Inquiry update - Developing Number Sense through Talk

This year, my inquiry focus question is:
How can I efficiently and effectively help my students learn the multiplication basic facts?

One strategy I’ve been using to develop my students’ number sense is Number Talk. Number Talk is a short, daily routine where students solve math problems mentally and then share and discuss the strategies they use. It focuses on building number sense, flexibility with numbers, and clear mathematical thinking. Below are 2 examples of the problems used for Number Talks.

So far, this approach seems to be going well. The children are enjoying it, and even our reluctant mathematicians are engaging in the activity. I make a point of saying at the start of each Number Talk that it’s good to struggle, it’s good to get things wrong, and we celebrate mistakes. My hope is that by doing this regularly, my students will become more confident in sharing their thinking and that it will help reduce their math anxiety.

At the end of Term 1, I recorded myself leading a Number Talk lesson and uploaded the video to Vosaic, an AI video analysis tool that provides unbiased feedback based on a given prompt. Below is the feedback I received. It was reassuring to see that I’m on the right track in developing my students’ number sense.

AI prompt: How effectively did the teacher create opportunities for the children to develop their number sense?

Opportunities for Developing Number Sense

The teacher effectively created opportunities for the children to develop their number sense through several strategies during the number talk session. Here are some key points that illustrate this:

• Encouragement of Mistakes: The teacher emphasized that making mistakes is a part of learning, stating, "It si good ot make mistakes... we only learn by making mistakes" (00:55). This approach helps reduce math anxiety and encourages students to engage with challenging problems.

• Individual Thinking Time: The teacher provided students with 2 minutes to work on a problem independently before discussing ti with peers (02:04). This time allows students ot formulate their own strategies and develop confidence in their mathematical thinking.

• Peer Collaboration: After individual work, students were instructed to share their strategies in groups, promoting collaborative learning. The teacher stated, "If you didn't solve ,ti your job is to

listen and learn from your peers" (04:40). This encourages students to articulate their thought processes and learn from one another.

• Focus on Explanation: The teacher encouraged students to explain their reasoning by using the word "because" when sharing their answers (01:30). This practice fosters deeper understanding and helps students articulate their mathematical thinking.

• Discussion of Different Strategies: The teacher facilitated a discussion where students shared different methods for solving the problem, highlighting both similarities and differences ni their

approaches (12:02). This not only validates various strategies but also reinforces the concept of

place value partitioning, which is crucial for number sense.

• Reflection on Strategies: The teacher prompted students to reflect on their strategies and

understand the reasoning behind them, stating, "Your job si to try and understand their thinking" ( 09:16 ). This reflection helps solidify their understanding of mathematical concepts.

Overall, the teacher's methods foster a supportive environment that encourages exploration, discussion, and reflection, al of which are essential for developing number sense in students.

Research:

Research indicates that collaborative learning and peer discussions can significantly enhance students' understanding of mathematical concepts (Cohen, 1994). Additionally, allowing students to make mistakes

and learn from them is crucial for developing a growth mindset, which is linked to improved mathematical performance (Dweck, 2006).

Teaching Inquiry 2025

Inquiry Focus Question

This year my inquiry focus question is: How can I efficiently and effectively help my students learn the multiplication basic facts?

This inquiry has arisen from yet again having a class of Year 7 & 8 students who struggle with their times tables. Only 27 out of 29 students can recall the 1-12 times tables effectively. This gap in knowledge is a significant barrier to their mathematical progress. Multiplication is a foundational skill that underpins division, fractions, algebra, and problem-solving. Without instant recall and a deep understanding of multiplication, students find it difficult to engage with more complex mathematical concepts, leading to frustration and disengagement.

Mastery of multiplication facts is not just about rote memorisation; it provides students with the confidence and efficiency needed to tackle higher-level math. Research indicates that fluency in basic facts reduces cognitive load, allowing students to focus on problem-solving rather than simple calculations. A lack of automaticity in multiplication can slow students down and impact their overall mathematical achievement.

