Vosaic Observation Term 4

 This year, I have been focusing on my maths teaching while implementing our new maths program Prime Maths. My students are doing very well and we worked hard to understand and implement this new focused way of teaching maths. 

For my final Vosaic observation of the year, my question was: Has the teacher implemented a lesson that allows students to explore mathematical concepts, using manipulatives as tools for discovery, while also facilitating meaningful mathematical discussions and problem-solving? 

The progam had this to say about my lesson: 

Yes. The teacher implemented a lesson that uses manipulatives for student exploration and supports mathematical discussion and problem-solving.

• Manipulatives used as tools for discovery: The teacher instructs pairs to each take 10 counters and to combine and split them to explore division. The class physically combines to make 20 counters and then splits into two groups, and later students are encouraged to use counters or draw on whiteboards/MacBooks for practice.
• Exploration of mathematical concepts: The teacher models and elicits conceptual understanding of division as “splitting into groups,” connects division to multiplication as its inverse, and demonstrates multiple symbolic forms of division. Concrete examples are used (20 rings into 2 groups → 10 each  ; 9 seahorses into 3 groups → 3 each ; 20 chicks into 4 nests → 5 each at.
• Facilitation of mathematical discussion and problem-solving: The teacher prompts pair talk and checks students’ grouping, asks guiding questions, asks students to write number sentences and explains how to record division, and has students both draw representations and use facts to check answers .
• Opportunities to justify/check answers: The teacher models checking division via multiplication and has students demonstrate by counting or using multiplication facts.

Evidence-based moments to highlight

• Moment 1 (manipulative exploration): Students combine counters and split into two groups to discover 20 ÷ 2 = 10.
• Moment 2 (conceptual discussion and representation): The teacher connects division to multiplication and shows multiple symbolic representations and a fraction connection.

Conclusion

Overall, the transcript shows a lesson structure that integrates manipulatives for hands-on discovery, prompts partner discussion, models representation and notation, and reinforces conceptual understanding and checking strategies—supporting meaningful mathematical exploration and problem-solving.

At the beginning of the year, I was most worried about how to best implement the use of manipulatives to springboard conceptual understanding and mathematical vocabulary development. Now, I fully believe that take the time to read the teacher notes and follow them as a guide for my maths lessons I can easily achieve this in my lessons on a daily basis. 

The summary of my lesson provided me with more feedback that I will consider moving forward into next year, primarily providing more opportunites for students to talk during our math sessions especially during the we do/you do portions of our lessons. 

Create Mini-Games with Gemini

 During our Manaiakalani Create teacher only day, I spent some time learning how to create mini-games with Gemini. It was a lot of fun and we were able to spend some time debugging through the AI prompt to make things run smoother.  To access each game click on the photo below. 

The first game I created was a Tetris-style multiplication game. In order to earn peices to play on tetris board, the play must accurately answer the multiplication facts.

The second game, (actually the first one I had a go with) was a solar system trivia game. It is very basic (game-wise) but the questions are pretty impressive given the parameters I set for the game in the AI. 

Mid Year Inquiry Reflection

After teaching from the Prime Maths program for a few months, I decided it was finally time to gather myself together and record a lesson to upload into Vosaic. Once I did, I was rather happy with the feedback that I received from the AI in the program. 

The summary of my lesson was: 

The teacher effectively uses hands-on learning by incorporating place value blocks for students to visualize subtraction with regrouping. This strategy helps students understand the concept of borrowing in subtraction. The teacher also encourages collaboration by having students work in pairs, which promotes peer learning and engagement. Additionally, the teacher checks for understanding by asking questions and prompting students to explain their thought processes, fostering a deeper comprehension of the material.

The teacher employs classroom management strategies such as setting clear expectations for noise levels, reminding students to work in a "whisper zone," and redirecting off-task behavior. The teacher also uses positive reinforcement by acknowledging students' efforts and correct answers, which helps maintain a positive classroom environment.

As far as next steps goes, I wasn’t all that surprised to find that the suggestions were right where I’ve been thinking about how to improve my maths teaching. 

Suggestions for future lessons:

Incorporate more student-led discussions to increase engagement and allow students to express their understanding in their own words. Utilize formative assessments throughout the lesson to gauge student understanding and adjust instruction accordingly. Provide more opportunities for students to explain their reasoning and thought processes to deepen their comprehension of the material.

