A Brand New Voyage!

 

I start, and finish every year off with such a great sense of excitement; Christmas, New Years, and long, merry days in the sun wondering what the LD50 is for ham.

This year brings even more excitement as I venture away from the place I've called home for the last 5 years and begin my journey as a Manaiakalani Facilitator.

If we've never had the pleasure of meeting my name is Gabriel, for the last 4 years I have been a Year 6 teacher at the superb Pt England School. I don't want to reflect on my time there too much, other than to say it has offered me the opportunity for a renaissance in my passion and love for teaching, and I am so grateful to Russell, Kent, Kelsey and all of my family over there. 

I grew up in the Tāmaki / Maungarei area, attending Sylvia Park School and Selwyn College and so it is such a privilege to be able to continue serving this community in the best way I can, returning all it has given to me over the years. 

In my time outside of teaching you can find me on the softball diamond (playing or coaching), on the oche (that's a word only dart nerds know), or trying to lift something heavy. 

I look forward to continuing to share my journey with you all, friends new, and old. Keep an eye out for what I'm getting up to this year.

CoL Inquiry 2025 - Part Seven (Finale)

 When I began my journey as a primary school teacher five years ago, I was terrified of teaching maths.  As a student, numbers scared me, and my biggest gripe with word problems was figuring out why a person would own 342 watermelons in the first place.

In my first year, though, I noticed something interesting. The students who struggled weren’t those who could calculate, but the ones who couldn't decode the word problems. Their fundamental barrier to success was not the math; it was the language.

To address this, last year, I introduced a neo-traditional approach to my teaching, borrowing elements from traditional and combining them with more contemporary approaches to improve conceptual understanding. This year, I wanted to focus on how we make sense of word problems in a more explicit way.

Our adoption of the Pr1me Maths program gave us an incredible framework, clear vocabulary, and the CPA approach. However, it quickly illustrated that our students were still having difficulty with the phrasing and unfamiliar terminology.

To tackle this, my first focus was to be deliberate and consistent in the language I used when teaching concepts. Answers were no longer answers; they were sums, differences, quotients and products. We didn’t “carry” or “borrow” I“regrouped.” This consistency helped my students feel more secure in making sense of the problems.

Secondly, I focused on making word problem solving a literacy task. We worked to identify what was being asked of them by using the “3 Reads Protocol” strategy, which forces students to slow down.

• What is the problem about? (Just the story, no numbers.)

• What is the problem asking? (Focus on the question.)

• What are the important numbers? (Identify the facts.)
  

This helped them move away from just hunting for keywords and their compulsion to calculate. I also created a guide book to help them categorise questions and apply the correct strategies, which further reinforced this new approach.

To test the efficacy of these deliberate changes, I used a customised eAsttle test and compared the results to the start of the year. The data provided powerful validation.

While the results didn't show a massive stanine shift, they showed a significant positive shift in their foundational understanding. When the language is direct—'solve,' 'model,' or 'find a rule'—the students now execute confidently. 

My focus group who initially struggled with single-step problems were now successfully translating those narratives into solvable equations. We built that language bridge for foundational skills.

However, the test also confirmed where the challenges lie next. The language barrier increases when the concepts become more abstract and the problems require multiple steps.

In order to continue building on this I will use explicit literacy strategies to pre-teach the conceptual and translational vocabulary before we extend deeply into a new topic. We will critically def
ine and understand the terms needed first.

The goal remains simple: to improve and grow their mathematical literacy so they can tackle new concepts with greater confidence. The journey continues, but I feel very confident that we are on the right path.

CoL Inquiry 2025 - Part Six

In order to gain quantitative data I constructed a customised eAsttle test for my inquiry group to take. It would assess Number Knowledge, Number Strategy, and Algebra. The results, while they don't indicate a massive shift in overall progress are incredibly affirming. They confirm that my previous focus on improving comprehension of whole number and single-step problems was the correct priority.

This has established a strong foundation: The group demonstrated 100% success in procedural objectives like "Model and solve linear, simultaneous & simple quadratic equations." They also performed strongly in finding and expressing rules for number sequences. When the language is direct and tells them what to do (solve, model, find a rule), they now execute confidently.

