In this blog post, I'd like to share the end-of-year data for my Year 3-4 class.
All results have been filtered to include only the 'same students,' ensuring a direct 'apples-to-apples' comparison of progress.
1. Mathematics Term 1- 4 PAT data
2. Reading comprehension Term 1- 4 PAT data
Year 4 (same students only) achieved a gain of 9 units, (=1.3 years of progress)
Since 2021, my inquiry focus has been on improving teacher practice and raising student achievement in Mathematics. Over the past years, the Maths achievement data has been consistently concerning across many Manaiakalani schools at all year levels. Furthermore, the issue of students underperforming in math has captured national attention.
At the start of the year, I discovered that almost 90% of our new Y3 students were working below and well below their expected levels in mathematics. Their Term 1 PAT results confirmed the data I collected during other summative and formative assessments. This group of students became my target group, or I prefer to call them my control group, as I always strive to deliver the best teaching to all students.
After analysing the school-wide T1 PAT results, I engaged in several professional conversations with my school leaders and teachers. We decided to adopt a more data-informed approach and redesigned and restructured our maths programmes across all year levels. We ensured a well-rounded focus on both Number and Strand, employing an integrated curriculum and fostering student agency.
I’ve been actively involved in supporting my school and other COL teachers by working on understanding various assessments, analyzing and using data for more effective planning.
I've supported a number of teachers and teams by discussing and collaboratively reviewing their maths programmes, by selecting the best resources for teaching different concepts, compiling and sharing practical resources, for example, maths-integrated Matariki resources for L1 to 4 of the curriculum, by observing lessons, providing feedback, unpacking it and planning next steps.
To share my expertise and passion for this subject, I provided in-class support by both modeling and co-teaching maths lessons.
This year, I’ve had the privilege of working as part of the Maths design group, with the goal of launching a new maths PLD program next year. I've already volunteered to pilot this program in Term 1. I really hope that this new Manaiakalani initiative will support our teachers in growing their capability and love for teaching mathematics.
To conclude my presentation, I’d like to share the end-of-year Maths PAT results of my targeted Year 3 cohort (Y3 learners in my class achieved 18.6 gain). We filtered the data analysis by "same students only" to compare apples to apples. The group achieved a gain of 17 points, compared to the national average of 9.2. This difference translates to nearly 2 years of progress and means that, with my team, we successfully accelerated their learning in Mathematics.
This year, I have been privileged to support and collaborate with the broader Manaikalani community to enhance teacher practice in Maths. This included working with individual teachers, teaching teams across Y1-8, COL colleagues, school and Kahui Ako leaders, and the Maths Design Group. I also provided support for our RTLB colleagues.
Here is a snapshot of my AS COL support:
In this post, I'd like to share two e-asTTle comparison reports based on the latest assessment conducted in September by my Year 3 and 4 students. I have nine Year 4 students in my class but only two of them didn't sit this test due to their overall learning difficulties (they focus on their IEP goals). There is no e-asttle data available for Year 3 students from other schools.
Using the concept of repeated measures, I've been tracking my students' progress in maths and sharing their results with both them and their whanau. We looked at their individual reports to set up new goals and to see how far they've come and how much they've grown. It was a great opportunity for my learners to talk about their successes and next steps during our end of Term 3 Tamariki Korero.
Report #1. How are my students doing compared to students in ALL other NZ schools?
Report #2. How are my students doing compared to students in SIMILAR schools (low decile)?
E-asTTle offers a range of individual and group reports that I've been using as formative and summative assessments to guide my students toward their learning success. Along with other assessments, I use e-asttle to keep a close eye on student progress and needs and to make teaching adjustments as needed.
Next year, I will administer the same test at the beginning of Term 1 and then each term to collect data for e-asTTle progress reports and to compare them with PAT results (out of my personal curiosity).
As we're approaching the end of term 3, I'd like to share my team's innovative weekly and daily planning format, designed to make our maths program transparent to all stakeholders: teachers, relievers, students and whanau. Through collaborative efforts with my team, we've refined our approach to create engaging learning experiences that are visible, accessible, rewindable, practical and efficient. Explore our format, complete with built-in formative assessments and easily accessible teaching and learning resources. Our planning promotes academic growth while enhancing teacher capability and subject knowledge, nurturing student agency and strengthening connections with whanau.
