North School Maths - How Long Does It Take To Implement a New Program?

he purpose of this article is to share my experience of implementing a new program and offering an insight into what ‘Maths by Myself’ could look, sound and feel like in a classroom. I have documented my challenges and adaptions with the intention of showing that a new program takes time, reflective thinking and willingness to try new things.

This method was found when investigating the Daily 5 in Literacy and provided a framework of ‘Maths by myself, Maths Together and Maths Writing’. The purpose of this time was to enable students to have ownership of what they needed to learn, peer teaching and learning as well as empowering the teacher to run conferences and workshops to address specific needs. The idea has evolved and taken on new forms over the last few years.

Although the title is ‘Maths by Myself’ Collaboration and together time are key elements to the success of this program. The ‘by myself’ reflects the personalised goal, reflective practice and time for practice. Using the ideas and work of Peter Sullivan and Jo Boaler are still important elements to this program and are integrated throughout the process.

What 'Maths by Myself' looks like

Pre-assessment to identify student stage of learning
Teacher/ student led introduction (could be an activity, number talk or modelling) clarifying misconceptions or method.
Students choose an activity to practice their identified learning goal (these should be tasks students can access without the teacher spending time giving them instructions)
When students feel they have achieved their goal and can SAY IT, MAKE IT, EXPLAIN IT, they show teach another student and/ or teacher. They can record this using a screencast or by creating a resource for others to use.
The teacher will be running conferences based on assessment data, observations and student reflections. These can be showing methods, correcting misconceptions or guiding students through an open-ended problem.
The expectation of the students is that they are working and progressing on their goals using the time efficiently with the teacher able to run mini lessons for differentiated experiences.
Students are trialling methods and explaining their thinking.
Students will take part in a reflective process to conclude the lesson.

Step by step guide for new users

Step

Activity

Things to consider

Conduct pre-assessment

Go through Mindset mastery and make the link that mathematicians show their thinking multiple ways using visuals, multiple methods and explanations

Collate data using ZPD

Students may need assistance the first time in showcasing their ‘methods’ and prompting them at this stage is ok.

Use ZPD to set student working goals

Explain to students that their goals may take 30 minutes or 2 weeks. We are all working on our depth of understanding. If they had forgotten it, most likely they will forget again unless they cement the learning.

Maths by myself

Allow students to have multiple exposures to similar content. No matter the stage, everyone is still saying it, visualising it / making it and explaining it.

The activities should enable students to problem solve and explain their method. Make time for peer coaching via tuning in time, reflections or teaching others.

Reflecting and reviewing

Provide time for students to share their methods, reasoning and reflecting on how they are progressing.

When students feel comfortable that they have achieved their goal they must showcase this by: teaching someone else, recording their method, proving and explaining, creating a resource that will challenge someone else.

Post assessment

Enable students to demonstrate their progress and make links with what they used to be able to do and what they can do now. Maths is a journey.

Examples of what the activities look like:

Here is a screenshot of what the staff and students see. Each page has activities for students to access. Some are open ended and some are closed.

This is an example of equations used as the starting point for students to model their methods and justify answers.

This is an example of a Peter Sullivan task used as a whole class prompt. Students were utilising their skills in showing that the equation they had created worked.

Problem 1: Setting up the activities

Problem

Setting up a system of differentiated subtraction activities that enable students to practice their specific skill without requiring teacher support during this time (the teacher is conferencing or teaching other students without having to spend time explaining instructions to multiple students every lesson). The second part of this creating a mixture of tasks that incorporate the four proficiencies.

What we tried

Our school uses OneNote as a digital workbook. All 5/6 students have access to a netbook that is linked to the class OneNote and can access our content library. We developed a sequence of stages of learning based on our scope and sequence and Victorian Curriculum. Within those stages we started to create a library of activities. Combining activities from Peter Sullivan, Nrich.org and typical maths worksheets from Essential Assessment and other sources. We also created a framework that students could create their own equations using dice and cards. Our biggest aim was that no matter what activity they chose to do, they were still required to SAY IT, MAKE IT, EXPLAIN IT. Although within MAKE IT, students could physically make it, draw it, or explain when needed what it could look like. We continued to use the Jo Boalar Mindset Mathematics Practice charts.

Reflection

SAY IT, MAKE IT, EXPLAIN IT was such an important feature of the program. This forced students to slow down and go deeper. I used the term ‘geeking out’ and we found enjoyment in discovering new methods. The students were quick to say, ‘I usually do it like this but I checked using the Wil Method’ or ‘Today I want to practice the Wil method so I can use it better’. Students felt proud to have their method recognised and others felt safe in trying someone else’s method. This enabled a simple ‘worksheet’ to be used to as catalyst for practice knowing that the answer wasn’t enough.