This is a significant positive step. Our work has clearly improved their ability to translate straightforward narrative into the correct mathematical procedures, which is critical for problem solving.

 The beauty of these results is how they align perfectly with the current curriculum map. The most significant gaps revealed by the test are in topics we simply haven't covered yet in our Pr1me program. I don't look at it as a failure in my current teaching; it's a powerful
alert about where I need to proactively prepare the students' language skills.

The biggest gaps (within the focus areas) sit in the three major concepts that Pr1me will introduce later this year:

• Negative Numbers: The largest gap is "Explain the meaning of negative numbers" (69% Gaps).
• Decimals: There's a 50% Gaps rate in "Write & solve whole number/decimal problems using all four operations."
• Fractions: Students struggled with "Write/solve story problems involving basic fractions" (25% Gaps).

The data tells me that when Pr1me introduces these units, the content itself will be the secondary problem; the primary barrier will still be the complex language because it's more abstract and intricate than the whole number problems they've mastered. They need to understand the words before they can do the math.

The comparison of the earlier diagnostic tests to our recent e-asTTle results has been the most powerful validation of my inquiry cycle yet. The data confirms what I hoped: the strategic focus on comprehension and whole-number strategy has successfully closed old gaps, providing a strong foundation for the Pr1me program.

Here is a quick look at where each student has shifted in their Number Knowledge and Strategy since the start of the year, followed by an analysis of the group's overall progress.

Individual Progress Snapshot: Closing Gaps

Student (Current Level) Key Improvement Area (Strategy/Comprehension) Remaining Challenge (New Barrier)

Student A (3P) Clear Word Problem Gain: They've overcome the language barriers they had in simple multiplication and division word problems. They are now successfully translating simple narratives. Large Number Language: The comprehension barrier remains for place value in large whole numbers and the conceptual language of fractions.

Student B (2A) Procedural Clarity: Johan gained competence in the language of order of operations and is successfully translating simple word problems. They've overcome their earlier struggles with visual strategies like number lines. Foundational Facts & Fractions: They're still struggling with basic addition/subtraction facts and the complex translational language required by fractions.

Student C (3B) Procedural/Algebraic Language: They shows strong gains in understanding the language of order of operations and the procedural concepts of powers of whole numbers. Fractional and Conceptual Language: The language of simple fractions is still a consistent barrier, as is the abstract definition of negative numbers.

Student D (3B) Place Value Mastery: They've successfully overcame their early struggles with interpreting the language of place value and is now applying that understanding to decimals. Translational Fraction Barrier: Their most consistent weakness is the inability to translate a word problem that includes a fractional quantity into an equation.

Student F (3P) Fractional Head Start: They are unique—they've showed success in the initial stages of fraction word problem translation, an area of difficulty for the rest of the group. They've made strong gains in procedural language. Algebraic Patterns: Their remaining weakness is translating the language of patterns and sequential rules, suggesting a distinct type of abstract language comprehension issue.

Student G (3B) Strategy/Procedural Gain: They've successfully transitioned from struggling with simple division word problems to mastering order of operations. Their highest score in Algebra shows excellent procedural command. Fragile Conceptual Language: Their understanding of negative numbers is fragile, indicating that the language used to define and apply the concept needs dedicated reinforcement.

Student H (3B) Strong Strategy Gains: They've moved from struggling with simple division to mastering multi-step problem combinations. This is the clearest example of a direct win for my inquiry on comprehension and translation. Advanced Algebraic Comprehension: Their struggles with the language required to use a rule to make predictions and describe patterns in sequence.

The comparison of the earlier PAT test results from the start of the year provides strong evidence that my inquiry cycle focusing on comprehension and whole-number strategy has been effective. We've successfully built the necessary language bridge.

1. Number Knowledge Progress: Success in Foundational Language

Positive Shift : Nearly all students have significantly improved their ability to read and interpret the language of place value in whole numbers and are now successfully applying that foundational language to decimal place value. This is a big leap from the initial struggles we saw at the start of the year.

2. Strategy (Number Sense & Operations) Progress: Mastery of Simple Translation

Positive Shift : Every single student who initially struggled with single-step, whole-number word problems is now scoring highly or achieving in "Write & solve whole number story problems." The most significant result is their successful transition to solving problems with combinations of operations. The language decoding for simple arithmetic is now working.

