## A problem solving routine for mathematics

December 13, 2016 § 2 Comments

Our team wanted to develop a problem solving strategy which allowed students of all ability levels to make progress in solving problems. The intent was to find a method which could be useful for most topics of high school mathematics, but it could also be useful for other subjects. In order to implement this project effectively it was important that each team member had input into each part of the process so that the final product was co-created.

So what is a thinking routine and who can benefit from using a thinking routine?

A routine can be thought of as any procedure, process, or pattern of action that is used repeatedly to manage and facilitate the accomplishment of specific goals or tasks.

Some of the team attended a great session with Mark Church and he highlighted some of the foundational aspects of thinking routines. The purpose of any thinking routine is to generate ‘thinking’ which students might not ordinarily consider.

Team process

In order for this routine to effective we developed it as a team using the design engage methodology which is based on design thinking. This allowed us to explore the steps of empathy, values, vision and desired behaviours in order to define the problem and develop solutions.

We eventually opted for a problem solving routine which is useful for students in standardised tests, as well as regular classroom problem solving questions. The final routine is also generic which allows for its used with other subjects.

We justified each of the steps in the following ways:

Ask the question in your own words – There was a habit that students were forming where they would ask for help before making meaning of the words and phrases within a question. We wanted to push back to the students so that questions that they posed from the original question were richer and had great purpose.

Break it down –  By identifying key items, numbers or words and then underlining or highlighting the same meant that students minimised transcription errors and were able to refer to important information quickly.

Connections – If a student can identify which part/s of their previous learning can connect with the current question then a process of elimination can help in identifying a strategy, starting point or next step. Muir, Beswick and Williamson (2008) note that ‘Problem solvers must be able to connect their own knowledge representation and the problem situation at hand and the extent to which they are able to do this, in turn, impacts on their success with solving the problem.’

Decide, do I need to draw a diagram? – There are some topics within mathematics where questions can be answered without the aid of a diagram however there are some topics where a diagram can play a helpful role in developing thinking and understanding. Should the student consider constructing a table, a 2 or 3 dimensional representation or a sketch? Van Garderen and Scheuermann (2015) state that students should receive explicit teaching on how to construct diagrams so that the process is meaningful.

Evaluate – Does the student’s response actually answer the question that has been asked? Does this answer make sense? Would a part time worker at a bakery be expected to earn \$54 000 per week? Too often students answer questions that have note been asked so this step allows for students to go back to their underlined/highlighted elements and ensure that the question has been answered.

Feedback conversations with students

With the use of our thinking routine we are finding that conversations with students are occuring on multiple levels. Firstly, teachers are providing feedback on conceptual and procedural understanding, and secondly, students receive feedback on how they have applied the thinking routine.

We have used a logo and then printed the logo onto pens in order to have students consider the routine and remind them of its use. The research on problem solving categories of students show that many operate as novices or beginners and the hope is that this routine will push them towards the expert end of the problem solving scale.

Could this routine work in other classrooms?

What improvements to the routine can you identify?

@markliddell

Muir, T., Beswick, K., & Williamson, J. (2008). “I’m not very good at solving problems”: An exploration of students’ problem solving behaviours. The Journal of Mathematical Behavior, 27(3), 228-241.

van Garderen, D., & Scheuermann, A. (2014). Diagramming word problems: A strategic approach for instruction. Intervention in School and Clinic, 50(5), 282-290.

## 3 Ideas to help focus on the important work

For the past 12 months I have been focusing on staff appreciation. I considered all of the different ways that I could best appreciate the hard work and commitment of the team and it boiled down to organisation. There was great help on hand from my mentor/coach and it was a year of putting in place routines, processes and feedback loops so that I could achieve the goal. There were 3 Ideas that proved very helpful in my work:

1. Write down your annual focus every day

I have many tasks to complete and not enough time to complete them so I have to make decisions. I was sick of doing 8 things half heartedly each year so I decided to pick just one task. Organisation. I enjoyed the Peter Bregman article and chose to write down my one task on a new post it note each morning. Each day I would write down organisation at the top of my post it note and each day I aimed to do at least one thing to help reach this goal. On other days I could put in a few hours work on this task.

