CoL Inquiry - Part Four (Testing Reflection T2)

 Last time we spoke I mentioned that we would be running an eAsttle Maths test. I always try to remember that tests are a diagnostic; a way of identifying areas of strengths, and weaknesses, and gives us, as teachers, a really good opportunity to reassess what has worked, and what we need to improve on, not a reflection of how good we are as teachers, or how well my students learn. It is merely a snapshot, and even if it feels discouraging, it is not the whole story,

In this round of testing I have a mixed bag; for context, at this stage (Term 2) students at year 6 who are achieving at the norm achieve a 3P in their eAsttle tests.

The testing results for the students in my inquiry focus group (names excluded) are as follows; 

- 3 scored a 2B (more than 2 years below norm)

- 3 achieved a 2P (2 years below norm)

-  2 achieved a 2A (1.5 - 2 years below norm)

- one student achieved 3B (0.5 - 1 year below norm)

- one student achieved 3P. (at the norm)

It can be difficult when trying to align the results to see progress; eAsttle, PAT and Gloss all have their own scales, and scoring systems which can make it difficult to get a clear picture of progress. One of the things I will be doing in Term 1 of next year is being consistent with the testing to ensure I have a clearer picture of their progress as the year goes own. This will be alongside the school wide testing that we are required to do (PAT).

I will also be conducting Gloss tests, and will share my findings as Term 3 goes on.

 

CoL - Part Three (CPA Approach)

 Teaching Maths was the thing I was most intimidated by when I made the move to primary teaching. I am an English major, and trained as a teacher of English. My learning journey with math was an interesting one. I did well when I was at in primary; I was good at following the "algorithms". I was lucky enough to live in and attend school in Chile, and was learning long division by 8 years old, but I think algebra was where the problems started. Dealing with unknown variables, and identifying patterns by applying formulas was very confusing. "What happened to 8 + 9 is 17, carry the one...?!" . It seemed that everyone who did well was in on a secret that I wasn't privy to. Their brains were able to unlock the mysteries of maths, and I felt like I was locked out.

I made a promise to myself, that I was going to do what I could to ensure that no student in my class was going to feel as lost, and confused as I was. I didn't know how best to do that, and 4 years after becoming a primary teacher I am still figuring it out, however. I think I have found something that has changed my view on maths, and I hope can help my own students to learn maths by giving them the keys that will help them unlock the "mysteries" of maths.

I found myself trying to read as much as I could about conceptual understandings; I felt like if my students could build a strong conceptual understanding in my next unit, that it would allow them to apply sttrategies to a wider range of problems, including word or picture problems which require inference, and comprehension on top of mathematical problem solving.

Identifying what my students problem is has been a multi-fold approach; I've looked at their results in PAT Maths, Gloss, and through my observations in class. My original hypothesis was focused around the fact that they needed support with their vocabulary, and that that was a major limiting factor in their ability to solve problems, like the ones in PAT tests, and activities in the Caxton textbooks. What I have observed and noticed is that a lot of them do not have much confidence with the overall concepts. If the question is easy to understand, even if the mathematical operation is challenging, they can apply their strategies to it. 

What I would like to do know is to continue supporting their vocabulary, but also to improve their confidence and self efficacy when it comes to solving the wide variety of problem types that they will encounter. 

The CPA approach was one that resonated with me early on; developed by psychologist Jerome Bruner it's focus is on building conceptual understanding of maths by working through stages; concrete, pictorial, and abstract.

The Concrete element involves the use of materials; for my students this was particularly instrumental in helping them develop their conceptual understanding of multiplication and division. Being able to move blocks, or beans, or money around, and physically manipulate these objects meant that strategies like grouping, repeated addition, or subtraction had practical meaning. I think this approach was the most pivotal, as I could see them responding, and understanding. Those "ah ha!" moments that we cherish so much as teachers were really evident in this stage.

We then moved on to the Pictorial stage, in which students could see visual representations of the problems; this worked really well with arrays, and grouping as well because they could see the objects they were being asked to apply their strategies to. 

The Abstract stage being the final stage of the approach is one that really threw me for a loop the first time I read about it; I grew up doing maths with symbols from a very early age, and it hadn't clicked to me that these symbols and digits were abstract representations. Once I started to think more carefully about when I gave my students these abstract questions it became apparent that my sequencing had been askew.

The other aspect to this was based on an interesting article that was shared with me from a couple of different people, and obviously it resonated with them, so I delved into it. The original article was an Op-Ed published by the University of Auckland, titled "What maths teaching could and should learn from cognitive science" - it spoke on the fact that these "exploration" type of maths lessons showed no discernible benefit to student's learning. Following up was the article that was referenced in the Op-Ed which was a paper titled "Why Minimal Guidance during Instruction Does Not Work: an Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching".