The resource bank suited the students who were capable and willing to take on the challenge. The students that struggled initially were the ones trying to locate their activities. I chose to give them a specific task instead of using the computer. The tangible aspect of the sheet enabled them to get started quickly from one session to the next and they could articulate what they needed to do in terms of SAY IT, MAKE IT, DRAW IT but required the teacher to model this first before they could be independent. I utilised the students in my grade to do peer coaching as part of the program. The students working in my group the first day, once confident, wanted to coach others using and help their peers. This became I powerful domino effect within the room.

By the end of the second week, students were recognising their growth and enjoyed working on goals and sharing with peers. A grade 5 boy who couldn’t do subtraction with 2-digit numbers at the beginning, was using MAB to model renaming with 3 digits numbers and saying ‘I’m using the block method and I proud because I could never do these before’.

Problem 2: Timing

My Maths lesson typically includes: A ‘problem first’ task or ‘Maths by myself’ time followed by our Maths together which had a focus to do with the project-based learning task that used mathematics elements to complete (see Dreamhouse).

For this article I will just focus on my timing for a ‘problem first’ task and Maths by myself.

I couldn’t get to the ‘clarity’ part during my ‘problem first task’ because I would run out of time in my lesson. Although I was happy with how the lesson was unfolding and students were engaged and involved, I was rushing my reflection (or did 30 seconds wrap-up) and felt there were students walking away still confused. I kept looking at the clock and wishing I had 10 more minutes or would continue after the break (who needs literacy?)

At times, I was conscience of too much talking at the beginning of the lesson that didn’t cater for all my learners. Some students already knew it and the students who needed it the most had lost interest because it was ‘too much talking’.

What I tried:

Question first provocation – see subtraction ‘geeking out’. This involved student analysing the problem and justifying their solutions. Short introduction. Long investigation and medium conclusion with students explaining their reasoning.

Using Peter Sullivan’s missing number problems, the students were given the same challenging problem. The students I had identified as needing to model renaming with manipulatives were my focus group. After a quick warm up using the manipulatives, they did the same challenging problem but had to explain how they were getting their answers using the MAB. These students chose to use MAB the next session to help with 3-digit subtraction.

Switches to timing of my lesson.

a.)

10 minute introduction

20 minutes working

5 minute reflection

b.)

A 5-minute introduction (student modelling method from yesterday)

15 minutes of working time

15 – 20 minutes of reflective time written. Choose one of these equations and explain your two methods for working them out.

c.)

15 minutes of working time

15 – 20 minutes teaching others. Show a peer what you have been working on. Convince them of how your method works and get their feedback.

Prompts for peers – why did you do that? What is that numbers value? Can you show me another way? How do you know you are correct?

10 minutes – reflection time.

REFLECTION

Peer coaching and reflective time became my highlights during the maths lesson. Students were able to articulate their methods to an audience and use reasoning to justify what they were doing. Students became teachers and showed patience and empathy while coaching their peers. They were engaged in trialling new methods and weren’t precious about ‘the right way’ to do subtraction equations and ‘I know because I do it in my head’.

Reflective time became crucial to the program. It sent the message to the students that they are working towards a goal and their thinking was valued more than the answer. I tell the students that the more they show me, the more I can help. It took me two weeks of this to get students to delve deeper into the reflective process to get more than ‘Thanks for fun activity.’ Although lovely to hear, they were avoiding telling me how their subtraction development was going.

The students understood that the practice time wouldn’t be as long as previous sessions as the emphasis would be on explaining their method and reflecting on how their goal was going. In this session there was no time for screencasts or creating resources, it was a pure practice and learning session. I modelled a method using MAB on the floor and the students were working at their tables. Mostly independently, but they were using each other as coaches.

My favourite moments as a teacher (aside from Netball and Soccer interschool tournament) is when you can have a conversation based on their reflection, helping them and seeing the next reflection say, they’ve got it!

I’m not sure if it was the combination of using different timings, students were just becoming more familiar with the expectations or an extra week had been allocated to subtraction created the feeling of success or it was a particular timing that worked. It was clear that when the program was working well, students were teaching students, the teacher was teaching students at their point of need, the class was calm and organised, all students were saying, making and explaining.

Problem 3: Optimising Learning Time

Problem

I felt the session was loose and students were accountable for working during this time. I was spending time managing rather than teaching.

When students had completed one or two equations correctly (based on their current goal) they thought it was best that they did a screencast to show they understood. The negative side of this was they found a quite spot in the building and spent the next 20 minutes attempting to record their thinking but starting over whenever there was a small problem like: not saying something exactly right, making a wrong move with their mouse drawing the numbers, forgetting what they were saying, sneezing etc.

The teacher and students were getting lost in the translation of what they should be doing in this time. Student agency is wonderful, but assuming they could just go work on a designated maths goal in a meaningful way was wishful thinking. The maths session felt loose, and it was too easy for students to not be accountable.

At the end of the lesson, I didn’t feel like I could accurately say what each student was working on and what they needed to do in the next session.