However, I think this comes along in this program more as the lesson moves into the “you do” portion of our problem solving and I didn’t record this portion of the lesson as it wasn’t what my focus was. 

Once I put it my inquiry focus question as an AI prompt:
Has the teacher implemented a lesson that allows students to explore mathematical concepts, using manipulatives as tools for discovery, while also facilitating meaningful mathematical discussions and problem-solving? 

I was pleasantly surprised with the analysis of lesson implementation from the Vosaic AI. 

Yes, the teacher has effectively implemented a lesson that allows students to explore mathematical concepts using manipulatives as tools for discovery. Throughout the transcript, several key strategies are evident:

• Use of Manipulatives: The teacher encourages students to use place value blocks to visualize the subtraction process. For example, at timestamp 01:17, the teacher instructs students to "pull out our place value blocks" and work in pairs to build the numbers 252 and 136. This hands-on approach helps students understand the concept of regrouping in subtraction.

• Guided Discovery: The teacher guides students through the process of borrowing in subtraction. At timestamp 03:31, the teacher asks, "What do you need to do?" prompting students to think critically about the need to borrow from the tens place. This encourages students to articulate their thought processes and engage in problem-solving.

• Encouraging Collaboration: The teacher promotes collaboration by having students work in pairs to build numbers and solve problems together. For instance, at timestamp 01:28, the teacher assigns pairs to build the top and bottom numbers, fostering a collaborative learning environment.

• Mathematical Discussions: The teacher facilitates discussions about the subtraction process, asking questions that require students to explain their reasoning. For example, at timestamp 06:13, the teacher asks, "Now what do we have left?" This encourages students to reflect on their calculations and engage in meaningful dialogue about their understanding of the concepts.

• Checking Work: The teacher emphasizes the importance of checking answers by adding the result back to the smaller number, as seen at timestamp 08:16. This reinforces the concept of verification in mathematics and encourages students to think critically about their solutions.

Overall, the lesson is structured to promote exploration, collaboration, and discussion, which are essential components of effective mathematics instruction.

Interestingly enough, the final statement says that the lesson promoted discussion, but I loved that the summary suggestions provided key ways to promote more student-led rich discussion. Looking forward to focusing on this more as the year progresses.

Prime Maths: A Different Classroom Environment

 We are moving along into our Prime Maths journey, and as we move along we have encountered many learning bumps along the way. However, as a class, I strongly feel like we have made the easy turn to understanding. The students now understand what is expected of them and they are working diligently to complete their learning in a timely manner. They had developed a deeper understanding for MathsPro (the online "assess" component) and now know that they must try their best, and seek help as needed, to obtain the highest score possible. They are independently asking to have their mathspro tasks reset so that they may resit a session after reviewing what they have done wrong the first time through. 

Students are taking it upon themselves to actively use the manipulatives we modeled and worked with at the beginning of each session when completing their work as needed. 

Check out this photo of students working independently all using different modes of learning. Such an amazing thing to see!

2025 Inquiry Intro

 This year we are implementing the new NZ Maths Curriculum and using the PRIME maths program in our year 4-8 classrooms. We began the year with a placement assessement that allowed us to determine the best placement for our students into our PRIME maths coursebooks. 

After we had PD with someone from Scholastic to talk through the PRIME maths program, I began  thinking about my teaching inquiry for this year and the question that I came up with is:

How can I implement lessons that allow students to explore mathematical concepts, using manipulatives as tools for discovery, while also facilitating meaningful mathematical discussions and problem-solving?

As term 1 comes to and end, I can say that I am enjoying teaching through a more structured maths program and I am enjoying the time it provides to focus on how I am going to be working with my students. We are on this journey together and so far, I am very pleased with how we are going as we begin to understand the structure of the program. 

Term 3 Update

 This term, has been action packed with so much amazing learning! We began looking at the properties of 2D and 3D shapes and I was so impressed with the level of understanding that my students were beginning to demonstrate. We continued having lots of whole class mat time review at the beginning of our maths sessions and it was evident that confidence amongst the majority of the class was soaring!

As we moved into symmetry, rotations, tesselations and translations, it was great to see the students across all learning levels embrace using and understanding the new vocabulary. We had lots of fun looking at and then creating our own shape patterns. This was fun because it allowed students with lower "number knowledge" to be successful in a different way. 