Initial Observations and Challenges

• Inconsistent Recall: While some students can recall multiplication facts effortlessly, others rely on inefficient strategies such as skip counting or using their fingers, which slows them down.
• Low Engagement: Traditional methods like timed tests and rote memorisation worksheets often fail to engage students, leading to boredom and resistance.
• Confidence Issues: Students who struggle with multiplication facts often develop math anxiety, leading to avoidance behaviours in math lessons.
• Lack of Transfer: Even when students demonstrate knowledge of times tables in isolation, they struggle to apply them in problem-solving or fraction work.

Potential Strategies to Explore

To address these challenges, I plan to trial a range of strategies and interventions to help students develop both fluency and conceptual understanding.

1. Developing Number Sense
Building a strong number sense is crucial for students to understand multiplication conceptually, rather than just memorising facts. Activities that encourage flexible thinking, such as,  exploring different strategies to solve a problem, using arrays and area models, or discussing patterns in multiplication can help students make deeper connections. Encouraging children to explain their reasoning and explore multiple approaches will strengthen their overall mathematical thinking.

2. Maths Games and Digital Tools

Utilising technology and games can make learning multiplication facts more engaging. Platforms such as Maths fact Lab,  Amplify Fluency, or Kahoot offer competitive and fun ways for students to practice in a low-pressure environment. Moreover, using math games such as Spiral and How Close to 100 will be a fun and engaging way children can develop their multiplication knowledge.

3. Daily Fluency Routines

Implementing short, daily fluency activities such as number talks, quick recall drills, and partner challenges can help reinforce multiplication facts. These will be brief (5-10 minutes) but consistent to hopefully build automaticity over time.

4. Peer Teaching and Collaboration

Encouraging students who have strong multiplication skills to support their peers can be a powerful tool. This could be through paired practice and games.

4. Real-World Applications

To help students see the relevance of multiplication, I will incorporate problem-solving tasks related to real-life scenarios, such as budgeting, cooking, and sports statistics. Applying multiplication in meaningful contexts can increase motivation and understanding.

Measuring Success

To assess the effectiveness of these interventions, I will track student progress through:

• Pre- and Post-Assessments: Measuring improvements in recall speed and accuracy.
• Student Reflections and Surveys: Gathering student feedback on their confidence and engagement.
• Observation and Anecdotal Notes: Monitoring how students apply multiplication in various math contexts.

Looking Ahead

This inquiry is an evolving process. As I trial different strategies, I will reflect on what works best and adjust my approach accordingly. My goal is to create a learning environment where all students feel confident in their multiplication skills and can use them as a strong foundation for further mathematical success.

If you have any insights, resources, or strategies that have worked in your classroom, I’d love to hear them!

Teaching inquiry update

 Inquiry Focus Question

How can I enhance the enjoyment levels of reading for my students and what effect will this have? 

Towards the end of Term 2 I gave my literacy class a reading challenge. The purpose of the reading challenge was two fold.

1 - To increase my students reading "muscle"

2 - To encourage my students to read for enjoyment

The reading challenge involves students selecting a text of their choice based on 15 genres (historical fiction, humour, poetry etc). As students finish reading each text they complete a quick create task, again of their choosing. As students read a range of genres and texts of their choosing I hope this will develop their reading muscle (ability to read texts more consistently) and their enjoyment of reading.  Time will tell.

Teaching as inquiry target group

Inquiry Focus Question

How can I enhance the enjoyment levels of reading for my students and what effect will this have? 

My target group for my teaching inquiry is made up of 6 year 7 & 8 children -  2 girls and 4 boys. 

Through the reading survey, all 6 children indicated they were not reading a book for enjoyment and they do not enjoy reading. 

NAME	YEAR	GENDER	READING AGE
JF	8	Boy	14
NG	8	Girl	13.5
NM	7	Boy	13
JF	7	Boy	12
TR	8	Boy	12
OV	7	Girl	12

Teaching Inquiry 2024

 Inquiry Focus Question

This year my inquiry focus question is very similar to my focus from last year: 

How can I enhance the enjoyment levels of reading for my students and what effect will this have?

I selected this focus because, generally speaking, my students do not read for enjoyment. A recent survey indicated about 1/2 of the students were reading a book for enjoyment however when asked about the book they were reading many struggled to talk about it. I wonder if they filled in the survey with the information they thought I wanted to hear.

I will be giving my students another survey to dig into this a bit deeper. 

