element.
Within our grade team, this deeper unpack led to a greater focus on Reasoning, Problem Solving and Communicating. This is because the skills that students display from the core of the Youcubed framework actually work hand in hand with working mathematically.
The many ways we see mathematics. – Problem solving
Mistakes are beautiful things. – Reasoning
When you believe, amazing things happen. – Problem Solving and Understanding
Conjectures, creativity and uncertainty – Problem Solving and Reasoning
Engaging visual pathways. – Problem Solving, Communicating, Reasoning, Understanding
Strategies for learning maths. – Reasoning and Fluency
Speed is not important – Problem Solving, Fluency, Reasoning
Our brains constantly change and grow. – Problem Solving and Reasoning
Believe in yourself. – All five areas
This led to – the influence of working mathematically when students are tasked with problems.
During our professional learning, our leadership team challenged us to develop our own PBL style driving question and mini project to present. In developing the driving question, it made me stop and evaluate exactly what I wanted to achieve or change with students from the beginning of the year. Throughout my teaching so far, I’ve noticed that mathematics anxiety is possibly the single most achievable change I can make to students mindsets. To develop be able to develop my students’ attitudes towards mathematics, I have dabled in the “Growth Mindset” use before within my classrooms, but I wondered what would happen if I was persistent in the use of the Growth Mindset disposition all year.
At the beginning of the year, we started our mathematical learning in the classroom with the Jo Boaler – Youcubed website. To be honest it was an extremely eye-opening experience not just to teach, but to experience as a learner. It is based on growth mindset pedagogy and its influence on a learners ability in Mathematics. The main idea being that Jo Boaler challenges the myth of “I’m bad at math“.
The Youcubed work falls under these categories.
The many ways we see mathematics.
Mistakes are beautiful things
When you believe, amazing things happen
Conjectures, Creativity and Uncertainty
Engaging Visual Pathways
Strategies for Learning Math
Speed is not important.
Our brains constantly change and grow.
Believe in yourself
There is a lot of evidence based on information and research behind the work students do. This can be broken into two different realms.
Displaying student voice and experiences
The Two Approaches
The first approach in terms of activities are either mathematical puzzles (1 cut geometry) or challenging questions such as Peter Sullivan’s approach, where students prefer math when you let them figure it out. These are fantastic learning opportunities for students to improve their knowledge and a deeper understanding of mathematics.
The second approach is providing students with evidence-based research; videos that are student friendly explaining having an open mind or growth mindset.
I believe it is the key to the whole learning experience.
The tasks are challenging, not just a little challenging, they are quite challenging for myself. So much so when we’ve posed these problems it has been totally and utterly important for the students to be able to walk away understanding that they don’t know the answer (Remember speed is not important) That said I’ve gone of and then either worked on it for hours afterwards at home or asked some of my friends that are mathematicians how we solve the problems.