Teaching as Inquiry 2019
Learning Inquiry
In undertaking this inquiry I have had to make significant changes to how I plan for and deliver my maths lessons. There have been a number of new initiatives that I have attempted with varying degrees of success, but fundamentally the biggest change has been in my mindset. Previously, my approach to maths planning and teaching was very much skill based with students learning strategies and practicing skills in isolation. Now, through P.D with Dinah Harvey, and professional reading, I now approach my planning and teaching in a completely different light.
At the heart of this change is the use of rich tasks. I now use rich tasks 3 times a week and run these as whole class sessions. Students can choose who they work with, which often leads to the natural formation of mixed ability groups. In planning these tasks, I have thought carefully about allowing for multiple entry points and allowing for more than one correct solution. When this has not been possible, I have graded questions at different levels so that students can self select what difficulty that they would like to try. I have also made a deliberate effort to add a visual/hands-on component to the tasks with the intention of helping students to see that maths is more than just numbers on a page, but it is all around them in their everyday lives. The way I respond to students asking for help has changed dramatically through this process. I am now vary careful not to 'save' students with an answer, rather my approach is to use questions to help them to re-think the task, or to see it in a different way.
Coming back to the focus of my inquiry, which was to improve students number sense and boost their self efficacy, if I were to look across my class as a whole, there has undoubtedly been an improvement in these areas.
Beginning with number number sense, it is useful at this point to go back to the definition of this term:
The term "number sense" is a relatively new one in mathematics education. It is difficult to define precisely, but broadly speaking, it refers to "a well organised conceptual framework of number information that enables a person to understand numbers and number relationships and to solve mathematical problems that are not bound by traditional algorithms" (Bobis, 1996) - Nrich.com
The thing that has stood out for me this year is the way students have been able to better connect different areas of maths. As I stated early, my traditional approach to teaching was to teach strategies and skills in isolation, often devoid of a context. Through rich tasks, students in my class have been able to identify and discuss aspects of maths that overlap. This was particularly evident when the focus was on finding area in measurement after doing multiplication earlier in the year. By teaching multiplication through the use of arrays, students were able to physically see how multiplication questions could be presented in different ways. When we shifted to measurement, students were able to draw on their knowledge of arrays in order to find out the area of shapes.
The second part of my focus was for students to see themselves as mathematicians. I have often heard students talk negatively about their abilities saying "I can't do that" or "I'm not good at maths". The drive for me at the beginning of the year was to get students to flip this thinking so that they could believe in their abilities and not be afraid to attempt different maths tasks.
The was I did this was to, where possible, present problems that had a low floor and high ceiling. Put simply, this means designing tasks that could be attempted by any student, regardless of skill level, but also had the scope for students to take it as far as they wanted to go.
By doing this, I had less students 'switching off' from the outset when they deemed that the learning was beyond them. Instead I found that my students were more willing to give problems a go as they felt confident that they could achieve a level of success.
Another way in which I have promoted student self confidence in their abilities is by providing a wide spread of maths tasks extending across number and strand. In the past I feel that my programme has been more weighted towards number activities. By providing more strand activities, I have noticed that some students who would typically struggle with number type activities have been able to shine and excel. I believe that part of the reason for this is due to the more hands on nature of strand. This was particularly evident during our focus on geometry where students which required students to design patterns and create lines of symmetry.
Looking specifically at my target group, the tables below show the data gathered in Term 1compared with data gathered in Term 4.
Target Group:
Beginning Data (Term 1)
End Data ( Term 4)
As the data shows, there has only been a minimal improvement in student test scores from the beginning of the year to the end of the year. I am not at all surprised by these results. It is my belief that changes in knowledge and strategy levels will occur more gradually over time. Teachers across the school are undergoing similar changes to their programmes, and as students become more familiar with this type of maths learning, they will naturally grow in confidence. Student confidence in their capabilities as mathematicians needs to first improve before there is any significant growth in their performance.
Maths Attitude Survey data shows no improvement in student confidence, in fact for some students, their survey results show a decrease in confidence. My observations of classroom learning, however do not fully marry with these results. Jess for example is now by far-and-away more confident in her abilities. I put this increase in confidence down to her working in mixed ability groups, who are often her friends. When working with her friends, Jess is more confident in sharing her ideas and she is able to glean new more efficient strategies from them that she would otherwise not have known.
In summary, I am now fully invested in this approach to maths teaching. The research supports this type of approach and If we continue to have buy across the school through continued professional development, then improvements in student confidence, and subsequently performance, will continue to trend upwards as they move through the school.
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