Inquiry Focus 2023

Inquiry Focus Question

This year my inquiry focus question is: 

How can I develop the dialogic discourse ability of my children so they can freely engage in discussions about a text and what effect will this have on their vocabulary and comprehension?

It is widely acknowledged that there is a reciprocal relationship between oral language influencing reading development, and reading influencing oral language development. The National Reading Panel’s (2000; p.230) historic report points out: “Vocabulary occupies an important position in learning to read. As a learner begins to read, reading vocabulary encountered in texts is mapped onto the oral vocabulary the learner brings to the task….The reader learns to translate the (relatively) unfamiliar words in print into speech, with the expectation that the speech forms will be easier to comprehend. … When the word is not in the learner’s oral vocabulary, it will not be understood when it occurs in print.” Therefore oral language and vocabulary development is crucial to improving reading comprehension. 

The Problem

Generally speaking, many of literacy student's struggle to engage in discourse about a text. I suspect this is due to a potential number of reasons such as:

• Feeling shy, anxious or worried about sharing. Sharing in a group is a vulnerable thing to do even for adults. The unknown responses from others in the group can cause a reluctance to share. 
• Having a 'can't be bothered' attitude. 
• They don't know how to have a discussion. 

Proposed Solution/Hunches

I suspect the process to developing the dialogic discourse ability of my children will require a number of actions:

• Creating a safe classroom culture where every contribution is valued and respected. 
• Getting buy-in from the kids. Demonstrating the importance of being able to share your thinking and opinions.
• Explicitly teaching/modelling how to have a discussion. This includes outlining Rules for Talk.

• Using texts that are engaging and provocations that evoke discussion. 

Next steps

Attain some baseline data such as:

• Easttle reading  results
• PAT vocabulary result
• Observe children having a discussion about a text recording what takes place

Teacher Inquiry

For my teaching inquiry this year I am asking the question: How can I foster the prosocial behaviour of my students? 

My target group is made up of 7 students, 5 boys and 2 girls. Each of these children struggle to demonstrate prosocial behaviours such as, following our school and class rules, helping and expressing empathy towards others. I find myself spending too much time and energy addressing their antisocial behaviours. It is time consuming and draining and not fair on the others in the class. My hope is that I can establish some protocols, or put some systems in place that will help develop their prosocial skills, which  in-turn, will create an environment that is more conducive to learning for everyone in the class.  Growling doesn't appear to be working so I need to change my approach. Watch this space.

Back In The Saddle!

This year I have returned to teaching at Pt England school after a 3 year break where I was pastoring and co-leading a central Auckland church. I am the team leader of our Year 7/8 syndicate which is made up of around 140 children and 4 other great teachers.

It has been an interesting time to come back to say the least! Initially, I hopped that the effects of COVID-19 on teaching in 2022 would be minimal, however that was wishful thinking. Like previous years we have had to adapt to the changes that COVID-19 has bought. I am so proud with how our children and teachers have adapted to the ever changing landscape. We all know that change is never easy, however the team, children and adults alike, have rolled with the punches and coped so well with the daily changes that came up. 

Currently, I'm working out what to focus my teaching inquiry on. I have wonderings around improving children's ability to discourse and share their opinions. I also have wonderings around engaging boys in reading that leads to achievement. I'll keep you updated with what I settle on.

Inquiry 2018 Summary

Inquiry Focus
This year I have been inquiry has been based around developing the mathematical dialogic discourse ability of my children. In particular my focus has been on developing their ability to explain and justify their mathematical thinking as this was an area of weakness for my children.

Target Children
My Target group were made up of 3 boys and 3 girls of varying mathematical ability. They were selected because they all struggled to express and justify their mathematical thinking.

What happened for my children?
 - More confidence to share
Every child became more confident to share their thinking in class. Anecdotally this is what I was seeing in class as the year progressed. Children who once shied away from sharing were now sharing and children were becoming more confident to speak up when they didn't understand something and question it. This Anecdotal information was verified with the data collected from a student voice survey.