The structure of the weekly and daily planning has been working well for our year 3-6 classes. Students are seen twice a week with a flow of purposeful activities to practice new concepts and maintain their maths knowledge.
Built-in assessments. Using ARBS, ixl.com (but it can be any math program, including StudyLadder, Splash Maths, etc), book tasks and Figure Me Out activities, teachers are collecting rich evidence of student progress and identifying their next steps - built-in formative assessment for learning.
This structure also allows for visible, accessible and rewindable learning. From my own experience, the students who were absent from school used this planning to continue learning and work on the same topics as the students at school. I only had to do a couple of quick workshops to support them when they returned.
Revision and review. This planning helps to review and revisit the topics when students are working independently on their own maths goals (self-reflection and teacher feedback)
Reliever-friendly. Relievers were also able to pick up this plan and continue to teach according to the weekly plan with limited learning interruptions.
Whanau feedback is also positive. Parents have commented that they know exactly what the kids are learning, and, according to some parents, this format has helped them better understand their child's math education (which was an interesting comment).
I've thought through my Causal Chain to identify the specifics of my inquiry and gain a deeper understanding of how I've been supporting teachers and improving student achievement.
This research paper caught my attention when I read a couple of the first paragraphs..."a common belief in education (is) that visual mathematics is for lower level work, and for struggling or younger students, and that students should only work visually as a prelude to more advanced or abstract mathematics. As Thomas West, author, states, there is a centuries-old belief that words and mathematical symbols are “for serious professionals – whereas pictures and diagrams” are “for the lay public and children” (2004). This idea is an example of a damaging myth in education, and this paper will present compelling brain evidence to help dispel the myth". (Boaler, J., Chen, L., Williams, C., & Cordero, M. (2016). Seeing as Understanding: The Importance of Visual Mathematics for our Brain and Learning. Journal of Applied & Computational Mathematics 5)
The study highlights the brain's capacity to process mathematical concepts through visual pathways. From number lines to manipulatives, visual representations play a pivotal role in making abstract ideas concrete and understandable. Integrating these tools in the classroom enhances engagement and achievement across year levels.
The paper advocates for embracing visual mathematics as a means of transforming students' mathematical experiences. By providing hands-on experiences and visual aids, educators can empower learners to develop a deeper understanding and appreciation for math.
I believe (and was thrilled to find a confirmation of my beliefs in the latest neurobiological studies) that using hands-on objects and visual aids is incredibly important for learning math. These tools help make abstract concepts more concrete and easier to understand. When you can touch and see things, it's easier for your brain to remember and solve problems. Studies have shown that using these tools can make students better at maths and help them do well in school. Plus, they work well for all types and ages of learners.
"A compelling and rather surprising example of the visual nature of mathematical activity in the brain comes from a new study on the ways that the brain uses representations of fingers, well beyond the time and age that people use their fingers to count. The different studies on the brain’s use of finger representations give fascinating insights into human learning and clear implications for mathematics classrooms."
I hope to see more manipulatives and visuals in our classrooms across all the year levels to enhance learning experiences, engage students and foster a deeper understanding of mathematical concepts. When we can touch and see things, maths becomes clearer and more exciting.
Recently, I have been updating my collection of purposeful interactive websites for my learners. These websites offer free resources for different maths concept development and practice. Here are a few of my favourites:
Maths Games https://nz.mathgames.com/ is a fantastic free website offering interactive maths activities for primary students. It covers various topics, including number knowledge, strategies and strands. Additionally, the website provides video explanations that help students learn from their mistakes. While Math Games offers a premium option, there are still plenty of valuable resources available at no cost.
Mathantics https://mathantics.com/ is a collection of lessons created specifically for teaching math concepts through animated videos. These videos are visually appealing and easy for our young learners to understand. Not only can students benefit from watching these videos, but teachers can also use them to refresh their own understanding of a topic.
Maths Is Fun https://www.mathsisfun.com/ (Free with a subscription option) is a user-friendly website that offers interactive games, puzzles and explanations of math concepts. These resources can be used as a modelling tool for Number Talks or guided lessons.