2. Schedule your most important work in the calendar

Most important work that I complete is not urgent. Most important work that I complete doesn’t have a 24 hour deadline. Urgent work can sometimes take over our focus on a regular basis and we need ways to combat this. I had a permanent booking with my mentor so that I could ensure the meeting would take place. This meant that I always had the opportunity receive feedback on my progress and could give account of my decisions. George Couros always asks good questions about priorities and effective planning.

3. Have a routine to measure progress

It’s easy to begin work on an annual goal but with the busyness of a school year it can be difficult to remain focussed. I found that by booking a one hour meeting with myself each week I could ask questions about my progress, reflect on aspects of my project and then see if changes were required to keep on track. By asking the same questions every week I was able to benefit from a consistent framework and enjoyed looking back on my reflections.

What routines do you use to focus on important work?

What accountability do you need to reach your goals?

## Are you in cruise mode?

I’m preparing for an ocean swim race in a few months and right now I’m building fitness by running. I downloaded RunKeeper to help record some of my times but never did I realise the impact that it would have.

Every 5 minutes, during my run, I get an update on how far I have run and the average number of minutes per km. At first these updates were annoying, but now that I’ve got into the swing of it, the reminders are pushing me to achieve times and distances that are well beyond my expectations.

I’m getting regular, objective and consistent feedback on my running and it feels great.

The key part of the feedback that was helpful related to when I was ‘cruising’ during my run. I found that along flat sections of the run, instead of trying to maintain a fast pace I was simply moving along but without much thought or motivation. So now this hits home to my normal day or week at school. How can I identify the times when I enter cruise mode and what can I do about it?

When am I most likely to cruise?

– If I begin a day without a plan. I like to use some of the elements from Peter Bregman’s 18 minutes.

– If I don’t have times assigned to the tasks that I wish to complete.

– If I haven’t clearly laid out the tasks of a project.

– If I sit in a work space where I will be distracted.

I have always found it helpful to reflect on my day and then see which parts were fruitful and which parts were not optimised. It has been satisfying to build up some self awareness of my productivity and I hope that it will continue. My mentor has provided some great tips and advice too.

What is your productivity level like?

Do you have a more successful Monday/Tuesday and then reduce productivity during the rest of the week?

Are you aware of your good and/or bad habits?

Do you need a mentor or coach to help with aspects of your productivity?

@markliddell

The Cole Classic Ocean swin race

## Saying thank you to each of my mentors

As I reflect over the past few years of professional learning I realise that I need to pass on a thank you to each of my mentors. They have played an important role in my development and these are some of the key ways that I have benefitted from their service.

1. Confidence – Each mentor has helped me to make sense of difficult and complex situations and offered advice that has provided me with confidence going into new situations. They have provided frameworks for decision making, routines for organisation and procedures for continually developing in leadership skills.

2. Humility – We all make mistakes and it was interesting to hear about how each mentor learnt from their failures. It spoke volumes of their character and convictions and has reminded me of the great importance that humility plays in leadership.

3. Courage – They have all encouraged me to reach for the stars, and this has made a huge difference to my outlook. They have encouraged me to have the difficult decisions, to get alongside team members and to not give up.

Thank you to each mentor who has invested in me.

## Students who can solve real-world problems

February 23, 2014 § 1 Comment

I spent a team day with @cwoldhuis and we created memories. Our goal was to make progress on a Year 9 Mathematics Learning Project and it was a very enjoyable day of professional and personal development. We started by visiting some Year 1 and 2 students at our school who were participating  in  a Maths experience where each student was teamed to solve a problem. The students we spoke with were aiming to describe their classroom to a teacher in Austria who wanted to build a similar classroom. It highlighted a number of important elements within the process that we were about to use. The PBL elements that we used stem from the Buck Institute (link below)

We then noted the syllabus outcomes for our students.

Aside from syllabus outcomes, we wanted to address other outcomes such as learning skillsthinking routines and aspects of growth mindset research.

Next we considered the development of our big idea. It was an interesting process because the first few attempts that we wrote didn’t stick but all of the follow up suggestions  were debated to an eventual outcome. We also got some help from our critical friends at this stage. This is the protocol that we’ll continue to use.

