Analysis of my teaching as inquiry this year

 How do mathematical practices in DMIC support learner identities in Maths?

The shift in student independence in solving mathematical problems has been evident in my anecdotal notes of lessons during this year.  There was also a shift in the students' reflection in their maths books of how they have been learning in maths. At the beginning of the year, many students preferred to let what they perceived as able mathematicians take over the problem solving. Towards the middle of the year, there was a gradual shift in students giving their ideas to discussions which lead to students leading or facilitating discussions. 

Through a consistent emphasis on participation, the students in my target group understood they were to take part in problem solving and if they did not know what was being discussed, that they could raise their hand and ask questions for clarification. Upon reflection, I have thought about do my students need to be taught strategies they could follow when they do not understand? Do my students needs to be taught how to ask questions? Clarify misunderstandings? Note take? I have concluded that students do need to be taught what they could do when they do not understand. Often, students will prefer not to ask because they do not want to be highlighted as the student who does not understand. How can I as a teacher, create and encourage an environment of collaboration and support for all students so they are able to learn and re-learn at their own pace?

The DMIC tasks are given to schools who implement DMIC. Teachers are to take the tasks and plan for their lessons using a template which was provided from the DMIC programme. Reflecting on the planning part of DMIC, I know that there needs to be more consideration about the students who are below their expected achievement level in maths. How can the students who have a lot of gaps in their knowledge, build on their knowledge so they are able to solve problems in their expected levels. We have been considering and anticipating misconceptions students can have in their strategies when solving problems, but I feel it is not enough for students to learn a new strategy and consolidate a strategy within a week. Possible solution? Workshops during the week. 

Student voice, peer collaboration. This is something I have worked very hard to implement in my lessons this year. From the start, we have included student voice and peer collaboration in our Community of Mathematicians norms. I am very confident to say that, in my class teaching, all my students are able to work with any peer they are partnered with. This is a great way to build inclusiveness in the class. For the whole class to be inclusive and to value the collaboration between peers. 

Assessment data

The summative data from the maths assessments shows most of the students in my target group have made progress in their maths testing. One student who did not do very well in their PAT test was due to lack of effort during the test (student JF Y8). Was really pleasing to see the students' progress in the Gloss test as well as the PAT maths test. During the Gloss testing, it was evident the students wanted to keep trying to answer the questions in the test. They had the perseverance and the determination to give all the questions a chance to solve them. 

Where to from here, while the learner identities and self confidence of the students were strengthened in this teaching as inquiry, I have realised, the assessment data proves that there are a lot of mathematical knowledge that students lack and therefore hindering their progress in mathematics as shown in the assessment results. 

What leads to students lack of confidence in maths? What can be done early in their education journey to address these? What is a good balance for problem solving to develop mathematical inquiry communities and mathematical workshops for student content knowledge?

These are some of the questions I have been reflecting on for further steps from this year's inquiry. There is a great need for students to have workshops to build their mathematical knowledge. Students also need to be assessed throughout the year in both formative and summative assessments. Another aspect I want to explore more into my practice is the collaboration between student and teacher in teaching and learning. How involved are students in the decisions making about their leanring? How can I consistently factor in student voice in their learning? 

DMIC practices: Mixed ability grouping

How do mathematical practices in DMIC support learner identities in Maths?

One of the arguments I had when we switched over to DMIC was that mixed ability grouping will allow the able mathematicians in the group to take over the discussion while students who are not confident in Maths will take the observer role. I also questioned how I would be able to cater for the diverse abilities if the students are in a mixed group. Reflecting now, those were the questions of a closed minded person. I was really trying to stay with what I was already used to in grouping my students for maths through ability grouping.

Mixed ability grouping is part of the DMIC practices. My class is split into two mixed ability groups for maths. When I group the students, I consider their mathematical confidence and social dynamics of the class. I like to have a balance of these factors into the grouping of my class. 

"Because Pasifika children tend not to talk, their teachers assume they don’t understand and put them in a bottom group. Once there, they become trapped in a self-reinforcing cycle of low expectations", Associate Professor Bobbie Hunter. 

I reflect to the start of my teaching career when I grouped my students in ability groups and feel a heavy sense in my heart about how my students in the 'low groups' must have felt knowing they were in the 'low groups'. How being in a low group might have been detrimental to their self confidence as a learner.

