Bursts and Bubbles 2020

This year's Burst and Bubbles was a lot of fun. It was great to hear what everyone was doing and how the classroom pedagogy had changed due to the Covid restrictions we faced during the year. Please read my Burst and Bubbles report below or click here to see the video of my presentation.  

The catalytic aspect of student learning my inquiry focused on this year was  providing opportunities for mathematical vocabulary acquisition to strengthen a student’s self-efficacy in maths.

I identified this as my focus when I noticed that many of my students were beginning to happily have dialogic conversations in literacy but were finding it difficult to carry that same level of conversation across to maths. Also, during my create based learning tasks students were asked to create videos of themselves discussing their thought process behind their problem solving strategies. Very quickly it became apparent that many students were unable to use the correct mathematical vocabulary when describing their solutions. 

To build a rich picture of my students’ learning I used PAT, strand based Easttle and GLOSS test results, personal observations/reflections, student voice surveys, and video recorded maths lessons and student interactions throughout the year.

The main patterns of student learning I identified in the profiling phase were that many of my students didn’t necessarily find maths difficult but they voiced that multiple step problems and the understanding of mathematical vocabulary were difficult. I soon realised that many of my low achieving students actually were able to complete the mathematical processes within an isolated step, but once the whole problem was put together or they were presented with an unknown mathematical term they shut off. 

My profiling of my own teaching showed that I had strengths in promoting a safe space for students to share their mathematical thinking even if that meant making a mistake.  My students indicated that I consistently provided ways for students to hear, understand and use new mathematical terms. But I felt my students would likely make more progress if I developed in my understanding of techniques used to teach mathematical terminology that would allow the opportunity for them to expand their abstract reasoning and move beyond basic operational problem solving.

The changes I made in my teaching were beginning each strand based unit with a “Diving Deeper” task that frontloaded students with definitions and examples of the mathematical terms that they would encounter during the course of the unit. I also began to insist that students used proper mathematical terminology when discussing their thought process. A basic (yet common) example would be saying, “I added 5 and 7” instead of “I plussed them.”  

The scholarly research (literature) that helped me decide what changes to make was a combination of scholarly articles, our own Pt England maths PD and discussions with other CoL teachers who shared their learnings from various professional development that they had attended. 

The easiest thing for me to change was the way that I was beginning each unit with a deep dive into the mathematical vocabulary for that particular strand.  However, the most difficult thing to change were the ideas I obtained from the scholarly literature that I had read. This was made difficult because of the changes in pedagogy we had to make in response to the various Covid levels and lockdowns. 

Overall I would rate the changes in student learning as decent for the type of year we have had.  The evidence for my rating is that 13/21 students who took the PAT test in both Terms 1 and 4 obtained the average yearly progress in their Scale Scores, not surprising is that the students who attended online distance learning and those who returned to school directly after each lockdown made the most progress. 

2020 Key Changes in Teaching

 

Summarise evidence about key changes in teaching and other factors that influence student learning. (WFRC ?15)

In order to summarise the evidence about key changes in my teaching and other factors that influenced student learning, I began reflecting on a blog post that I wrote in August entitled, "What Evidence?" In this post, I spent some time reflecting on the types of evidence that I hoped to collect when thinking about the types of. things that I could do as the teacher to influence the way that my students were learning.

1.  One of the key things that I changed in my pedagogy last year, was keeping very detailed DATs for reading. This year, I thought about how I was writing up my DATs and reflections in maths and what I could do to make them more effective for my time in the classroom. I tried my best to be purposeful in my planning for both whole class (especially from home during the lockdown and while at school during times of COVID restrictions) and small group interactions. I found it very helpful to keep detailed notes of students involvement, understanding, and next steps when reflecting on a lesson, especially with all the disconnect in student attendance this year.

2. Making a conscience effort to provide topic specific mathematical vocabulary for my students to think about and begin recognising at the beginning of a unit of learning provided many opportunities for students to hear the correct terminology and begin using it in their own mathematical conversations.  