This was again, pretty eye opening; it spoke about the fact that simply allowing students to explore concepts with little or no scaffolding or support in the form of explicit teaching, meant essentially that we were relying on students to learn simply by exposure or osmosis. There needed to be concrete, explicit teaching of these concepts if they were going to be able to learn, retain, and apply them to the wide range of problems they will be faced with.

We have recently come to the end of a 5 week unit, beginning with multiplication, moving on to division, and then to applying strategies, and will be conducting an eAsttle test on them in the next week, I'm excited to see if the results reflect the progress they have made in group work; knowing they can do it with me, it's time to see if they can apply these concepts with the training wheels off, so to speak. 

I'll see you guys in the next instalment!

References:

Bourtzinakou, E. (2023). Developing Mathematical Reasoning; The role of the CPA model in students’ progress from standard to Reasoning and Problem-Solving questions. https://www.et-foundation.co.uk/wp-content/uploads/2023/02/The-role-of-a-CPA-model-in-developing-mathematical-reasoning_Gateshead-College-CfEM-action-research-report-2021-22_compressed.pdf

Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why Minimal Guidance during Instruction Does Not Work: an Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching. Educational Psychologist, 41(2), 75–86. https://doi.org/10.1207/s15326985ep4102_1

Main, P. (2021). Concrete pictorial abstract approaches in the classroom. www.structural-learning.com. https://www.structural-learning.com/post/concrete-pictorial-abstract-approaches-in-the-classroom

N.A What maths teaching could and should learn from cognitive science - The University of Auckland. (n.d.). Www.auckland.ac.nz. https://www.auckland.ac.nz/en/news/2024/04/10/What-maths-teaching-could-should-learn-from-cognitive-science.html

CoL Inquiry - Part Two (Diagnostic Tool)

 After deciding that I was going to create a diagnostic tool to determine my student's understanding of different mathematical concepts it was now time to create the tool.

I wanted the tool to function as a standardised way of checking if they were able to understand what the different strands of mathematics were asking of them, and not assess whether or not they could solve the problems.

In this question, I wanted to know if they would be able to match the term, to the definition, to the example. 

In this one, they needed to be able to order the sequence of problem-solving steps.

I ran the test with a sample group of students; I didn't use my target group for the prototype testing - my rationale for this was to try and get a sampling from a range of different abilities, reading levels, and attitudes towards maths. The prototype was tested by 11 different students, and the results were a little disappointing - not because I felt like they hadn't succeeded, but because I felt that the test itself was too confusing. In the reflections with students they were unsure what they were being tested on, and that some of the questions were confusing, even for the extension students.

This leaves me at a bit of a crossroads, is the test tricky because I have made the questions and the tasks too confusing, or is it an indication that this test actually challenges their ability to comprehend the maths concepts, and it's actually revealing holes in their understanding?

I am going to gather feedback from my colleagues, adapt the test using Google Forms to see if the more rigid structure can work as a scaffold them and remove ambiguity. Hopefully the results will show me there is merit in continuing to pursue this diagnostic tool.

In the mean time, I am continuing to explore the CPA Approach to my maths teaching. Check out the next post to learn more about CPA, and how it has been working out in Room 8.

CoL Inquiry - Part One

It's been a couple of weeks since my students sat their PAT Math test, and so I've spent a lot of time reflecting on their results. At the start of each year we use these tests to help us to understand our students better; to see which areas of maths they succeed at, and which ones they are struggling with. 

The target group for my inquiry cycle will be a group named Storm; students in this group have OTJ's which place them around Level 2 of the NZC and they averaged a 3.3 Stanine in PAT testing. 

There are 10 students in this group, and with a group this large there is a wide variety of self-efficacy, interest, and enjoyment when it comes to maths, so, to get a better understanding of who they are as Maths learners I conducted a Student Voice survey; of the 10, only 3 felt that they were "good at math", the others did not know (good news is, none of them thought they were not good). 

They were pretty divided on how they felt about maths; a couple of them used only positive words to describe maths, words like "fun" "interesting" or "exciting", but what was interesting was that almost half of them used the word "stressful" to describe it, including some of those students who also said it was fun, and interesting.

I found this dichotomy super interesting, because, to me, it mirrors my own feelings towards maths. As a student when I encounter concepts that I do not understand, it is stressful. It's like trying to solve a puzzle, but half of the pieces are from another puzzle, no matter how I try to apply my learning and try to make the puzzle pieces fit, they just won't; however, if I find the other pieces, if I strengthen my understanding of a concept, or a formula, or a strategy, suddenly the pieces start to fit, and that is what lead me to the most recent development in my inquiry.

Do my students have a well-rounded understanding of the concepts and vocabulary that we cover? 

Do my students understand that addition is calculating the combination of 2 or more numbers, or that multiplication is the repeated addition of the same number, for example. How do we expect them to apply strategies to concepts that they are not fully aware of? How can they be adaptable, and flexible with their application if they do not first understand what they are being asked?