Because the students are in mixed ability groups, there is a lot of teaching which goes into ensuring the students work well together and that collaboration is a 'norm'. How I start each year with my maths groups is by setting up group norms for each group. It is very important to set up the group norms at the beginning of the year to build a sense of whakawhanaungatanga in each group. Setting up group norms is also supported in the work by Jo Boaler setting up positive norms in maths class. 

On going tweaks are needed to ensure the mixed ability grouping is working in my class. To ensure the students are all leanring together and the confident mathematicians are not taking over the discussions, we have set up norms where there is only one paper and one pencil per group. There can only be one scribe who writes down what is being discussed and anyone can have a turn during the discussion to be the scribe.

Questioning is also another leanring practice we have focussed on during our lessons. We have time and time again discussed the importance of listening of understanding and asking questions when we are unsure. There have been many discussions where we have unpacked the understanding that, when we question, we are deepening the learning discussion and we are not judging or challenging the person who is sharing their ideas. 

Through mixed ability grouping, I have noticed how caring students are towards each other. There is a true sense of collaboration and aroha with how the students work together. The confident mathematicians in the class take time to explain their ideas to students who are not confident in maths and take time to ask if they understand the strategies being discussed. 

Casual chain for my inquiry

This is the casual chain for my 2023 inquiry. I have identified what I will do in my practice to make changes and add effect to what the students are learning and how they are learning already in maths. While we continuously have support from the DMIC facilitators, I also know a lot of this inquiry is focussed on my individual actions as a teacher.

There are aspects of this casual chain such as the Community of Mathematicians which has been implemented already and is often referred to by the students and myself. This is displayed on our maths wall and is constantly referred to during our lessons. 

I know the planning of learning is a vital part of teaching and that is one of the focusses of my inquiry. To plan mathematical problems where the big idea is identified and the problem relates to the big idea. DMIC encourages students to solve the problems using strategies they are able to use. Through the connect, the teacher is able to teach or reinforce the strategy at the learning level for the students. In my case, it is level 4 strategies because I teach year 7 and 8 students. 

I have also changed routines in my class to ensure I am able to see both groups each day. The main group for the day is the group I problem solve with, the other group I see to discuss their independent tasks and to give feedback.

This intervention is to magnify the effects of my implementation of DMIC practices and notice if they change the attitude of my target learners towards maths and improve their progress. Through what I have been implementing so far, I have noticed changes in the korero my students have in their problem solving. 

Amy casual chain 2023

TAI focus for this year

 How do mathematical practices in DMIC support learner identities in Maths? 

I have decided to focus my teaching as inquiry into the learner identities of my students in mathematics. This decision was made based on my reflections, observations and data from gathering student voice. 

My hunch is that students who have low self confidence in mathematics, do not identify themselves as mathematicians and therefore, are reluctant to participate in maths lessons or engage in maths learning. 

Mathematical learner identity is not fixed and therefore, teachers can do something about it. Mathematical learner identity is concerning the mathematics learning the learner has been exposed to, rather than the learner themselves (Education Hub). Often as a teacher I have questioned if the students who are reluctant to participate in maths lessons are doing so deliberately or because they are not able to understand what the lesson is about and disengagement is their refuge. Through this inquiry, I will be exploring in depth my own assumptions and actions as a teacher and how I can change my mindset and practice to cater for my target learners. 

Our school have been implementing the DMIC programme since 2019. We have had many professional development experiences where we have discussed the importance of giving students the autonomy to learn and share their leanring without teacher input. The DMIC programme puts student voice and participation at its heart. There are a variety of mathematical practices which I will be focussing on for this inquiry and analysing how effective they are in supporting students in growing their learner identities in maths. 

Gathering literature on maths teaching and learning in New Zealand

The Education Hub is a resource I often refer to when searching for articles or materials for my teaching practice. Through my search for articles on mathematics, I came across this research article written by two lecturers at the University of Auckland, Dr Lisa Darragh and Fiona Ell. 

The article is called Five research-derived themes to consider when teaching maths. The article begins with this statement, 'The task of teachers of primary mathematics is to bring important mathematics concepts and skills together with students’ attitudes, beliefs, prior knowledge and thinking – and to do so in dynamic learning spaces'. I have highlighted the words - attitudes, beliefs, prior knowledge and thinking because as I keep observing, planning, teaching and reflecting on what is happening with my students in maths, I keep coming to the hunch that it might be my students' attitudes, beliefs, prior knowledge and thinking that is hindering their progress in maths. 

The articles by Dr Darragh and Fiona Ell talks about five key themes that teachers need to consider when planning and teaching maths. 