3. I have also recorded some of my maths lessons this year and as a result I was able to hear the student interactions using proper vocabulary and correcting their peers with they used their maths slang. For example, many students say "Timesing" instead of "multiplying."  

4. A key change that I made in my teaching this year was definitely around best practise for effectively running an online Google Meet maths program to teach new concepts and vocabulary.  During our time in lockdown, my maths delivery changed as our time in lockdown progressed. I started out providing my students with very similar tasks to what we were doing before the lockdown. However, I slowly began to make changes to best suit the needs of my students. Some of these changes were discussed in these blog posts: Rethinking Lockdown Maths and "Equivalent Fractions".

Thinking Ahead to 2021

What achievement challenge are you considering as an area of focus in 2021 and why? Include in your WHY both evidence and your own passion/expertise.

The achievement challenge that I am considering for 2021 is:

Increasing the achievement in years 7-10 in maths, reading and writing.

I would want to focus on my reading pedagogy in response to the PAT data compiled by the school and collectively shared through the WFRC that shows while the students at our school are progressing in reading at a steady pace, we are still struggling to achieve or surpass the national norm. As a school, we have been working to create a common language of success for teaching our students who are learning to read and extending our students who are reading to learn.  I am really interested in inquiring into ways to increase student engagement in reading to learn. I often find that my students read because “the teacher said so.”  I want to open the doors of possibilities for the students to read because they want to.

 

What learnings from the 2017 - 2020 CoL teacher inquiries have informed or inspired your thinking.

I have been looking back at blog posts and over the past four years as a CoL Teacher I have really enjoyed the professional conversations I have had about our Inquiries with other CoL Teachers. Some of the key principles that I have picked up along the way are: being intentional about discussing student test results with the students and using those results as a springboard for goal setting, finding ways to make vocabulary acquisition and dialogic conversations a normal occurrence across the curriculum and promoting self efficacy to enhance student achievement. 

 

How would your work support Manaiakalani pedagogy and  kaupapa?

One of the ways that I would work to support Manaiakalani pedagogy is by using the technology affordances that we have in the classroom to open up doors of opportunity that would allow the students to explore the world outside of our own backyards. I am very interested in having my students explore topics of interest that could lead to me connecting them with experts in those fields using Google Meets for face to face interactions. Students could then take what they have learnt and create their own movies or even sites to share their new understanding with others. 

 

Which elements of the extensive Manaiakalani research findings inform or challenge you as you think about this?

I was really interested in what Naomi had to share with us at the last Manaiakalani staff meeting about Student Design for learning, while aiming for high leverage thinking practices (video/voice recordings) used to compare. I would love for students to create a tool (or set of tools) to be shared with others to learn about their topic of interest. A collection of these tools could be a launching pad for student led tasks in the future. 

 

How would you like to be supported in 2021 as you undertake this inquiry?

In 2021, I would like to be supported by hearing more from the WFRC and their ideas behind the concept of MAPIC that was presented during the Create cluster meeting. I would also love the opportunity to have more higher level professional development opportunities from the WFR Team about the types of things we could be trialing and implementing in our classrooms based on what they have seen working across our clusters and the country. 

        

How would you plan to support your colleagues in your school with THEIR inquiries and/or teaching in the area you are exploring?

I plan to continue supporting my colleagues with their inquiries and teaching in the area that I am exploring by providing detailed descriptions of my inquiry and findings on my blog and orally during our in school inquiry meetings twice a term. I will also continue to have discussions and offer my assistance to teachers across the school who have come to me for help or ideas based on something they have read on my blog. We also share regularly with our team of year ⅞ teachers the things that we are learning about during our CoL Meetings that pertain to the shift between years 8 and 9 and our daily teaching practise.

Equivalent Fractions

Auckland is still at Level 2.5, which means the desks in my classroom are very spaced out with students remaining in their seats during the lessons.  We are currently not teaching in small groups, which means that I am teaching my maths class using a whole class approach. Keeping this in mind, I decided to try a more investigative approach to discovering equivalent fractions and I recorded this lesson for Manaiakalani Class On Air.