BBC Bitesize - https://www.bbc.co.uk/bitesize/subjects/z826n39 (free) provides a diverse collection of interactive math games and activities suitable for primary students. While some resources are available for the UK only, the website still offers great content for New Zealand classrooms, including a variety of free basic facts games.
By incorporating these interactive websites into your classroom program, particularly during independent purposeful practice, teachers can effectively enhance students' math skills while keeping them engaged and motivated.
Have fun learning and teaching maths!
Matariki is coming! This special time of the year is not only about cultural celebrations but also offers an incredible opportunity to weave Maths into teaching and learning. From exploring symmetrical patterns in Māori art to analyzing data related to Matariki traditions, we can engage our students in a fun and meaningful learning experience. So, let's embrace the spirit of Matariki and embark on an exciting journey of integrated maths learning together!
Here is a LINK to some wonderful Matariki lessons on nzmaths. It covers levels 1- 4 of the NZC and provides a lot of ideas for cross-strand and integrated units.
I highly recommend exploring these great resources as they contain excellent lessons and ideas for teaching and learning various maths knowledge and skills in a relevant practical context.
Happy teaching and learning during and about MATARIKI!
Today, we had great opportunities to connect with many Manaiakalani educators and engage in numerous discussions about effective practices for teaching literacy. With the support of my team, I led a CREATE workshop where our group explored toys from both the past and present. We had a blast learning about different types of toys and then had the opportunity to unleash our creativity by making our very own toys. We had a lot of fun learning, creating and playing this afternoon!
Please feel free to visit my presentation below, which includes a multimodal site "Toys and Games Then and Now".
Haskell, Robert. Transfer of Learning.
Dr. Robert E. Haskell was a Professor of psychology at the University of New England (passes away in 2010), whose work in the area of learning transfer spans a range of disciplines, including math, science, education, business, and psychology.
Haskell's insightful book, 'Transfer of Learning: Cognition, Instruction, and Reasoning,' explores the interesting topic of how we can effectively apply our knowledge in diverse contexts. By exploring the historical roots of transfer and underscoring the importance of building a solid knowledge foundation, Haskell convincingly argues for the significance of explicit teaching and practice. emphasizes the importance of understanding key concepts, strategies, and declarative knowledge in facilitating successful knowledge transfer. The book provides valuable insights on fostering critical thinking and problem-solving skills in students, empowering them to apply their learning to real-world situations.
Just in case, I'd like to explain that declarative knowledge in math involves knowing and understanding the key ideas and concepts that form the foundation of mathematical thinking and problem-solving. It is like the building blocks of learning, providing a solid foundation for further learning, deeper understanding and the ability to apply what you know.
In conclusion, Haskell's work aligns with my belief about the importance of teaching before testing. By emphasizing the need for a strong knowledge base and providing students with explicit instruction, educators can empower students to transfer their learning effectively. Teaching before testing ensures that students have the necessary understanding and skills to approach assessments with confidence. By incorporating Haskell's insights into our teaching practices, we can create a solid foundation for students' academic success and foster their ability to apply their knowledge in real-world contexts.
John Hattie is a Professor of Education and Director of the Visible Learning Labs, University of Auckland, New Zealand and we all know his famous work "Visible Learning. A Synthesis of Over 800 Meta-Analyses Relating to Achievement" first published in 2009.
I decided to reread his book, especially some parts that I found important for my teaching inquiry this year. According to J Hattie, "The effect size of 0.40 sets a level where the effects of innovation enhance achievement in such a way that we can notice real-world differences, and this should be a benchmark of such real-world change."
This research also provides valuable insights into instructional strategies that yield positive results for student learning. When it comes to teaching math, a well-structured program and direct teacher instruction have been found highly effective factors (Hiebert & Grouws, 2007). Explicit teaching, clear explanations, and demonstrations have a significant impact on student understanding and achievement.
Manipulatives play a crucial role in the early years of mathematics education and show a great effect when working with low-achieving middle school students. They provide concrete experiences that help students build a solid foundation and develop a deep understanding of mathematical concepts (Mitchell, 1987). By engaging students in hands-on activities, manipulatives foster conceptual understanding and lay the groundwork for later abstract thinking.