Without trying to cover the wide spectrum of concepts in the math curriculum I chose to focus on the two areas of maths in which my students achieved the lowest results; Number Strategies, and Algebra, and to work out where their understanding of the concepts within them are.

It is easy to assess their ability to solve problems in these areas, we teach a strategy, we give them a problem, and either they solve it correctly, or they do not. Testing their understanding of the concept is proving to be a little harder. After discussion with my colleagues, and conducting research of my own I could not find anything that fit my needs, GloSS testing where students explain their strategies, and eAsttle tests gave me some insight, but not an umbrella view of what they understand these concepts, and words to actually mean.

What I would like to do is build a diagnostic test, or interview that can assess whether or not they understand what a concept like "addition" is, rather than test their ability to add together numbers.

I'm working on putting together a prototype at the moment, so check back in to see what I've got soon!

MIT 2023 - The End of the Journey

As my father always told me  "All good things must come to an end", and this MIT journey for 2023 has finally come to an end. It is a bittersweet goodbye. I walk away from this project with a tremendous sense of pride in what we have accomplished together. MIT 2023 has been one of the most significant highlights of my year and has opened up so many opportunities, discussions, conversations, reflections, and friendships that have improved my practice and my outlook on teaching; the value of the MIT project goes far beyond the tools we have created, it is an opportunity to take part in a community of learning that is equal parts fun, inspiring, and motivating.

MathVentures is just the beginning; starting my investigation into math vocabulary has inspired my next inquiry cycle; investigating how we can continue to help our students comprehend the word problems they encounter in maths, and how we can support our students to build a robust math vocabulary that will help them to better understand how maths is applied in more real-world contexts.

Check out MathVentures here!

 In a way, the end of this journey opens up a door to a whole new set of opportunities to learn and develop my practice, and in turn, improve the outcomes for my akonga. As lifelong learners I think it is so critical for us to continue to pursue these avenues as they open up to us, and while MIT has come to an end this year, it is the start of a whole new journey.

I would like to first acknowledge my fellow MIT alumni for 2023; Crystal, Michelle, Essie, Jayne, and Maiken. You guys have been a blessing to work on this project with. Without the support and encouragement from you guys, I don't know if my project would have reached the stages that it is at now. Thank you so, so much. I am so lucky to have been a part of such a cool crew, and I won't forget our adventures any time soon! That boat trip to Russell is easily one of my favourite memories. 

Secondly, I would like to acknowledge the tremendous work put in by Matt Goodwin, Dorothy Burt, Justine Todd, and Jenny Oxley; the knowledge, experience, and feedback they have given us along our journey have been invaluable, and their contributions to our projects cannot be understated.

I cannot recommend this program highly enough, if you are thinking of applying, please do. You will gain invaluable insights, relationships, and confidence in your own practice that is hard to come by elsewhere.

Kia ora rawa atu,

Gabe

Response to Manaiakalani Kāhui Ako - CoL 2023

What achievement challenge are you considering as an area of focus in 2024 and why? Include in your WHY both evidence and your own passion/expertise

The Achievement Challenge I have identified as an area of focus is to lift achievement in maths through the building and development of math vocabulary. For my MIT23 project, MathVentures, I focused on how to help support students unpack maths problems with unfamiliar vocabulary, and while this tool was engaging, and effective I believe I need to develop something more robust in my own practice to help them build the literacy vocabulary needed to accelerate, and perform to their full capabilities in maths. I fundamentally believe that being literate is the key to success in academia; not just in reading prescribed texts, but also in being able to tackle unfamiliar texts, across a range of subjects, and having the confidence in their skills to make sense of increasingly complex, and more subject-specific texts as they continue their learning journeys into intermediate and secondary.

What learnings from the 2017 - 2023 CoL teacher inquiries have informed or inspired your thinking?
Looking over a variety of the different inquiries from CoL teachers I have found a number of them that are focused on accelerating our student's maths progress (Hannah, Clarelle, Elena), and a number that focus on vocabulary building (Robyn, Dianne) but none that I could see which focused on inquiring into our student's subject-specific vocabulary in maths. I feel like there is a great opportunity, which will also align itself with the new developments in NCEA with subjects now having a literacy co-requisite, to build our student's confidence in decoding and comprehending written math problems. I hope, as a result of this inquiry, that my students will feel confident in tackling a wider range of word problems in maths.

How would your work support Manaiakalani pedagogy and kaupapa?
By making my inquiry visible, and accessible to all through both my blog and our Team 4 Class Site I can support teachers through my visible planning, reflections, and my own decision-making processes. Following the Manaiakalani model of "learn create share" I will ensure that not only does the work that my students are doing follow these principles but that my own learning journey through this inquiry mirrors them too.