 - Increase in ability to explain and justify their thinking
My target kids had a small increase in their ability to explain and justify their mathematical thinking. As mentioned in previous posts this has been an area of frustration for me as I have not been seeing the gains I thought I was going to see.  Below shows the data of my target children taken from the measuring tool I designed to capture their ability to explain and justify. It needs to be pointed out that this data was taken when children were working independently on their maths problem these responses were unsolicited. This was not a teacher facilitated discussion.


 - April

  - June

  - August

 - November

The greatest improvement has been in the children's use of the word 'because'. In the last few months we have really been focussing on using 'because' to justify our explanations. My kids would often explain what they did but would not justify it. This data matches with what I'm seeing with the rest of my class too. It has been slow going and we have a way to go but we're getting there. 

Anecdotally the children are talking more and developing the ability to discuss and justify their thinking. Children who were once not engaged are now showing engagement and children who once would not participate in discussions are which is encouraging.

Has this had an impact on their maths achievement?

The jury is still out on this. The Maths PAT data below shows minimal increase in their achievement however these results have been effected by our schools' teachers and children learning and adjusting to DMIC maths. 5/6 of the target children made progress. Their progress average was 4.3 scale points. According to NZCER the national progress average for year 7-8 is 5.4 scale points. The average for the whole class that made progress was 5.1.

 - PAT data

What did I do to make this happen?

 - Waka paddle prompts
There was deliberate teaching on the type of things one would say if they were effectively explaining and justifying their mathematical thinking. These phrases and words were made into little waka paddles. The children would hold a bundle in their hand and the key was to use them in a maths session. Once you had used a prompt you would discard it. the idea was to get rid of all the waka paddles from your hand. This was used as a way of introducing the phrases and vocabulary into to the children and reminding them to use it.



 - Insisting on a response
In our maths sessions opting out was not an option. If I child was called upon they had to give some sort of response. "I don't know" was not an option. If they didn't have a response they had to say "Can you ask someone else please?". At that point I would ask someone else but then come back to them.

 - No hands up
Hands up was banned in our maths sessions. The children soon learnt that anyone could be called on to share their thinking which encouraged them to participate in the problem solving. They couldn't really on the usual eager beavers. At times the eager beavers found this frustrating as they really wanted to be the one to share but as time went on they adapted to the new system and no no hands up is the norm.

 - Discussion based games and activities
I used games to help get the children used to using the discussion vocabulary. For example to help ingrain the word 'because' in the children justifications they had to each say the following.

"I'm going to a dessert island and I'm taking _____________ BECAUSE _____________."

The focus of this was on the because. Starting a maths session with this simple game helped the children explain and justify more effectively when it came to their maths.

Next steps
As mentioned before this inquiry has been pretty slow going and I haven't seen the maths achievement I had hoped to see. I'm interested to see if next year the maths achievement will come now that the children have had a year learning how to effectively engage in dialogic discourse. My hope is that with this embedded in the children they will be able to focus mainly on maths in their maths sessions not on developing their dialogic discourse ability.

Patience Young Grasshopper

PROBLEM: My kids struggle to explain and justify their thinking and reasoning in maths.

WONDERING: How can I develop the mathematical dialogic discourse ability of my children?

I recently presented my inquiry to a group of people at the Manaiakalani hui. While presenting I was asked what have I learnt about myself throughout this process. My response was that I didn't have as much patience as I thought. It is taking much longer than I would like to see a change in my kids which is really frustrating. At times I see glimpses of significant shift in their ability to explain their mathematical thinking then at other it times it's like it's week one, term one all over again.  I'm assuming that this is par of the course however it's still frustrating. I long for the day when those glimpses of effectively explaining and justifying are no longer glimpses but the new norm.

So where to from here? My advice form others has been to keep persevering and keep doing what you know works. The latter part is a good reminder as it's easy in the moment when it's not going well, when I'm feeling frustrated/tired etc to put aside the things you know work. For example using the waka paddle discussion prompts or requiring the kids to speak in full sentences and use the word because in their explanations. So,  I'm going to keep implementing that things that work, persevere, keep the long game in mind and get back on the horse.

Going into Term 3 Reflection

As term 3 kicks off I've been reflecting on my inquiry this for this year. In this reflecting I was reminded of the inquiry that I did last year. I found that I have been so focussed on my inquiry this year that I have forgotten about the things I discovered the previous year.