I decided it was important to start the lesson with a low "on ramp" and then progress through the mathematical stages building upon the knowledge that we had just gained (or reviewed for some). To read more about this lesson, check out my page on the Class on Air website here.  

This lesson was a fun way to have the students conduct an investigation to discover a mathematical concept. I feel that my students were able to grab onto the lesson from the beginning no matter their maths learning level and by the end of the lesson, all students were able to understand how to multiply the numerator and denominator by the same number to get an equivalent fraction.  I also realised that since each student had their own piece of paper, they were responsible for figuring out the new fraction. Since I was able to see them trying to figure it out, I was able to provide the correct amount of wait time for all students to be on the same page before moving on.

What Evidence?

*Describe how you will collect information about the implementation of your changed practices/intervention. (WFRQ? #12)

*Identify informal/formal ways you are monitoring the effects of your changed practices/intervention on learner outcomes. Explain the reflections/tweaks you are making along the way. (WFRQ? #13)

*Describe how you will keep a record of each of the above in a manageable way. (WFRQ? #14). 

It is important to remember that during the Inquiry process that you are ultimately looking at the things that YOU the TEACHER can do to make YOUR teaching practice more effective. 

The focus of my 2020 Inquiry is "How can providing opportunities for mathematical vocabulary acquisition strengthen a student’s self-efficacy in maths?" 

Although my intended route has been altered some due to the Covid-19 Lockdowns, and changes made in our school timetable as a result, I have been able to implement the following interventions in my teaching. Due to the nature of the questions asked by the WFRC, I decided it was best to link my responses in one blog post.

 

1. Very specific purpose to our whole class problem solving and small group micro teaching sessions. In my lesson plans (DATs), I try to specifically think about what I want to do with/focus on with each maths group prior to our problem solving sessions. In doing this, I am able to clearly know (and remain on task) with the mathematical concepts and vocabulary that I am trying to work on with that group of students. In addition to my actual DAT plan, I also keep rather in depth reflection notes often indicating where certain students have successes and failures, in addition to thinking about my next steps as a teacher. 

                         

2. I started out the year, providing students with "A Closer Look" learning tasks. Before beginning a new section of a unit, I decided to try front loading the students with the vocabulary that they should know

(at Level 4) in order to be successful working on that specific topic. This is an idea that I based on the work we had done as a team last year with Dr. Jannie van Hees around Genomics and our Literacy program. Once students have had a closer look at this vocabulary, I plan my problem solving questions using these specific vocabulary words in a way that will get students using them as they discuss their problem solving strategy and solution. 

3. I have been capturing student voice, and my own teacher voice, through video recording our lessons and monitoring the amount of times students use, are prompted to use and I, as the teacher, use proper mathematical vocabulary. An example of this can be found on my blog post entitled, "Formative Assessment and Baseline Data"

4. The last thing I plan to do differently is implement the use of some strategies that I read about earlier this term: the Four Square and Feature Analysis approaches (as discussed here).  Unfortunately, I don't feel confident implementing these new strategies while we are Distance Teaching. My hope it to be able to implement the use of these strategies once my class is back in the classroom as a regular Level 2 class.  Students will be able to keep a personal record of these tasks on their class blogs. 

In order to keep a record of everything, I will be using student blog posts, reflection and DAT spaces on my weekly lesson plans, and learning tasks monitored and filed appropriately in my Google Drive. Student voice will be collected through student blog posts and in class videos that I record during specified lessons. Once I find something worth sharing, I will be publishing regular updates on my blog, which  provides a quick and reliable place to share change in my teaching and student shift data. I also keep regularly updated spreadsheets that monitor student shift (PAT, eAsstle, etc) and my own anecdotal notes on student progress. 

My Theory of Action

 Restate your inquiry question and your theory of action/chain of events (WFRC#11)

My inquiry question for 2020 is:

“How can providing opportunities for mathematical vocabulary acquisition strengthen a student’s self-efficacy in maths?”