1. Talk 
2. Tasks
3. Tools
4. Thoughts
5. Together 

As I was reading through the five themes, I came across ideas and understandings which I am familiar with and have been implementing in my teaching already. For example, the theme of TALK talks about using mathematical language, encouraging talk, ensuring all students have a chance to talk, changing the balance of teacher/student talk. 

I have gradually been making changes in my maths teaching through the problem solving programme our school started and also now with following the DMIC programme. One strategy I use in my class is ensuring the students are in a group of three to work out problems and the groups are always random. The students do not know who they are working with each time so they are open to working with any other student in their group. 

Another is, unpacking the problem and identifying words we do not understand in the problem. I always emphasise to my students that problems to be solved is a story, not just a mathematical problem. This changes the mindset of the students from quickly jumping into the mathematical work to trying to discuss and unpack the problem to be solved. 

As I was analysing PAT results for my class, I noticed some of my confident students in maths got some problems wrong probably because they did not understand what the question was asking them to do. Therefore, it is valuable for students to unpack the problem and analyse, interpret, decide what the problem is and what the mathematical problem to be solved is. 

We also do not use the hands up technique during our lessons. I have a saying which is 'When you raise your hand, you are stopping someone else from thinking'. I feel that students who are trying to think of a response will be put off their thinking or give up when they see another student with a raised hand as they will think that student has solved the problem or have the answer to the question. This also promotes learning conversations between the students and the teacher. 

Another theme which I reflected upon was the Thoughts theme. Theme number 4. 

'This theme has two components: the teacher’s thoughts and the students’ thoughts[vii]. What teachers think about mathematics, and what they think about their students, are key determiners of the progress that students will make. Seeing them as capable, taking an asset-based approach, and regarding mathematics as valuable and fun will set teachers up to design learning opportunities that will help all students progress'. 

What are my thoughts about maths and how do I promote 'maths is fun' to my students?

Another question which struck me from the article was this question: What messages do I give my students about my view of them as capable mathematics learners? I teach Year 7/8 and my students can easily infer meaning from my actions and what I say. This question highlighted to me that in gathering student voice, I need to put a question similar to the question the students answer for Asttle Writing - My teacher thinks I am good at writing but in my context, maths. 

All given themes have golden nuggets which I believe are valuable for teachers to consider in teaching maths but the theme which really relates to my hunch is theme five. TOGETHER. 

The theme Together is about the idea that maths is for everyone and not just for the elite or the SMART students in the class. The idea that smart students can do maths and the dumb students can't do maths. I know some of my students think they are the dumb students who can't do maths. These students can also point out the smart students who they believe are good at maths. This also emphasises why I always pick the small groups of three for group work, so the students are not pick and choosing who they want to work with. I am a firm believer in being inclusive and supporting each other so absolutely no pick and choosing who one wants to work with in my class. 

'When teachers design opportunities to learn, it is important to think about how to include everyone and make the ideas as accessible as possible'. My class are grouped in mixed ability groups. Making learning as accessible as possible is ensuring my task design and how I teach the lessons cater for all students in the groups. 

Students' self efficacy plays a huge role in how a student learns and interacts with others not only in a school setting but outside of school. That is why I am going with my hunch that, when students are not confident in maths, that is a barrier to how they learn and progress in maths. 

So, after reading this article, back I go to the drawing board to frame my inquiry question for my teaching as inquiry. 

Profiling my class in maths

'Promoting a positive mathematic learner identity for all students and communicating the belief that mathematics is for everyone are important components of effective teaching and learning in maths', (Education Hub). 

I have been observing my class with their learning in maths. I have also been making notes on their behaviour during our maths lessons and reflecting on my conversations with students about maths as well as the students' conversations with each other. Other conversations I have been drawing from, happened during our recent Three Way Conferences. 

Assessment data provides information about the level of achievement the students are at but, I also believe that gathering background information about the students and their attitudes towards maths is as important as assessment data. When I was in discussions with my students and their parents, many of my students shared that they find maths challenging because the learning is new or hard for them to understand. 

My reflections on what I have observed about my students' learning in maths? (These reflections are of my whole class. There will be another post profiling my target group in detail).

Making changes and encouraging mathematics in my classroom and whanau community

Many of my students feel mathematics is too hard for them especially when it comes to Decimals and Fractions. I am sure many teachers can agree with this. I have noticed throughout my teaching that many students have huge learnings gaps in decimals, fractions and also percentages. 

