This will be our last blog week for 2018! We wish all teachers, educators and their families a happy holiday and we hope you all get a well-deserved rest. We will be adding up some resource and courses over January so look out for new items and keep coming back to the site to see what’s new.
Although most teachers need, and will take a break, next year is always looming and it’s hard to stop your brain from starting to plan! So, with that in mind, I thought it would be good to share some ideas for things to read, explore and ponder over the school holidays.
1. Books for your own growth as a (mathematics) teacher
Becoming the math teacher you wish you had by Tracy Zager
This has been one of a couple of amazing books I have purchased this year that has consolidated much of what I already knew or believed and also provide ideas for future directions and ways to build and encourage young mathematicians’ minds. The book is published by Stenhouse and there is a companion website for the book that is a treasure-trove of awesomeness that you’d most definitely soon see is the ‘Inception’ of websites- in a good way.
Necessary conditions: Teaching secondary math with academic safety, quality tasks and effective facilitation by Geoff Krall
I’ll admit I don’t actually have this book, as my focus is on primary education, however there has been many mentions of this new book on Twitter by teachers and researchers I admire. So, if you teach in a K-12 school or are specifically a secondary teacher, this may be a good purchase. This book is also published by Stenhouse and they have a companion website for this book as well.
2. Readings, to keep up with current research
Some current trends in mathematics research that might be of interest to classroom teachers include challenging tasks, building teacher capacity and student engagement.
The focus on challenging tasks has been emerging over the last few years as research studies increase in number. These studies focus on what challenging tasks are, when and why are they useful, when to use them in a lesson, how do teachers and students perceive them, just to begin with. A starting point might be to read Sullivan, Askew, Cheeseman, Clarke, D., Mornane, Roche and Walker’s paper Supporting teachers in structuring mathematics lessons involving challenging tasks. The article sets the scene for why using more open-middle or open-ended tasks may be beneficial for students.
“… the traditional lesson structure of teacher explanations followed by student practice and correction of answers is inadequate. The alternate structure of launch-explore-summarise (see Lappan et al. 2006) is more likely to facilitate the conversion of tasks with potential for Doing Mathematics into lessons.”
Supporting teachers in structuring mathematics lessons involving challenging tasks, by Sullivan et al. (page 125)
I have included some further papers on challenging tasks below in the reference section, this is not an exhaustive list!
Dr Catherine Attard from Western Sydney University (whose own research on student engagement is well worth reading, see below) shared this article last week concerning Constructivism as a learning theory. This is important to understand that it is a way students learn not a way teachers teach.
Interesting article with implications for how we teach maths. Constructivism is a theory of learning, not a theory of pedagogy. Neuroscience explains why this is important https://t.co/xiHujXUI17 #npjscilearn @MTLC_ACU @AISNSWPrimary @learnPSNSW @mav_info @TCM_at_NCTM @aamtinc— Dr Catherine Attard (@attard_c) 7 December 2018
As teachers we are all still learning. Research into how to build teacher capacity and capabilities through quality professional learning is a continual focus for schools and teachers. There is no magical list of how to go about creating the ‘best’ professional learning, different things work in different places and there are many external and internal influences that effect how we as consumers (the teachers) take on, or not take on, what we have learnt. Rob Proffit-White tweeted about his keynote at MAV conference last week where he was sharing research from Queensland schools that participated in collaborative communities of practice.
“The project developed a cluster model for bringing together primary and secondary school teachers to build their curriculum knowledge, confidence, and enthusiasm for teaching mathematics.”
Sustaining and scaling up research-informed professional development for mathematics teachers, by Goos, Bennison, and Proffitt-White
3. Think about online resources
Whether you are thinking about this as an individual teacher or as a whole school, it’s a common question I see on social media or that I am asked about directly. Which online (if any) mathematics program should we subscribe to?
It’s hard to answer as I’m not keen to be seen as ‘endorsing’ products but here is my current thinking. Any online product your school purchases will have good and bad aspects. Online mathematics ‘games’ or programs are not a replacement for quality teaching and should be used within a balanced classroom program to support practice of specific skills that need consolidation- none of them provide ‘teaching’. I would prefer not to use any of them as I don’t like that there is a cost involved, that being said, if schools are still keen to invest in some form of online product you need to be able to critique and justify your decision.
Most products will be appealing in some way to students, either the ‘bells and whistles’ of the graphics or the competition side of the product- this doesn’t necessarily equate to ‘student engagement’.
Whichever way you choose to go, just be critical, get a free subscription, think about how it may help students, how it may hinder them, what aspects are good, what aspects may not be so good etc. There are a couple of researchers that provide advice about critiquing online resources Tracy Zager makes some good comments, scroll down to her added clarifications for her ‘brain dump’ of what to look for. In a nutshell she asks three important questions:
- Is there time pressure?
- Is it conceptual?
- How does it handle mistakes?
These questions are a great place to start when contemplating any online ‘program’. See Catherine Attard’s paper below as well.
Some free places to visit include:
These are sites that are good for building student skills and problem solving which is helpful in supporting students.
4. Teaching ideas to think about
Along with Number Talks and quick images, I have recently seen the emergence of #unitchat on Twitter as another way to hook students and engage them in mental computation. I suggest you check it out on Twitter, be careful, it can get addictive!