My Theory of Action:

As a year 7/8 teacher, I feel that there is often a struggle with our students who do not have the necessary mathematical vocabulary to back the skills that they are acquiring. As a result, students are often at a loss for what to say to describe their mathematical thinking and reluctant to openly share with their peers. We have also noticed that students do considerably better from year to year on easttle tests than they do when taking the PAT Maths test. I wonder if this is due to the open subject matter of the PAT so students know more directly what type of problems they are solving. 

The changes I am making to my teaching to improve their outcomes are still being implemented at this time, especially due to our change in teaching during the Covid-19 lockdown. However, prior to the lockdown, I was using a "Looking Closer" format embedded into my learning tasks that provided students with an opportunity to interact with new grade level appropriate mathematical vocabulary. In the past, students have been primarily taught at the level of curriculum that they were working at. This caused a larger gap to develop with student mathematical vocabulary because students were not using grade level appropriate terminology for mathematical concepts. For example, students often still come into Year 7/8 saying things like "I got the answer 13 from plussing 10 and 3" instead of "I got the answer 13 from adding 10 and 3." 

As we prepare to enter into a more "normal" phase of teaching and learning, I am interested in implementing some of the ideas and concepts discussed on the professional reading that I have recently done in the past few weeks. These include, the Four Square and Feature Analysis approaches (as discussed here).

The reasons why I think these changes in my teaching will be effective to my learners are that they will provide a more solidified understanding of the terms used to describe various mathematical processes and concepts. Students will be provided with a visual reminder of what those words and phrases mean. Students will also be given multiple opportunities to put their new vocabulary to use describing their problem solving process. 

2020 Reading Progress

In our Year 7/8 block, we have the honour of working with our students over the course of two years. This means that the majority of my Year 7 literacy and maths students will be in my class again as a Year 8.

Last year, I worked with my Reading group to move them from reading at a Level 3 (Year 5/6) to reading at Level 4 (Year 7/8). This data was discussed in the blog post entitled, "End of the Year Reading Age Shift"It is important to note, that the graph on this post has different student identification letters than the graph on the 2019 blog post as my 2019 Year 8s have moved onto High School and I have included some students in my 2020 focus group who were not part of the 2019 focus group.

We have been extremely pleased with the progress our students have made before, during and after the lockdown. We have seen great shift in the majority of our students. As we look at moving out of our Covid-Level Classrooms and back into our regular Literacy/Maths rotations, the teachers of Team 5 have been spending some time looking at the shift of our literacy students and as a result we have decided that some students needed to have a change in teacher because of the progress they have made. This is because there may now be only 1-2 students in their literacy class reading around the same age level as they are.

This has happened with two of my students who were part of my initial CoL study last year. Students B and D have both made 3 years progress in the year and a half that they were in my class. They are now working above the curriculum level for their age and they will continue the school year working with a teacher who has a class of students working above Level 4. Students A, C, E, F, G have all made six months progress in the first six months of the 2020 school year. Student H, I,  J and K have all made a year's progress during the first six months of 2020. This means that in the past year and a half of school, each of these students have had 1.5-3 years progress in their reading age, except Student E who joined us midway through last school year and has made a year of progress.

As we break for the Term Holidays, this is such a great thing to celebrate. I am so excited to see what Term 3 will bring as our school begins a Professional Development focus on Reading. I would love to continue looking into what stretches the thinking and reading age of our Level 4/5 students, as well as learning new ways to engage those students in my class who are still reading well below their curriculum level for their age. 

Reflection on Teaching and Next Steps

Write a reflection in which you summarise your main learning about your teaching and next steps. This will prepare you to design an intervention next time. (WFRC #10)


The main learning about my teaching that I have made during this round of evaluation (as discussed in my blog post here) is that I am teaching my students how to have an academically based student-led discussion. It took some changing in my own teaching practise over the past few years to implement this change across the curriculum level, but I now know that I provide adequate think and respond time for my students instead of jumping in right away with the correct answer. My students know that they are allowed to have their voice and opinions heard. When it comes to maths, even my struggling students are not afraid to voice their opinions on how to properly solve a problem or identify what they believe the next step in a problem solving process should be.