Which elements of the extensive Manaiakalani research findings inform or challenge you as you think about this?
The data in EdPotential provided by the Manaiakalani Research team, and Woolfe Fisher, as well as a closer examination of my classes' PAT results, indicated to me that there is a need to make an accelerated shift in our progress in maths. Anecdotally I found that a lot of my students had conceptual knowledge of different number strategies, and place value, however, when faced with a word problem that required comprehension, as well as the application of a strategy, they fell short. I would like to undertake an inquiry that focuses on a larger, and more overarching area of maths instruction (vocabulary building) that I feel doesn't get the attention that it needs through deliberate planning and implementation.
How would you like to be supported in 2024 as you undertake this inquiry?
I have applied to be a participant in the Maths Program Intensive as a way of developing my professional understanding of how to construct and plan for maths effectively, as well as any other PLD opportunities that are available. I will also take on all opportunities to discuss my inquiry process with my colleagues and to gather feedback on what they feel they need to best accelerate learners across different levels. I hope to be supported in finding academic research, and PLD that will help me to guide my inquiry.

How would you plan to support your colleagues in your school with their inquiries and/or teaching in the area you are exploring?
As with everything that I do, my findings will be ubiquitous and visible throughout my journey; I am also willing and able to share this process through opportunities like Bursts and Bubbles, the CoL meetings, classroom observations, and the Manaiakalani online toolkits. I will not have all the answers, but through this process, I hope I can engage other teachers, and demonstrate my own learning process in the hopes that it can offer them something by which they can accelerate their learners' progress too.

MIT 2023 - Bay of Islands Summit

What an experience! Sorry, this could be a long post.

As part of our journey for MIT23 we are lucky enough to be presenters at the Bay of Island's Teacher's Summit 2023. This summit was an incredible opportunity for so many reasons; meeting new people, discussing interesting ideas, and learning new skills, and tools that we can take home for our akonga. 

The journey up began bright and early on the first Saturday of the school holidays. Forgoing the usual bliss of the first sleep-in of the holidays, I gathered my bags and was dropped off at school. I load the school van and pick up my trusted travel companion, Mr Goodwin on the way. The weather on the way out of Auckland had me dreaming about the "Winterless North". Rain poured for hour after hour, when finally we reach Kawakawa, less than half an hour from our destination, and more than an hour ahead of our airport run. We were feeling good. With our satnav turned off, and arrogance coursing through our veins we follow the path through Kawakawa, and head north over the "up downs" (iykyk). 

After another hour of driving we become suspicious that something had gone awry. "Surely we should be there by now. Surely we can't have missed the signs." Ahh, yeah. We had. I'm not sure how familiar you are, reader, of New Zealand geography, but let me give you a fun fact. Oponone (where we were) and Paihia (where we should have been) are on opposite coasts. Feeling about as dumb as it's possible to feel, we reluctantly turned on the satnav to inspect the situation. Maps said we should be okay, we continue this road, hang a right, 9km of bush road, and we'll be right back to where we should be. I'm still thankful to whoever decided, as we made our way through hairpin turns, and narrowing unpaved roads, to turn the rain off. The only dry part of our drive was through the bush, and by golly, that was lucky. 

What was even luckier was that after the slight detour, we arrived at the Kerikeri Airport just as my fellow MIT colleagues walked out of the airport, none the wiser that they might have been stuck there had we not made it out of the bush.

On our way to the accommodation we catch up; it's been such a lovely experience working alongside these teachers. They are creative, passionate, and as the title of our program would suggest, innovative, and I'm so lucky to have worked alongside them this year. We remark that this will all soon come to an end and that we're going to have to make sure we keep in touch after this is all said and done. 

We're up bright and early for our first day of the Summit. The day begins with a beautiful powhiri, and a korero from the respective rangatahi. The keynote speaker for the event was the principal of our gracious host school, Bay of Islands College, Mrs Edith Painting. 

The first day was comprised of several wonderful workshops, a beautiful kai for lunch, and an awesome cultural experience. I chose to visit the Waitangi Treaty Grounds; I hadn't been since a teen, and my knowledge and understanding of Te Tiriti had definitely increased my hunger to learn more about such a significant place in Aotearoa New Zealand history. 

Day two was our turn. We were the first presenters, and unlike the other presenters, who were only presenting to a classroom full of teachers, we presented in the hall in front of all of them. I'm sure many of you will empathise; the classroom is our safe space, and where we feel most comfortable speaking publicly. Speaking in a hall, at an assembly, or at a summit, that's another kettle of fish. 

One of the best parts of this program is that we never have to do anything on our own. The support and encouragement that we give to each other was such a strong help, and I don't know if I would have been able to do the same on my own. 

I'll leave you with a couple of links to explore if you'd like to see more of our adventure! It was honestly such a blast, and an experience that I will not forget.

Bay of Island's Summit