We kept meeting in small groups to continue to develop our understanding of place value, using place value blocks as needed. We did a lot of review of adding 2 and 3 digit numbers and near the end of the term, we began introducing subtraction and even some place value multiplication to those who were ready. I love having those "light blub" moments in my classroom when something finally clicks with an individual student, and we have had many of those moments during this term. 

It is lovely to see students confidently working in mixed ability groups and helping each other by discussing the process to find the outcome. Students really enjoyed moving into algebra as the term came to an end, and since we started out with shape/colour patterns our lower level learners were once again able to be successful by achieving that initial launch into the topic. 

I am looking forward to next term, and our end of the year assessments to see exactly how much information the students have retained and the growth in these areas. 

Term 2 Inquiry Update

After our initial "launch" lesson, we have been working very hard in mixed ability groups to complete our learning tasks. I have noticed that my students are developing a stronger sense of confidence when they are able to discuss their learning with their peers. Students who were already working at Year 3 are now able to accurately discuss their thinking process and many working at Year 1 and Year 2 are becoming more confident asking for further clarification and help as needed. 

The next class session (or near the end of the class session), we regroup as a whole class and work our way through the task together modeling how to solve the problems. This has been exceptional especially for students realising how to use our multiple posters to skip count aloud when problem solving with fractions or converting from cm to mm. Many students are now able to use the posters to problem solve independently and others are now able to make the connection between skip counting and solving problems using multiplicaiton. 

It's been good to see that there has been a positive shift in student learning levels during the first half of the year (as seen on the graphs below). There were only 7 students out of the class that did not shift in learning levels. 

As the year progresses, I will be working to continue to provide opportunities for my students to continue disucssing their thinking and building their own confidence in maths. I am very keen to work with the group of students at Year 3 to solidify their understanding of problem solving with numbers to 1000 while building a deeper understanding of place value to help in their problem solivng. 

Summarising the Challenge

 Summarise the challenge of student learning you plan to focus on in this inquiry.

Focus Question: How can I effectively build self-efficacy in my maths students to enable them to clearly share how they got their answer?

The past few years, I have put my teaching inquiry focus into reading and through my inquiry (combined last year with the Manaiakalani RPI programme) I have really found some things that work best when promoting students to feel that they are "allowed to be aloud" when sharing their thinking with others.

I'm hoping to be able to bridge that same principle into my maths class especially when working with my students who are just below year level. This year, I have a lovely group of six students working at Year 3 during term 1 and the beginning of term 2. 

The graph below shows their Mathematics PAT score from Term 1 of this year. The red line, shows the average score for a Year 4 student on this standardised test. 

As you can see, four of the six students scored at or above the average, while two scored just below the average year 4 student. However, I have noticed that when we are working in a small group, they are very happy to write down their answers but they are not as confident explaining their thinking or sharing their answer orally. 

This year, my maths class currently consists of 24 Year 4 students who are all working below year level as of the beginning of the 2024 school year. It is my intention to bring these 6 students up into a Year 4 maths group by the end of term 2. This will allow them to continue to grow in their understanding and end the year working "AT" year level before moving into Year 5 in 2025. 

PES PD: Maths With Fiona Fox

Today, the teachers at Pt England were once again able to spend some time working with Fiona Fox (Manaiakalani Maths Facilitator). We had a lovely time looking at the importance of subtising, promoting fluency and sequencing/developing mathematical strategies. Fiona brought along a wide variety of maths games that we explored in our year level teams. It was a great opportunity to look at resources that are available to us to implement into our weekly classroom plans. 

Subitising

-Using Number talks (show for 3-5 seconds)

Fluency

-Being able to provide mathematical answers instantaneously without having to think about it.

Sequencing and Developing Strategies

-Foundational Facts

-5 Frames

-Doubling

-SKip Counting

-10 Frames

-Arrays for mult/div

-Mulitpication Loopy

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. 

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. 

Lockdown Maths

 As a team, we have decided to try something a bit different with our classes at this point in the lockdown. We are meeting with our Maths Class three times a week on a Google Meet, and we have decided to try breaking down our learning task and teaching points into smaller chunks of information to be presented throughout the week that will build upon each other to create a complete mathematical concept. 