Next Barrier : The strategy breakdown occurs when students must translate a multi-step word problem that also contains complex number language (fractions, decimals). The inability to "Solve problems using fractions of whole numbers or decimals" is the new strategic weakness, showing that the strategy itself needs a more advanced layer of comprehension.

The work we've done has provided the necessary language bridge to move from non-comprehension to solid procedural understanding in foundational arithmetic. My next step—pre-teaching the language of upcoming complex units (fractions, decimals, negatives) before the Pr1me program introduces them—is perfectly validated by where their progress is currently stalling. My inquiry remains focused on comprehension, but it must now shift from addressing prior gaps to proactive preparation for upcoming units.

A revitalised look at my inquiry focus is: How can I use explicit literacy strategies to pre-teach the conceptual and translational vocabulary of concepts? I will be tracking my target group as I learn to better support them, not by teaching ahead of the Pr1me program, but by teaching the language of the concepts ahead of it. The goal is to improve their literacy toolkit so they can tackle new concepts with greater confidence.

The journey continues, and the data confirms I am focused on the right path for supporting my students' mathematical language development.

CoL Inquiry 2025 - Part Five

 As part of our inquiry cycle we have the opportunity to use an awesome tool called Vosaic. Vosaic allows teachers to record and upload lessons, and it's AI tool is able to analyse the lesson, looking for specific elements depending on the prompts it has been given.

We did a lesson which focused on estimation, front-end, and rounding.

I am unable to upload the video; it ended up being a 30 minute session, but here are the findings of the lesson. If you would like to watch the whole lesson, please email me and I can share it with you.

Vosaic:
"Analysis of Maths Vocabulary Use in the Lesson

The teacher effectively supports students in learning and using mathematical vocabulary throughout the lesson on estimating products. Here are some key strategies observed:

Explicit Definitions: The teacher begins by defining key terms such as "estimating" and "product." For example, at  → , the teacher asks, "who remembers what estimating means?" and reinforces the definition by stating it involves finding an "approximate answer" ( → ).

Contextual Usage: The teacher uses vocabulary in context, such as explaining that "product" refers to the answer of a multiplication problem ( → ). This contextualization helps students understand how the terms apply to their work.

Repetition and Reinforcement: The teacher frequently revisits key terms throughout the lesson. For instance, the term "rounding" is mentioned multiple times ( → ,  → ), reinforcing its importance in the estimation process.

Encouraging Student Responses: The teacher prompts students to use the vocabulary themselves, asking questions like, "What does reasonable mean?" ( → ) and "Which of the two numbers, 45 or 2, are we rounding?" ( → ). This encourages active participation and reinforces their understanding of the terms.

Visual and Practical Examples: The teacher provides practical examples of how to apply the vocabulary in calculations, such as rounding numbers and estimating products (e.g., 45 rounded to 50 at  → ). This hands-on approach helps solidify their understanding.

Comparative Analysis: The teacher contrasts different estimation methods, such as rounding versus front-end estimation ( → ). This comparison not only clarifies the vocabulary but also helps students understand when to use each method effectively.

Overall, the teacher's approach to using mathematical vocabulary is systematic and interactive, fostering an environment where students can learn and apply the language of mathematics confidently.

Research: Research indicates that explicit vocabulary instruction, contextual learning, and active engagement are effective strategies for enhancing students' understanding of mathematical language (Beck, McKeown, & Kucan, 2013). Additionally, encouraging students to articulate their understanding through discussion and practice can significantly improve their mathematical literacy (Hiebert & Wearne, 2003).

Reflections:
I felt really positive after reading this; it can sometimes be hard when you are in the midst of the lesson, to ensure you are doing the little things right; for me the focus is on the language, and vocabulary; for the students it is to learn and reflect on their prior knowledge of the topic. Ensuring that I am covering both aspects is critically important, as I don't want to lose sight of the goals for either students, or myself.

CoL Inquiry 2025 - Part Four

 Part of the challenge this year has been that my students are very capable of solving word problems when they are scaffolded, and I guide them through the steps.

What I need for them to be able to do is to independently identify what procedures they need to complete in order to successfully solve the word problems.