If you're looking for an incredibly captivating set of images for counting, talking about units, how many you see, number talks, and countless other reasons, please check out the mesmerizing art from @witenry at https://t.co/2t4syFhrGP #unitchat #howmany #tmwyk #iteachmath #MTBoS pic.twitter.com/HI4E1YdRpn— Robert Kaplinsky (@robertkaplinsky) 17 November 2018
“the hashtag #unitchat, for prompts and discussion of fun and ambiguous counting challenges.”
Talking math with your kids, by Christopher Danielson
5. What will my first-week-back mathematics lessons look like?
Assessment of students’ prior knowledge, skills and processes I’m sure is a focus for most schools at the beginning of the year but what could these look like in the classroom?
If we are focusing on the working mathematically processes of the NSW K-6 syllabus then assessing students beyond purely content knowledge is necessary. I think there is merit in organising your fist week around Kilpatrick, Swafford and Findell’s proficiencies of mathematics strands. These strands are overlapping and intertwined, just as our working mathematically processes are. Using them to organise your lesson investigations and pulling them apart allows you to focus on specific aspects of mathematical proficiency that students may be excelling in or are needing assistance in developing. I have purposefully left out specific tasks for [procedural] fluency as I see fluency as an overarching organiser of proficiency in mathematics. Fluency comes as these areas develop and as students move towards ‘mastery’ or ‘proficiency’.
Conceptual Understanding and Adaptive Reasoning
- Start by having students write everything they know about a specific concept. You can do this by writing a statement on the board and allowing students time to talk and write about if they agree or disagree with the statement. E.g. For number structure write, ‘All two-digit numbers can be represented using tens and ones’ True or False?
- Place a range of stage-appropriate mental and written strategies on the board (name only e.g. compensation). Ask students to draw and or write examples of what they look like. Then ask students to talk about and give an example of when you might use them and why, when you use it, it would be the ‘best’ strategy. This encourages students to both show their number sense knowledge and show transference of this knowledge into a variety of familiar and new situations.
- Ask students to write about how they feel towards mathematics or within mathematics lessons. There are two great tasks used in research for this. One is drawing a picture of yourself learning in mathematics class (e.g. Drawing on Math) and the other is using metaphors, if mathematics was a food it would be… (Taing, Bobis, Way, & Anderson, 2015).
Well, thanks for reading our blogs! We look forward to starting up again mid-January when everyone has hopefully had some rest, relaxation and time to reflect.
Attard, C. (2018). The Euclid Project: Improving Middle Years Student Engagement With Mathematics Through Action Research.
Attard, C. (2018). Financial literacy: Mathematics and money improving student engagement. Australian Primary Mathematics Classroom, 23(1), 9.
Attard, C. (2016). Research Evaluation of Matific Mathematics Learning Resources: Project Report. Penrith, N.S.W.: Western Sydney University. doi:10.4225/35/57f2f391015a4
Attard, C. (2014). ” I don’t like it, I don’t love it, but I do it and I don’t mind”: introducing a framework for engagement with mathematics. Curriculum Perspectives, 34(3), 1-14.
Cheeseman, J., Clarke, D., Roche, A., & Walker, N. (2016). Introducing challenging tasks: Inviting and clarifying without explaining and demonstrating. Australian Primary Mathematics Classroom, 21(3), 3.
Goos, M., Bennison, A., & Proffitt-White, R. (2018). Sustaining and Scaling up Research-Informed Professional Development for Mathematics Teachers. Mathematics Teacher Education and Development, 20(2), 133-150.
Kilpatrick, S., & Swafford, J. (2017). Findell.(2001). Adding it up: Helping children learn mathematics.
Lappan, G., Fey, T., Fitzgerald, W. M., Friel, S., & Phillips, E. D. (2006). Connected mathematics 2: Implementing and teaching guide. Boston, MA: Pearson, Prentice Hall.
Livy, S., Muir, T., & Sullivan, P. (2018). Challenging tasks lead to productive struggle!. Australian Primary Mathematics Classroom, 23(1), 19.
Russo, J., & Hopkins, S. (2018). Teachers’ Perceptions of Students When Observing Lessons Involving Challenging Tasks. International Journal of Science and Mathematics Education, 1-21.
Russo, J., & Hopkins, S. (2018). Teaching primary mathematics with challenging tasks: How should lessons be structured?. The Journal of Educational Research, 1-12.
Russo, J., & Hopkins, S. (2017). How Does Lesson Structure Shape Teacher Perceptions of Teaching with Challenging Tasks?. Mathematics Teacher Education and Development, 19(v1), 30-46.
Sullivan, P., Borcek, C., Walker, N., & Rennie, M. (2016). Exploring a structure for mathematics lessons that initiate learning by activating cognition on challenging tasks. The Journal of Mathematical Behavior, 41, 159-170.
Sullivan, P., Askew, M., Cheeseman, J., Clarke, D., Mornane, A., Roche, A., & Walker, N. (2015). Supporting teachers in structuring mathematics lessons involving challenging tasks. Journal of Mathematics Teacher Education, 18(2), 123-140.
Taing, M., Bobis, J., Way, J., & Anderson, J. (2015). Using metaphors to assess student motivation and engagement in mathematics. Proceedings of PME 39, 4, 233-240.