Things like:
- How effective materials are for learning new mathematical concepts and knowledge.
- How hands on follow up activities are effective in concretising new learning.
- How combining create to learn tasks with hands on follow up activities and materials is effective in    consolidating new mathematical concepts.

Problem
How do I keep inquiring into this years inquiry while still applying the things I learnt last year? The simple answer is to 'just do it' however when you're engaging in a whole new maths pedagogy (DMIC) this is easier said than done.

Possible solution
DMIC maths sees myself working with half the class while the other half works on independent activities. My plan is to incorporate my learning from last year into the activities the children are doing when they are not with me. I haven't quite worked out what this will specifically look like however I'm determined to put something into place so that my learning from last year doesn't go to waste.

Quick Inquiry Update

PROBLEM: My kids struggle to explain and justify their thinking and reasoning in maths.

WONDERING: How can I develop the mathematical dialogic discourse ability of my children?

Anecdotally my target group are making progress in their ability to explain and justify their mathematical thinking. They are speaking with greater confidence and are using the word 'because' more frequently. They still often need teacher prompts but I'm finding they don't need as many teacher prompts and are more willing to share their thinking.

The waka prompts have been helpful in giving the kids something to launch from and they they are using them more frequently without me reminding them to use them. Unfortunately the kids still like to play with them and they can be a distraction but they are more useful than not. It has been great to see some of the kids request to not have waka prompts as they are confident they don't need them.

This week I will again be recording and measuring the mathematics discourse of my kids. I just hope the data reflects my anecdotal notes.

Waka paddle prompts

PROBLEM: My kids struggle to explain and justify their thinking and reasoning in maths.

WONDERING: How can I develop the mathematical dialogic discourse ability of my children?

The data I collected confirmed my suspicions that my kids struggled to explain and justify their reasoning in maths. My hunch is that the kids don't know how to do this effectively. To help them learn I have made prompts of the kind of things they should be saying when explaining and justifying their thinking.

The idea is that each kid holds a few prompts in their hands and their goal is to meaningfully use the prompt in their maths session. Once they have used it they can discard the prompt. My hope is that over time using these prompts will become second nature and they will no longer need them. I used the symbol of the waka paddle as we often talk about how we are one whanau and we are all in one waka. We need to all paddle in the same direction if we are to get anywhere. 

Inquiry update: Let the recording begin!

PROBLEM: My kids struggle to explain and justify their thinking and reasoning in maths.

WONDERING: How can I develop the mathematical dialogic discourse ability of my children?

While I had every intention last term of recording my students in order to measure their mathematical dialogic discourse ability, due to the business of school life and external factors (a baby being born 5 weeks earlier than expected) this did not happen. 

However it's now week one of term two and I will be recording this week! It's going to be great to have some baseline data on my kids, a reference point to build from. I only wish I had done this earlier as anecdoatally I have already seen my target kids become more confident in their ability to engage in mathematical dialogic discourse. 

Student feedback

Recently I gave my class whole class a survey to complete around speaking in class. I wanted to hear from them their thoughts about sharing their thinking and speaking in class, how difficult they find and what makes it difficult etc.

Below are some of the interesting trends collected from my target group survey responses. My target groups responses to all questions can be found here.

- Every target child noted 'I'm afraid of what others will think of me' as a reason for what stops them from sharing their opinion in class.

- 4/6 noted 'They don't want to get a wrong answer' as a reason for what stops them from sharing their opinion in class.

- 4/6 said their equally happy sharing their thinking in front of either gender. 2/4 noted it would be easier sharing the thinking in groups f the same sex as them.

- Overall they are not interested in listening to others thinking


It's evident from these responses that I we have a lot of work to do in creating a supportive mathematical community where kids feel safe to share their thinking and one where they value the thinking of their peers.

My target group

PROBLEM: My kids struggle to explain and justify their thinking and reasoning in maths.

WONDERING: How can I develop the mathematical dialogic discourse ability of my children?

My target group is made up of 3 boys and 3 girls. They were selected because they struggle to vocalise what they are thinking but more importantly they are kids who work well when given a task and would be up for a challenge. Three of the children are naturally quieter than some which may be a contributing factor to them struggling to share their thinking.