When it comes to effective teaching strategies, certain approaches have shown particularly promising outcomes. Strategy-based methods, guided practice, peer tutoring, teacher modeling, specific forms of feedback, mastery criteria, sequencing examples, and instruction responsive to feedback have demonstrated high effect sizes (Hattie, 2009). These strategies actively engage students, provide guidance, and create opportunities for practice and feedback, leading to significant improvements in mathematics achievement.
On the other hand, research suggests that peer group strategies and independent practice with technology have relatively lower effect sizes (Hattie, 2009). While they still have some value, working within a peer group and relying heavily on technology for independent practice may not yield as substantial improvements in mathematics learning compared to other approaches. (I have personally observed similar situations where students collaborate on their independent activities, and despite my reminders that they should only help by explaining rather than telling, it can be challenging to monitor.)
Reading "Visible Learning" by J. Hattie confirmed my hunch and hypotheses about the most important and effective components of teaching mathematics:
Citations:
Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students' learning. In F. K. Lester Jr. (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (Vol. 2, pp. 371-404). Information Age Publishing.
Mitchell, M. M. (1987). The effects of manipulative materials in mathematics instruction. Journal for Research in Mathematics Education, 18(6), 449-457.
Hattie, J. (2009). Visible Learning: A Synthesis of Over 800 Meta-Analyses Relating to Achievement. Routledge.
Based on my previous TAI steps, I identified the following most important hunches for my inquiry:
will improve students' learning outcomes and enhance their learning experiences.
Reevaluating and adjusting my, my team's maths programme to include all the effective elements of the maths programme (research based): number talk, targeted teaching sessions, teacher designed consolidation activities, independent activities and opportunities to apply their knowledge and create in maths (rich tasks and investigations).
By unpacking the term 1 results with students, educators can help them understand their strengths and weaknesses and take ownership of their learning.
Taking a more data-driven approach by consistently using formative (and summative) assessment tools to inform our teaching.
Training students to self-assess using Maths Matrices to help them identify areas where they need additional support and extra practice. By providing students with the tools they need to support their own learning, educators can help to foster a sense of agency and responsibility in their students.
Teacher collaboration and data sharing are essential in Maths education. By working together and sharing data, educators can identify areas for improvement, set goals, create and share resources, and adjust their teaching practices to improve student outcomes.
After publishing my post about PATs areas that we test on without teaching, I recalled and decided to share a story about my last year Y4 student who scored Stanine 9 in PAT but struggled with one particular question - "Visualise which shape a net will fold to make."
At that time, I was placing an order to buy more maths resources for our school including a set of 3D folding shapes, which we used with our Year 3-4 classes. I wanted to provide our students with a hands-on way to explore and visualize 3D shapes and their nets. Little did I know that this tool would have a significant impact on their learning, even a year after using it. Surely, you can fold 3D shapes using paper, but we had an opportunity to purchase this maths equipment and students loved it!
Out of curiosity, I looked at random Y4 and Y5 classes to find out their answers to this particular PAT question for the past 3 years.
2020 - Term 4
2021 - Term 4
2022 - Term 1
2022 - Term 4 - our Team excelled in the PAT "visualise a shape" question that had previously stumped many of Year 4 and 5 students.
2023 Term 1 (after the summer break, mostly the same students with some new intakes)
"Visualize which shape a net will fold to make." This question could be challenging for some students because of a specific skill we often do not cover in our maths programme.
As seen from the examples above, after using the folding shapes in our team, students were able to visualize the 3D shapes and their nets with ease. They were able to apply their knowledge to the PAT assessment and, in Term 4 2022 for the first time in three years, most of Team Kea's students answered the question correctly. Furthermore, the majority of learners retained their knowledge after a summer break (this is not clean data as we have a number of new students from other schools and teams).
This set of data highlights the importance of analyzing assessment data to identify areas where our students need explicit teaching or additional support.
Describe the tools/measures/approaches you plan to use to get a more detailed and accurate profile of students’ learning in relation to that challenge. Justify why you chose these approaches and tools.