What I tried

We had a conversation about making mistakes and the importance of showing our mistakes. Mistakes were part of the learning process and we agreed it would be more impressive if someone made a mistake and could correct themselves then just getting a scripted product. The goal of the screencast was to show their learning journey rather than something polished and not authentic because it took them 20 tries to get it right.

If students went out of the class to do a screencast, they had to have one done in a 15-minute window and if it wasn’t completed they would have to complete in their own time.

Screencasting was done in our room. The expectation was that they would use a microphone and the working noise in the room would enable them to do it efficiently.

At C.N.P.S, we use the pro-social skills program called Play is the Way by Wilson McCaskill. After my colleague came back from the PD I was reminded of the Self Mastery Checklist. As a class we discussed the reasoning behind this method and how they need to continue to practice self-mastery to make the most of their learning opportunity. The phrases ‘Am I doing the right thing or the wrong thing?’ ‘Am I making a strong decision or a weak decision?’ ‘Am I being my own boss or am I inviting my teacher to be my boss?’. Then during the session, I would guide students back on track by saying something like, ‘Right thing or wrong thing Sammy?’ Can you sort that out?

I put greater emphasis on reflections and peer teaching.

Results

The tighter restrictions, such as not leaving the room, not spending time on computer issues, specific goals and a selection of ‘hard copy’ activities enabled students to spend more time practicing and minimal time getting organised.

The emphasis on showing and explaining was a turning point. I believe students understood that the practice time was going to be shorter and the lesson was building to them sharing with others. This put the emphasis on students knowing what they should be working on before having to share it with a peer. The reflective time enabled the work on their goal with a peer with the illusion of the showing, but it was a collaborative process.

Problem 4: Getting More Out of Reflections

Problem

Students were producing shallow reflections that didn’t really give me information I could use. Commenting on if the task was fun, saying it was easy (interestingly the students that got a lot of it wrong were the most vocal about this) and that they liked me as a teacher (could be worse).

Due to my timing issues, reflections were an afterthought and a way to get out to recess or lunch.

Students weren’t giving true indications of their subtraction skills or what they wanted from the teacher in the next lesson.

What I tried

Modelling examples using students. Using questioning to get more than a short answer. Prompts such as what did you try? How did it go? What was your biggest mistake today? What method is worth investigating? Why? What went well today? How has my subtraction improved? What do I still need more confidence in doing? My biggest challenge today was, what I need to work on next time.

Prioritising time for the reflection. We stopped earlier (sometimes felt too early) had a short discussion and students had time to create their response. I set a time of 10 minutes without them coming up to me with prompts on the board.

Trialling different methods of reflection. Verbally, written, addressing persistence over math content, whole group and individually.

I used the Dear Me, Dear Mr. Scott prompts. Dear me was something they were proud that they did or something that needed to remember for next time. The dear Mr. Scott was to let me know how they were going with the tasks, what they wanted help with or what they were ready for next session.

Results

I have found the reflective time to be crucial to the program. I feel that students are willing to be open and honest about their skills if they know they are safe and will get help. I made sure that I looked and responded to their reflections either verbally, using a stamp or a written comment. It was a simple as the next day, responding to their work, or saying I’ve organised this mini lesson because these people asked for it or addressing their problem. This part has enabled me to ‘direct’ the next lesson by using the students to teach others or model effective methods.

I tell the students that the more they show me, the more I can help. My favourite moments as a teacher (aside from Netball and Soccer interschool tournament) is when you can have a conversation based on their reflection, helping them and seeing the next reflection say, ‘they’ve got it!’

I am conscience of over doing reflective time (as pointed out by a grade six girl last year). As a result, I have been trying different strategies.

Maths by Myself

As you can see, getting the program running ‘smoothly’ in my classroom has required time, reflective thinking and small adjustments. After each session I would pick out one aspect that didn’t satisfy my aim and implemented a small change for the next lesson. I was very direct with my intentions with the students and my reasoning for the changes. I wouldn’t say that anything I did or didn’t do was a disaster, but the lesson didn’t feel satisfying. It wasn’t until the last few sessions of a two week cycle, that the look, sound and feel was amazing.

Students were engaged with their goal, they were supporting and teaching one another, I was running a mini lesson with a group working on decimal numbers, I had a group of four students pumped about finding more ways to solve a problem solving question (they were up to 67 ways that didn’t work before they found a pattern that enabled them to do 24 ways that worked, but wanted to find the next pattern) and others were modelling and recording subtraction equations.

In regards to my question, ‘How long does it take to implement a new program?’, I don’t have a definite answer. For this program it took two weeks of trialling and tweaking, but I knew how I wanted it to look, sound and feel like from the beginning. I still have elements that I would like to work on with the program and my own teaching techniques, but saw the success of ‘Maths by Myself’ in the classroom. When the program is working well, students are engaged in developing their maths skills, they support each other, they feel achievement in working towards their goals and the post assessment results were positive.

This article definitely became bigger than expected. I am hoping that it will show that no program will be implemented seamlessly and requires bravery and persistence.