My next steps involve hearing from the children themselves. I want to find how they feel about  sharing their own opinions and thinking, how easy they find it and if they find it a challenge what are the contributing factors that make it a challenge. Watch this space.

Manaiakalani COL Inquiry 2018

“Recognising and spreading sophisticated pedagogical practice across our community so that students learn in better and more powerful ways...”

The Manaiakalani Community of Learning is working together on this task using the expertise existing in of our community of learning.

Like last year I have selected the following CoL achievement challenge for 2018.

#6. Lift the achievement in maths for all students years 1-13.

More specifically my focus question is : How can I use Developing Mathematics Inquiry Communities (DMIC) pedagogy to develop the vocabulary of my kids?

The teaching as inquiry framework I will be using in 2017 has been specifically co-constructed for Manaiakalani schools using our familiar Learn Create Share structure.
The elements in this framework share close similarities with other models New Zealand teachers use.

I will be labelling my posts as I update my inquiry throughout the year to make the content easy to access.

Labels:

LEvidence, LScan, LTrend, LHypothesise, LResearch, LReflect,

 CPlan, CTry, CInnovate, CImplement, CReflect,

SPublish, SCoteach, SModel, SGuide, SFback, SReflect

Label Key:

LEvidence	Learn - Gather Evidence	CPlan	Create - Make a plan	SPublish	Share - Publish
LScan	Learn - Scan	CTry	Create - Try new things	SCoteach	Share - Co-teach
LTrend	Learn - Identify Trends	CInnovate	Create - Innovate	SModel	Share - Model
LHypothesise	Learn - Hypothesise	CImplement	Create - Implement	SGuide	Share - Guide
LResearch	Learn - Research	CReflect	Create - Reflect	SFback	Share - Feedback
LReflect	Learn - Reflect			SReflect	Share - Reflect

Dr Jannie Van Hees and Dr Bobbie Hunter PD

Today Dr Jannie Van Hees talked to the COL teachers about how to better develop the language acquisition of our children. She had a lot of great things to say but what really stood out for me was closely it aligned with Dr Bobbie Hunters PD on Developing Mathematical Inquiry Communities DMIC. DMIC see's the children doing the speaking, explaining and justifying their thinking.

Both Dr Jannie and Bobbie had these goals as part of the social norms of the classroom:

 - Every contribution is valuable
 - No hands up
 - Everyone's effort is honoured (by teacher and children)
 - Children valuing/taking seriously/actively engaging with other children's thinking.

This Year I will be endeavouring to make these social norms part of my classroom as I explore DMIC maths with the lens of language acquisition.

The power of co-constructing the WALT

One of my significant takeaways from PD with Jo Knox was how she co-constructed the WALT with the children at the end of the lesson. The WALT was written in language the children used and could understand.

I have since done this with my maths groups and it is working a treat and has a number of benefits.  By co-constructing the WALT the children are reflecting on their learning straight after the lesson and it has helped them cement the lesson content.

I have also seen higher levels of engagement when co-constructing the WALT.  By not letting the cat out of the bag at the start of the lesson there is an element of the unknown. This unknown creates a level of curiosity within the children which leads to greater engagement.

Finally, it has empowered the children and given them greater agency over their learning which can only be a good thing right?

If you haven't done this with your class you should give it a whirl. At the very least it's nice to mix things up a bit for both you and your kids.

Book Da Teacher Update

Back in June I initiated Book Da Teacher. This is a system where the children can book in time with me one on one or in groups of up to three to work through something they are struggling with or want help with. This came about after data I received from a student survey that indicated the children would like more time with me to help them with their maths.

Initially Book Da Teacher got off to a rocky start as none of the children booked in. After some clarification about it soon a trickle of booking started coming through. However, now in Term 3,  one and half months on Book Da Teacher is still struggling to take off. Week two, term three and I have no bookings despite my best efforts to remind the children about it. This makes me think that maybe the data was wrong and the children don't really want more teacher time or  I need to scaffold the system more so the children feel confident about using it. I suspect the latter is more likely.

Going forward I will be endeavouring to scaffold Book Da Teacher discussing it daily with the children and booking them in myself. My hope is that this will get the ball rolling. If you have any ideas please let me know.