While planning for this week of Geometry, I wanted to be sure that I was asking students to complete tasks while supplies that they all had available to them while at home. I found that in order to keep things consistent (to help the students helping each other from different homes) with the manipulatives they were using was key. Therefore, I decided to find online tools for us to use to help build our geometric knowledge. 

PES PD: Equitable Outcomes in Maths

Did our shift in maths pedagogy create equitable outcomes?  What can we do to make it a more PES equitable experience?

Our students need tangible materials to help with their understanding of a problem (when needed). However, they also need to be TAUGHT how to use those materials.  We, as a school, need a little more structure and sequence with our teaching paths that will incorporate the concepts and teaching styles of DMIC. We will be unpacking this as a staff this week.

While we still we be structuring culturally relevant problems, our groups will be extremely fluid. Socially, academically, and structurally allowing for ability stretching are great ways to structure learning groups for different opportunities.

This was such a valuable PD session as a staff as we reflected on what worked well and what was successful for our students during our two years of DMIC roll out and mentoring. Although we gained a tremendous insight into culturally relevant problem solving and how that could look with our students while providing formative data, we also had to step back and realise the gaps that we were now missing in the content knowledge that could be measured formatively.

I am excited to explore this more this year as I begin my 2020 Inquiry into teaching.

PES: DMIC PD

PES PD: DMIC 11 March 2019

The hardest part of learning something new is not embracing new ideas, but letting go of old ones.

Justifying and Arguing Mathematically:

-Require that students indicate agreement or disagreement with part

of an explanation or a whole explanation.

-”Do we agree? Does anyone not agree?”

-Ask the students to provide mathematically reasons for agreeing or

disagreeing with an explanation. Vary when this is required so that

the students consider situations when the answer is either right or

wrong.

-”Why did you do that?”

-Ask the students to be prepared to justify sections of their solutions

in response to questions.

-”Can you explain why you (or your group) did that?”

-Everyone in the group presenting is held accountable for the solution.

               -Require that the students analyse their explanations and prepare collaborative responses to

                 sections they are going to need to justify

-Model ways to justify an explanation

-”I know 3+4=7 because 3+3=6 and one more makes 7”

-Structure activity which strengthens student ability to respond to challenge

-Expect that group members will support each other when explaining and justifying to a larger group

-Explicitly use wait time before requiring students to respond to questions or challenges

-Require that the students prepare to explain their thinking in different ways to justify it

Questions to support student justification/extension?

-Why did you….

-How did you know…

-What do you mean by…

-Why did you do this...and not this…

**Encourage “so” “if” “then” “because” to make justifications**

Questions to extend an explanation into a generalisation? (CONNECT to GENERALISE)

-Does that work for every number?

-Would this work for “X”?

-Can you make connections between…?

-Can you see any patterns?

-How is this the same/different to what we did before?

Developing Generalisations

-Representing a mathematical relationship in more general terms

-Looking for rules and relationships

-Connecting, extending, reconciling

-Ask students to consider what steps they are doing over and over

again and begin to make predictions about what is changing and

what is staying the same.

-Ask the students to consider if the rule or solution they have used

will work for other numbers

-Consider if they can use the same process for a more general case

-”What happens if you multiply the number by 2?”

Revisiting how we Develop Proficient Mathematical Learners

-Attend to classroom culture

-Choose high-level, problematic tasks

-Launch tasks in contextual ways

-Anticipate strategies and monitor group work

-Select and sequence the sharing

-Allow student thinking to shape the direction of discussions

-Plan for anticipations and how the connect could look

Revisiting the Launch

-First focus on the context. The problem should be in front of each

group of students. Let Y3 up read it themselves.

-Use Talk Moves to help students with lower literacy levels to

access the information of the problem

-”What is happening in this story?” Ask for others to add on or

repeat and revoice until you know they all understand the

story.

-20% Teacher Talk 80% Student Talk

-”What do we need to find out?” Do not let them say an

operation, focus their attention on concepts not how to do it

-5 minutes work time (Jr School) 15 minutes (MAX!! Seniors)

-Think through grouping carefully, think social grouping or

what individuals can bring to the group work

-Never ‘High Half’/”Low Half’

-Regrouping Regularly

-Keep groups close together to work on the mat

-Teacher role: roving, monitoring, etc

Connecting and Summarising

-Plan explicitly!

-Draw connections between solutions

-End with a summary of key maths ideas so students leave with

a “residue” from the lesson. This provides a way of talking about

the understanding that remains