Within these learning experiences the students will get to make choices about how they present and communicate their work. We wanted to design a statement that gave direction but also allowed for student voice/choice.

The entry event for these projects is a time to give students an inspirational experience that can help to direct their thoughts and ideas. We plan to enlist some other staff members and ensure that the students are impacted on many levels. The discussion around this event got everyone excited about the possibilities of this project.

The timeline is an important aspect to plan and we will continue to work on this in the next few days. You’ll see that feedback and critique is a vital part of the process. This example helped for some of the team members to see its power. The public audience is another vital ingredient so we will lock in our location and times soon.

We are in the learning phase of Project Based Learning for Mathematics at our school and it is an amazing journey. If you can see any gaps in our process or would like to offer some advice then we will be all ears. It’s helpful to note without the PBL process, real world problem solving can be both boring and unengaging as Dan Meyer points out. We are using PBL because we want to provide room for student curiosity and personalisation within an environment that normally treats every student the same.

@markliddell

Buck Institute of Education – elements of PBL

## So what is deep learning? #DLMOOC

December 21, 2013 § 1 Comment

I’ve just signed up for Deeper Learning MOOC which begins in January 2014. Earlier this year I had the opportunity to spend a few days at High Tech High (a leadership partner of the MOOC) and it was a great experience. The leadership of the school have set in place a culture of learning for teachers and students alike.

Through a series of workshops, conversations and sessions I was able to learn about their use of physical space, the design principles for project based learning and the priorities for mentoring of teachers. A number of twitter friends will also take the MOOC and I’m looking forward to learning by debating, reflecting, reading, prototyping and comparing.

The first MOOC that I undertook was the #howtolearnmath course with Stanford University Professor Jo Boaler. It was a fantastic course that offered some amazing insights relating to learning, psychology and motivation. There are three main reasons that I enjoy taking MOOCs:

Flexibility

I can listen when I need to. I can reflect when it suits me. I can chat with others at most times throughout the day. I’m being presented with learning opportunities from some of the most respected leaders in the field and I like to have freedom in when/how I respond.

Purpose

Professional Development doesn’t have a good reputation for assisting ‘development’ in one’s learning journey. Most of the time it’s just ‘sit hear and listen to this’ and then we’ve ticked the box. I like how this DLMOOC has been set up to model purposeful and passionate learning. One of the lines from the course states:

Our aim is for you to leave each session with a new idea, tool, or practice that you can put into practice the next day.

Modelling learning

I want to ensure that I am modelling learning skills to my students. There must be aspects of critical thinking, creativity, communication and collaboration to my professional learning. To go beyond the ‘surface level’ learning and into the territory of deep learning, teachers need to be intentional and consider routines/opportunities that students can develop. A few months ago Ron Ritchhart presented in Sydney and provided this helpful self assessment that I’m going to begin using in 2014. By participating in this MOOC I hope that I’m not only developing great skills for teaching and learning but I’m also developing skills as a learner.

@markliddell

## The major principles and strategies of learning

November 5, 2013 § 1 Comment

On Thursday we are beginning the first session for our book club. @eduruminate has got the ball rolling and suggested John Hattie and Gregory Yates’ ‘Visible Learning and the Science of How We Learn’. I’m excited for a number of reasons:

• Reading new research makes me feel good. I like to know what researchers are investigating and then finding out the implications for teaching and learning. Education is a very exciting field right now. Research is constantly providing new insights and ideas that requires us to evaluate our practices, structures and beliefs.
• The people in this reading group are going to provide good debate. They are from all different parts of the school and I can guarantee that with the number of different perspectives I will learn things that I would have missed without their contribution. Lately I’ve found that primary teachers provide very helpful strategies for high school teachers because they care about students and they care about learning. (Some high school teachers may be known for just caring about ‘their subject’).

• John Hattie has a great reputation for providing insights that are focused on learning. I spend a lot of time focusing on aspects of technology, Maths, leadership, team work and productivity so it will be nice to focus in this direction of student learning.
• It’s always nice to share learning and so I’m looking forward to tracking the journey of twitter. We’re in the process of confirming a hashtag and I’m pretty sure that #hattiechattie will be used.

@markliddell