I decided it was necessary to provide my students with a guide book; a set of slides which would support them in determining what kind of word problem they have been given. This guide supports students to read questions, to categorise them, and then to apply the correct strategy.

Once they have categorised the question they will be able to apply their strategies. I found this more effective than my previous iteration of this; 

The reason being, if I simply give them the key words in the question they are constantly searching just for the words that they need, rather than comprehending the scenario/story. By understanding the scenario and the context in which the problem occurs they are able to apply strategies like visualisation that can help them to make sense of the question itself, and in turn, make it easier to solve the problem. 

By consolidating the reading, visualisation and application of strategy my students have shown an improved understanding and confidence when it comes to independently solving problems.

I am going to ensure they have access to these slides so they are able to rewind it and use it when they need it. The next steps are going to be to continue reinforcing the specific terminology and vocabulary used in each concept.

CoL 2025 - Part Three

This year, we've been working hard to implement a more structured approach to maths using the PR1ME Maths program, which I’ve found incredibly helpful for building strong number sense and step-by-step thinking in students. Each lesson scaffolds understanding clearly—Understand the Problem, Plan what to do, Work out the Answer—and students respond well to the predictable structure.

But I started to notice something. Despite the structure, many students were still getting stuck on multi-step problems, especially when the wording got tricky. Even with a model or clear number strategy, some students weren’t quite sure what was actually happening in the problem.

That’s when I decided to trial the 3 Reads Protocol alongside PR1ME. 

What is the 3 Reads Protocol?

It’s a comprehension strategy borrowed from literacy and adapted for maths word problems.

1.  What is the problem about?

(Just the context—no numbers yet. Are we talking about muffins? Trains? People?)

2.  What is the problem asking?

(Focus on the question. What are we meant to find out?)

3.  What are the important numbers or facts?

(What do we need to solve the problem? Which strategy might work?)

How Does This Compare to PR1ME’s Approach?

The PR1ME problem-solving routine (like the image above) follows a similar flow:

1. Understand the Problem; Students are prompted to ask questions:

How many blue buttons? How many fewer red? What do I need to find?

2. Plan what to do; They draw a bar model, or visualise with a known strategy.

3. Work out the answer They solve, step-by-step.

There are a number of similarities in each of the protocols:

- Encourage thinking before solving

- Focus on the story behind the numbers

- Encourage visual strategies like drawing or bar models

- Build mathematical language through questioning

But here’s the key difference:

👉 The 3 Reads Protocol slows down the reading comprehension process even more.

It makes students treat the problem like a piece of reading rather than just a maths equation hiding in a story. Strategies which can then be applied are to use manipulatives, or visualisation strategies like bar models that can help students turn a confusing question into a problem they can understand and solve without needing as much reading comprehension.

In practice:

In large group/class instruction, I stuck to the PR1ME structure, as it aligns with the scope and expectations of our program. The vocabulary and worked examples help all students—especially those who thrive with repetition and visual modelling.

We’ll continue using both. The PR1ME problem-solving routine is here to stay—it’s well-structured, scaffolded, and clearly links to our curriculum refresh.

But I see real value in making room for the 3 Reads Protocol in:

- Small group problem-solving

- Mixed-ability collaborative tasks

- Problem-solving challenges or rich tasks

In short:

We’re not replacing one with the other. We’re building a toolkit—and giving students more ways to understand, approach, and solve.

I am excited to see the results of this; we have had a very staggered end of term, but moving into the next term we will administer a Chapter Test which will require students to solve word problems; am unsure how well they will be able to independently apply the protocol. We will continue to build on this in Term 3.

If you’re noticing students can’t make sense of the maths problem even though they know the strategy, try the 3 Reads approach. Sometimes the barrier isn’t the maths—it’s the language.

CoL 2025 - Part Two

Conversations with my colleagues have been different this year compared to last year; a brand new curriculum document, and structured maths programs have meant that a lot of us are still in the learning stages too - having to familiarise ourselves with new pedagogies, vocabulary, and realising that there is a great of work to cover before our students can perform at the expected level under the new curriculum.

What has not changed is the common struggle; our students are struggling to solve word problems independently. I have discussed this with colleagues in the junior and senior school and with CoL colleagues working at secondary level and it a common thread with students in our schools. 