My next step is to implement new vocabulary recognition strategies such as the Four Square and Feature Analysis approaches (as discussed here). I hope to provide my students with more opportunities to recognise the language of mathematical success. It is my intention to keep a record of mathematical terms students have used during a lesson (by providing opportunities for students to share their thinking in a Screencastify more often). 

Decimats: Rewindable Learning

 Now that we are back in school under Covid restrictions, I am remaining very aware of the students that I have in my class that have yet to return to school. The majority of these students are still working from home, but without the classroom connection and direct teaching that was available when we were offering Google Meets. As a result, I decided to make another rewindable teaching video showing students how to use a Decimat since it was the first time that many of the students have experienced this learning tool. 

This rewindable video was a great resource for my students who were in the classroom and those at home. It was also used by students in other learning areas of our. teaching block to help them to further their understanding of decimats. 

Formative Information and Baseline Data

Plan and conduct detailed inquiry into specific aspects of your current teaching that are relevant to the hypotheses you identified in the literature. Inquiring into your teaching should give you:

1. Formative information about your current strengths and areas for development
2. Baseline information that you can use at the end of the year  to provide evidence of shifts in teaching

Use multiple tools such as self- or peer-observations, analysis of your class site, student voice. (WFRC #8)

As a Manaiakalani Class on Air teacher, I have the opportunity to routinely capture my teaching on camera. Part of the editing process for my Class on Air episodes requires me to analytically watch the footage that has been captured multiple times to find the best portions of student voice and teaching to share for each episode. Our episodes are also watched and feedback is provided by Anne Sinclair (University of Auckland and Manaiakalani) and other Pt England Class on Air and CoL teachers. 

One of the things that I know I have been working on over the past two or three years is providing more time for students to talk and lead the discussion during our maths sessions. I work hard to create problem solving stories that enable my students to connect with the problem and discuss what they understand before they move into their problem solving groups. Once there students wrestle with the problem, and I roam from group to group providing "nudges" to promote student thinking (How many 5s are there in 100?) and questions about their strategies (Why are you dividing by 5?). It is also very clear throughout the video that I provide adequate opportunities for students to ping pong the conversation from one to another and I only pop into the game when something needs to be clarified or redirected in hope of the students gaining more insight to the topic. When watching the video, it is clear that my students often revert to the more basic names for mathematical operations that they have picked up along the way instead of reaching for the actual name of the concept (ie plussing/adding, taking away/subtracting).

I hope to take a look at a video of a lesson (or have a peer observe) how many times my students use proper mathematical terms and alternative names during a problem solving session.  By adapting and trialing the Four Square and Feature Analysis approaches (as discussed here), I hope to provide my students with more opportunities to recognise the vocabulary of mathematical success. I would also be interested in having a record of the mathematical terms they used kept during the lesson (maybe another video) to see how many of the terms being used are actually terms that we discussed an recorded at some point during the year. 

The edited video from this lesson can be seen below. (click here to view the entire Class On Air episode). After watching the lesson, Anne Sinclair stated, "Loved the shots of the girls struggling with the problem and wrangling with the possible solutions. This is real stuff Angela and what we want to see. It is getting into the heads of the learners to see how they think." I think that's the big thing. Getting into the students' heads to see how they think. Do they have the correct terminology and vocabulary to adequately explain their thinking process. 

As part of this lesson, students also created a video describing their thinking to put on their blogs. Examples from these blog posts can be found here:

• Laolao
• Punaiuru
• Daniella
• Toni

This is another place that I will be able to evidence in shift of teaching, By providing students opportunities to share their thinking in a video on their blog, I will be able to compare the number of correct mathematical terms they are able to use in their descriptions.

Professional Reading #3

Share three pieces of academic or professional reading and explain how they and other sources helped your form hypotheses about aspects of teaching that might contribute to current patterns of learning. (WFRC#7)

Professional Reading #3:
What's the Big Deal about Vocabulary?
By: Pamela J. Dunston and Andrew M. Tyminski

When reading this article, I found myself wondering what techniques I use to teach mathematical terminology to my students that allow the opportunity for them to expand their abstract reasoning and move beyond basic operational problem solving.