Recently, I had the opportunity to analyze PAT assessments from our school and discovered some concerning learning gaps among our students. Many students struggled with questions that were not covered in our classroom maths programmes or were only briefly covered (based on my personal, team and other teachers' reflections)
If students have never been exposed to specific maths concepts or skills, expecting them to answer questions on those topics is not fair. In fact, testing students on material they have not been taught is not only unfair, but it is also not an accurate reflection of their true understanding of the maths curriculum.
The PAT exams are designed to assess a student's understanding of the broader maths curriculum, but this does not mean that students should be expected to answer questions on topics not taught in class.
I used the 'individual items' report for all our classes and identified similarities in topics that most students struggled with: Statistics, Geometry, Measurements, Fractions and Algebra. Some examples are below:
Year 5:
On the other hand, I also analysed which areas of Maths we delivered effectively. This is just a great illustration of "what we taught - our students learnt!" We just need to review our maths programme and include the areas that we neglected before.
Year 4:
Year 5
A hypothesis I developed was that our current maths programme was not adequately covering all the topics included in the PAT assessments. To create a rich picture with a high degree of reliability and specificity, I plan to create an e-asttle test including all the areas tested in PATs. Gloss data also will be used to support Number knowledge and strategies results.
Along with these 3 tests, I will collect student voice. I already interviewed a few students after their PATs and discovered that many of them experienced frustration due to their lack of knowledge on certain topics. Formative assessment is ongoing.
1. Design for Learning in mathematics involves creating a comprehensive plan or roadmap for teaching and learning mathematics. This design should consider the specific needs of the students and align with the NZC.
I believe that mapping an effective maths program should include clear learning objectives, a scope and sequence, lesson plans and resources, PLDs for teachers, and monitoring student progress using formative and summative assessments.
2. Assessment for learning (AfL) is a critical aspect of teaching mathematics in primary schools. It involves a process of ongoing evaluation and feedback to help students understand:
In the context of mathematics, AfL is particularly important because it allows teachers to identify areas where students are struggling and tailor their teaching to meet individual needs.
I discussed my 2023 inquiry focus with a number of leaders and teachers at my school and was impressed by their responses. I'm ready to embark on a new challenge and thrilled to be doing so with the GTS collaborative team.
In 2021 I analysed our school data in Maths and raised my concerns with the management. I was thrilled that my voice was heard! This initiative led to a school-wide collaborative inquiry into improving the teaching of mathematics. Last year, we took this inquiry to the next level. After reviewing school Maths Matrices, we focused on two powerful areas: teacher practice and student agency. That meant that we needed to give students both the option to make choices to direct their own learning and the information they needed to make strong choices. Interestingly enough, after unpacking Maths matrices with their students, our teachers began to use these Matrices for their planning.
Thanks to Johanna's (DP at GTS) data analysis before and after this intervention, we can provide clear evidence of the positive impact of this collaborative approach.
Sharing success! We love Mathematics! Starting in 2021, my inquiry into improving teacher practice and student achievement in Mathematics led to our whole school's goal for 2022-2023. We have been working hard to set our tamariki up for success and enjoyment in their maths learning! Evaluating my team’s “progress over time” T1 2022 - T1 2023 PAT data, I was excited to see good progress and not a significant 'summer drop' for our last year's Y3-4 learners. This data proves that our collaborative team and school inquiry worked for this group of learners, and I look forward to building on our achievement this year! (Note: *These students were also affected by the covid years!).
Then I referred to another set of data available on Ed Potential for our school. We can clearly see some great progress over the past years amongst Y4-6 students which confirms that our collaborative approach was effective.
I am excited to see this data and continue with my inquiry into improving teaching and learning of mathematics this year!
Thinking of my 2023 inquiry focus. I observed my team’s new Y3 students and discovered that about 90% of this cohort is working below and well below their expected levels in mathematics. Their PATs confirmed the data I collected during formative assessments. I believe that this is a result of previous years of disrupted learning. The current Y3 students missed out on timely development of very crucial fundamental skills and knowledge as young students were very hard to reach and keep engaged during lockdowns and hybrid learning. When they returned to school, the main focus was on developing positive attitudes towards school and love of learning.