They have been taught the strategies, can apply them in supported environments, can solve linear problems very easily, however when the problems add multiple steps, or are phrased in a way which challenges students ability to comprehend or infer the obvious path to solving the problem they are unable to apply their known strategies confidently.

Let's look at some examples taken from the Pr1me Practice Books

Example Question One:

A shopkeeper has 378 apples, and 53 oranges. How many apples and oranges does the shopkeeper have altogether?

Straightforward. Linear problem solving. Clear numbers of objects, clear scenario, and a key word which indicates to the students clearly which operation/strategy they need to apply. The reality of problem solving in questions like this is that problems like this do not require much of a problem to be solved. The question is a straightforward story, no twists, no turns, just straightforward combining of two numbers to find a total. 

The very next question:

After selling 185 muffins, a bakery had 269 muffins left. How many muffins did the bakery have at first?

Questions like this require students to understand the story of the problem before they are able to even think of which strategy to apply. The question requires the same mathematical strategy, it is just simple addition, right? 185 + 269 = 454 - however this problem caused confusion, and I wondered why.

I have a hunch, I'll talk about it in the next blog post. Stay tuned to see how we address this.

CoL 2025 - Part One

This is my third year reflecting on this very same question; How can I support my lower literacy students with their comprehension of word problems in maths?

Last year I thought I'd worked out an effective solution; use the CPA approach to strengthen their foundational and conceptual understanding, however there was a limitation in this. Most frequently the A in CPA was symbolic, it was using digits, numbers, and operational symbols. It did not address the hole in their understanding that was decoding, and comprehending what the word problems they faced were asking of them. 

 

For the first time since I began teaching I have struggled to find a focus for my inquiry; not because I haven't identified areas in my student's learning that needs further support, but because for the first time in my own career I am teaching to a structured program.

This year, like all of you, I have been tasked with rolling out a structured Maths program, in our case Scholastic's Pr1me Mathematics, and boy has it been a learning curve. 

First, let me start by saying I am thoroughly enjoying the program so far; as someone who can be very pedantic about the resources I use in my class I have spent countless hours trying to create learning experiences that are engaging, interesting, and enjoyable for my students to use. Pr1me has done an incredible job of taking that job off my hands.

However, it is through the using of resources not produced by me that I encountered the first obstacle for my students. The first part of the Pr1me program is a diagnostic test. This test is used to determine which Book of the program the students will take on for they year. For our students this was a gruelling experience. 14 pages, back and front. Writing with pencils, instead of their mouse. Questions with a wide variety of difficulties, some straightforward, some multi-step problem solving. This was definitely not something our students were used to. The results of the test spoke for themselves; most students answered between 5-10 of the 30+ questions in the test with some accuracy, or indication of strategic thinking.

After they finished the test, we did a little bit of a debrief; 

How did you find the test? What was the hardest part about it? What did you find most confusing?

There were a wide range of answers, however the fundamental theme throughout them was a lack of understanding around what the question was actually asking them to do. 

I rewrote 3 questions on the board, mimicking the style of questions they had just done in the test. We went through it together, drawing out the key numbers, and finding the operative words in the question. With plenty of support and guidance we ended up turning the word problem into a numerical equation, that the students were able to very easily solve using strategies they had been learning with me.

So where's the barrier; what is it that they are not understanding? It has to be the words. It just has to.

So; here our journey begins. I'm narrowing down my target group, but I am going to look at the students in my class with lower level literacy, and low level of maths, and tracking their progress, as I learn to better support them, now with the structure, (or restrictions) of the Pr1me program.

Follow along to see where how far we'll go!

CoL Inquiry - Using Evidence to Guide Practice - Part Five

My math practice this year has made considerable changes; personally I like I've grown in confidence with my practice, the research, the conversations (with colleagues and students), reflections, and all of it has left me feeling more capable as a teacher, and it has translated into students who feel much more confident and are enjoying math. One of the pieces of qualitative data I gathered at the start of my inquiry was their voice; how were they feeling about maths; here's what they said.

I will be reissuing this same questionnaire this week, and I am super excited to see the results; in speaking with my students they are feeling more capable, and demonstrate this on a regular basis in class.