At the moment, our focus through our DMIC programme is on decimals, fractions and percentages. I have noticed that I am teaching mathematics with a lot more passion than I ever have. 

Reflective question: Have I been so focussed on my literacy pedagogy that I have neglected Maths? 

 

I am encouraging my students to learn their times tables from 2 - 12 as this will help them with their basic facts knowledge and also with their multiplicative strategies. It is part of an on going home learning focus we have and majority of the class 80% are learning their times tables at home. I also received some feedback from parents during our Three Way Conferences that they were happy to see their children learning their times tables. Some parents also expressed they are quite the experts at recalling their times tables. 

Reflective question: How else can I harness whanau support in my Teaching as Inquiry in Maths?

Our school distributes our school newsletter every month. In our class page I often used to put maths questions which we were solving in class for whanau to solve. Not one whanau responded. 

Reflective question: What do other schools do to encourage whanau participation in student learning?

As I have been on leave for Term 2, I am now having to decide what my focus will be for this teaching as inquiry. I have identified my curriculum area of focus and now reflecting, analysing and reflecting on the changes I will make to my practice to accelerate student learning. The other outcome I hope for my teaching as inquiry is to change the mentality of my target group from 'I am not good at maths' to 'I enjoy learning in maths and I can do this'. Where in literacy we aim to encourage life long readers, I am aiming to encourage life long mathematicians. 

Ero review report on Mathematics

It is important when inquiring into a curriculum area to look at what the literature and what has been happening in this curriculum area in other schools. I came across a review conducted by ERO titled: Teaching approaches and strategies that work KEEPING CHILDREN ENGAGED AND ACHIEVING IN MATHEMATICS published in 2018. 

The review was one of a series of reports on teaching strategies that work. It featured strategies and approaches which were observed in 40 primary school from across New Zealand. The schools came from a database of 129 schools with rolls of 200 or more where the proportion of students in the upper primary years had increased in their achievement. 

Raising achievement in primary schools: Accelerating Learning in Mathematics (ALiM) and Accelerating Literacy Learning (ALL) June 2014 This report shared how some primary schools were using the Ministry-funded support projects Accelerated Learning in Mathematics (ALiM) and Accelerated Learning in Literacy (ALL) to enhance learning and raise achievement. 

The report found that, in schools where teachers’ involvement in the ALiM and ALL projects had accelerated children’s progress, 

• students were active partners in designing their own learning plans; they were supported to monitor their own progress; they knew what they needed to learn next; and they were able to provide feedback about the teaching actions that worked for them. 
• parents and whänau were formally invited to be part of the process; they were involved in workshops to develop home activities and in frequent, regular, three-way conferencing in which teachers emphasised progress and success.
•  teachers knew they were expected to critique the effectiveness of their practice and to make changes; they had a willingness to seek both positive and negative evidence of progress; and they were open to new practices that make a difference.

The report discussed that, for schools to be effective in accelerating student progress, they needed:

• leadership capability 
• teacher capability 
• leaders and teachers with assessment and evaluative capability 
• leaders with the capability to develop relationships with students, parents, whänau, trustees, and other teaching professionals
• leaders and teachers with the capability to design and implement a curriculum that engaged students.

The report states that 'in schools where mathematics achievement was improving, and leaders knew the reasons for this improvement, teachers had usually participated in well-planned and targeted professional learning and development (PLD). Leaders had identified each teacher’s strengths and needs and then organised internally or externally facilitated PLD to respond specifically to those needs. They carefully selected teachers from within the school who could lead development work successfully with their colleagues to spread the agreed practices. They made time available for these selected leaders to increase their own knowledge and to work with others'. 

The above statement highlights the value in identifying staff members which strengths in the curriculum areas of focus. For example, the schools in the report identified teachers who had strengths in mathematics and gave them lead roles to implement good practice across their schools. 

Other valuable insights I took away from this report were the use of teaching practices which my own school have been implementing  throughout the years. These practices include: mixed ability grouping, using Talk Moves, teacher collaborative planning, problem solving approach and using Teaching as Inquiry. 

I reflected on how these teaching practices have been introduced, implemented and then the focus on continuing these practices slowly diminished as time passed. I also have noticed it is not highlighted to our new teaching staff as they begin their teaching in our school. Thus highlighting a break down in how we as teachers have a uniform understanding about practices in teaching mathematics. 

From this report, I will move on to discussing with our teachers what their mathematics programmes are and how they implement DMIC which is our current school wide mathematics focus.