PAT Y3 2023 Term 1 data
In this post, I'd like to focus on some activities that develop number fluency without blind memorisation and drill. I often refer to Jo Boaler's article 'Fluency Without Fear: Research Evidence on the Best Ways to Learn Math Facts' to remind myself about the importance of engaging maths activities instead of boring memorisation.
Here are some simple activities that develop number knowledge fluency and mathematical reasoning skills in a fun and engaging way. Kids LOVE them!
Game#1
What is the tallest Robot Monster that you can make using one head, one body and one set of legs?
What is the shortest one you can make using one head, one body and one set of legs?
How tall would the Robot Monster be that was made from the three bits left over after you had made the tallest and the shortest?
How many Robot Monsters which are all different heights can you make with the nine pieces (all with one head, one body and one set of legs)?https://nrich.maths.org/2404
Activity #4 - Maths language and communication, active learning
Recently, I was asked by a few teachers to describe some main elements of Effective Mathematics Instruction. I reflected on my teacher practice and classroom programme, referred to the literature and identified the following main components of Effective mathematics instruction:
Developing positive norms: growth mindset, mistakes are great, productive struggle etc - developing positive mathematics learner identities.
Systematic and explicit teaching of new concepts
Use of different best-suited visual representations (manipulatives and/or digital tools)
Developing mathematical discourse and reasoning (Number talk using Talk moves, problem-solving)
Problem-solving in flexible learning environments: groups, mixed-ability, pairs or individual work
Teacher and peer feedback
Creating opportunities and allowing time for deliberate practice in order to develop students’ ability to transfer their knowledge and skills and be able to apply them in different contexts
Student agency - teaching students to use choice boards and maths matrices to set up maths goals, self-reflect and practise
Integrated maths activities, developing creativity in maths
This list might be overwhelming for some teachers, especially if they are at the beginning of their educational journey. Let's start with 3 steps:
1. I suggest beginning with establishing positive norms and developing positive mathematical identities. Why? Because your learners have to feel confident to make mistakes and learn from them - mistakes are part of maths! Here is a great website to teach your students about Growth Mindset: https://ideas.classdojo.com/b/growth-mindset
2. Plan at least 1 hour for learning Maths every day four or five times a week. Maths is better to learn in the 1st or 2nd block; however, you can still do some integrated activities in the afternoon (measurements, tesselations, etc)
3. Use various manipulatives and visual representations to teach mathematics. Use digital tools to make maths visual.
Remember, “The journey of a thousand miles begins with one step”. I wish you all the best on your teaching journey!
Kia Ora, I’m Elena Terekhina, a Year 3-4 teacher at Glen Taylor School. I’m also a Year 3-6 team leader.
Over the past years, I inquired into different aspects of my own teacher practice and effectively supported colleagues within my school and wider Manaiakalani Kahui Ako in the following areas:
Maths (developing an effective classroom programme)
Reading (T-shaped literacy and high-leverage practices)
Integrated Curriculum and LCS)
Student critical thinking and cognitive engagement
Student agency
Teacher collaboration
To see more details about my inquiries, please visit my professional blog.
In 2021, I shared my practice via Class onAir; one of my episodes was used for the Reading Practice Intensive Programme along with my team’s choice board. I always participated in Manaiakalani LCS cluster meetings and ran some workshops.
This year, I’m excited to share my knowledge and skills as an across schools teacher. I’m especially passionate about Maths but can support teachers with all their questions, inquiries and needs by:
Developing balanced classroom programmes
Planning
Developing student agency
Designing engaging LCS projects (integrated curriculum)
Curriculum progressions
Understanding and using various assessments
Analysing assessment data and using it for planning
Selecting the best resources to teach different concepts
Co-teaching, observing, giving feedback and modelling
Number Talk and the use of various manipulatives and digital tools in maths
Creating multi-modal sites
Support with your movie for the Film Festival
😁😁😁
Please feel free to reach out for support or ask questions. I really look forward to working together to help our students achieve their full potential.
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3. Writing Term 1- 4 OTJ (supported by e-asttle) 