In terms of data the previous blog post has what we have done so far, eAsttle test provided me next steps, and Gloss testing is being done - as I write this I am nearly finished with my inquiry group, and even without another Gloss Test from the start of the year (reminding myself how good they are, and that I need to do more of them)  I can feel their conceptual understanding has improved. In terms of quantitative results, I have now tested 6 of the students in my inquiry group. Each of them has reached Stage 6 in Addition/Subtraction, most, if not all have reached Stage 5+ in Multiplication and division. 

This still means they are working towards achieving at the level that they should be, however, they have all shifted upwards; their OTJs had them placed at Year 4, some early, some late, but definitely below the expected level. A single test is not indicative of their progress, but I can't help but be excited to see this acceleration.

Cook Islands Summit

In October I was privileged to be a presenter at the 2024 Cook Island Teacher's Summit, and I'll start of by saying WOW. What an awesome experience, and opportunity; to be able to connect and share ideas with a wonderful group of teachers is something that I will always treasure. It is opportunities like this that make me so thankful to be a part of the Manaiakalani family.

I thought it would be cool to share with you what I presented, and share some of the awesome PLD that I got a chance to be a part of;

I'll get mine out the way first. My presentation focused on my inquiry question for 2024 - How can I improve my student's conceptual understanding of mathematical concepts?

This question was one that built on my MIT '23 project of improving students comprehension of word problems, and came about because I realised that vocabulary and comprehension was only a small part of what my students were finding difficult; they also needed support in their retention of basic facts, and number knowledge. Some of them needed additional support through the use of manipulatives to make connections between abstract equations, and the real world applications of them.

This was where T-Shaped Mathematics came from; an adaptation of a learning model that we use in our literacy planning; the idea that in order to improve conceptual understanding of a topic our students must be offered a range of learning opportunities, exercises, and strategies that best suit them. By offering this wide range we can ensure that students can find the one that works best for them.

I have built my mathematics program this year on the foundation of the CPA approach, as well as elements of traditional, and reformist pedagogy; rote learning through the regular practice of multiplication and division, and addition/subtraction through repeatable exercises as warm ups; a range of questions which required the use of manipulatives, both physical and digital, and fun and engaging games that we can play in math that foster collaboration, and learning from their peers. The aim of this was, in simple terms, to do the mahi, and then get the treats. Following this principal has been instrumental in the improved engagement, and results I have seen this year.

Examples of how this is done can be seen in the slides below; 

The best part of the Cook Island Summit, aside from the amazing location, weather, people, and places we got to see, was the opportunity to learn from expert teachers, and to spend the time talking, and sharing ideas with them;

I was fortunate enough to be able to attend some awesome workshops; the first was a workshop entitled Beyond the Reef; presented by Pelu Leaupepetele, the principal of Kedgley Intermediate. This workshop was focused, primarily on leadership in schools, but carried with it some critically important messages, particularly for teachers of primarily Pasifika schools, of vulnerability, honesty, and openness, and how relationships between the leadership, teachers, and students can create a school environment where students and teachers open up, and can share and be vulnerable with each other, and in doing so, can build trusting relationships which foster a school which is healthy, and happy.

The second workshop is one I am very thankful I was able to attend, it was extremely popular, and with good reason. The workshop was titled Ruapekapeka, and the title, which I knew to be a famous battle in the New Zealand Wars, was so much more. Presented by Ian McGee and Tess Whelan from Taylormade Media we were introduced to matautanga.co.nz, an absolutely incredible resource. The ins and out of which I could spend all day writing about, however I simply implore you to explore their resource. It is amazing, and absolutely free. I will 1000% be using this as the foundation for my Aotearoa's History unit starting off 2025.

The first day done and dusted we all gathered together to experience Captain Tama's tour. What an awesome day - I cannot empasise enough just how beautiful the Cook Islands are, and we were gifted an incredible, and hilarious trip out to a small island, maybe 10 minutes by boat from Rarotonga. We were kept fed, and entertained by the wonderful Captains and spent a lush couple of hours swimming, sunbathing, and nearly being eaten by an overly friendly Giant Trevally. 

I will share with you more details about Day 2 of the Summit in another post, because there is simply too much to read in one go.

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!