Some important points to note from the article are:

• Combining conceptual approach to mathematics vocabulary with research based literacy strategies can improve student maths learning. 
• The article provided three ELA approaches, and I have decided to give two of the approaches a chance in my class.
• It was once again reiterated that students and some teacher's see mathematical language as a completely foreign language (or second language) to learn. 

3 Approaches:

• FRAYER MODEL: Students use two topic lists to compare the qualities of the items being discussed. This model is one that I believe our students would have difficulty using on a daily basis.
• FOUR SQUARE: It is important for teachers to limit the number of new words students are working with to 5 or less.
• 1. Teacher provides the pronunciation and spelling of the new word.  It is written in the top left square of the document.
• 2. Teacher explains the meaning of the term, and students write their definition in the bottom left square
• 3. Students write their "lightbulb word" in the top right square. This is the word or phrase that students think of (or associate) the mathematical term with
• 4. Students draw a picture or figure to remind them of the definition (or they can write an equation/Illustration)
• FEATURE ANALYSIS: Illustrates relationships between terms/concepts.
• Features of the topic word are listed across the top of the page and concepts are found along the left side. 
• Allows students to form connective views of the characteristics and properties and make conjectures regarding the relationships between various definitions.

I really believe that I will attempt to use the Four Square and Feature Analysis approaches in the upcoming terms as we go back to our regular classroom learning circumstances. 

Professional Reading #2

Share three pieces of academic or professional reading and explain how they and other sources helped your form hypotheses about aspects of teaching that might contribute to current patterns of learning. (WFRC#7)

Professional Reading #2:
Learning Mathematics Vocabulary: Potential Pitfalls and Instructional Strategies
By: Denisse R. Thompson and Rheta N. Rubenstein

While reading the introduction to this article, I found myself asking the question, "Do my students speak "Mathematic'?" 

Other important points from the article are:

• Students need to master the language if they are to read, understand and discuss mathematical ideas. 
• The language of mathematics is largely limited to school
• It is important to recognise that students think and learn in many ways, and we must propose a spectrum of approaches including oral, written, visual and kinaesthetic modes. 
• Vocabulary learning and mathematical understanding are intertwined
• Student can record the new terms and meanings with diagrams in a maths glossary (**HYPOTHESIS: If students keep a digital record created with a special template and label on student blogs of new vocabulary terms, would they gain a deeper understanding in the long run?)
• I thought that VOCABULARY WORD was___________. Now I know that VOCABULARY WORD is _______________.
• Language fluency requires intensive language use and working in groups allows students with opportunities to "talk mathematics"
• Provide visual tools/cartoons for vocabulary connections

Using Baseline Data at a Future Date

Explain how some of the data you have used to build a profile of the students’ learning will be used as baseline data at the end of the year. (WFRC #6)

Based on my previous blog post about preliminary findings, I am planning to use those results as baseline data at the end of the year in the following ways.

GLOSS Survey: The results from this survey will be collected at various times during the year to provide an ongoing assessment of student understanding and gaps for future instruction. By comparing the data each term, I will obtain a clearer picture of student understanding. 

PAT Mathematics Test: Term 1 test results will be compared to the student data from the test administered at the end of the year. Hopefully, I will also be able to look at the progress each student made during the 2019 school year and compare it to the progress made this year as well. 

e-Asstle Adapted Number Maths Test: This is an assessment that we (as a team) will administer periodically throughout the year to monitor gaps in student understanding before beginning a "Number Knowledge" strand focus and achievement at the end of each focus. This data will also be collected at the end of the year to comparatively show student acceleration in this particular strand throughout the school year. 

Once back at school (after the Covid-19 lockdown ends), I will also administer iKANN tests with my students and it is my hope that each student will take this test 1-2 times a term for the remainder of the year, to help provide students with a clear picture of their individual progress.