Thinking Things Through - Review

Thinking Things Through, Problem Solving in Mathematics

Leone Burton

Introduction

Problem solving requires questions to be based in a real world context, providing students with more authentic engaging tasks.

It is only real when pupils take responsibility for their own mathematical thinking. To support this, teachers need to change their view of their own role from that of one of responsibility to one of a resource for students.

Problem solving in seen as a challenge for the students so they are more engaged and motivated in the work.

What makes problem solving different?

This chapter of the book looked at two different solutions to a problem solving questions and odd and even patterns and relationships.
Talked about problem solving not requiring a 'correct' approach to solve questions and that the students in the examples may well have achieved the same learning/understanding despite working in different ways.

Why is problem solving important?

'The ability to solve problems is at the heart of mathematics' (Cockford Report, 1982). This idea puts into concern the disconnect that students experience in a modern maths class between the skills they are learning and the knowledge to use them.
Problem solving improves pupils' attitude, confidence and achievement in class. It also embraces the spirit of inquiry which is a quintessential aspect of maths.
In a problem solving classroom there needs to be evidence of questioning. Over flow questions can be recorded on a question board to be discussed later.
There needs to be evidence of challenging. Both as a noun and a verb. Challenging questions for the students and challenging their answers between themselves.
Finally, there needs to be evidence of reflecting around the problem by the students.
Teachers need to look at the process students use, rather than the outcome they achieve.
Often teachers are surprised that there is a stark difference between what students actually know and what they use to solve problems.

How to get going

Problems can easily provide differentiation. This makes problem solving an ideal technique for whole class, multi-level teaching.

Students should be offered a choice of problems to select from, although don't overwhelm them with choice either.

Problem solving could be integrated into homework.

Using representations to help solve the problems is key - teachers must make sure they have a lot available for the students to use.

Students need to understand the cyclical process of problem solving. No more 'I'm finished!'

Teachers need to promote inquiry and curiosity in their class with these questions.

Pupils should keep clear records as they go so they can easily share their thinking and present results well.

Modelling problem solving together is essential in showing pupils that the skills and process is an important one that is valued in the class.

The problem-solving process

Burton talks about the problem solving process consisting of four different phases of activity.

1. Entry - where you are trying to understand the question,
2. Attack - trying to find a resolution to the question.
3. Review - examining and reassessing resolution to make sure it answers the question.
4. Extension - investigate new problems that have arisen from the original question.

What about individual differences?

Again, student choice is essential in supporting individual differences. Students undertake the problem solving work in groups, but all children monitor their own work. After some time working together to answer problem solving questions students work out their own dynamics in groups and work together effectively.

Teachers need to focus on giving students space and acting more as a resources for students.

Have the pupils gained?

Developments and growth in the students may take a long time to become apparent. Patience is the key as problem solving covers a wide range of skills.

Students can share their understanding by writing a message to their friends to help them solve the question - they must think clearly and articulate their working well to help them understand.
Another extension activity could be to write another question that uses the students answer.

Problems 1-30

This book also features a section with 30 problem solving questions. These are well laid out and provide teachers with prior information students need, materials required, skills covered, suggestions for solving the question and extension ideas.

Opinions

Problem solving seems to be an easy access technique to use in class that has a multitude of benefits. It not only allows students to become more articulate with their maths skills but also develops social behaviours and thinking skills.

I like how easily problem solving caters to mixed ability classes.

Using problem solving as part of weekly homework sounds like a good way to continue to develop students reasoning skills, but must be supported by in class teaching around how to approach this type of question effectively.

Last Child in the Woods - Review

The Last Child in the Woods
Richard Louv

Part 1: The New Relationship Between Children and Nature

Part 1 touches on some of the benefits that can be gained (for adults and children) through a relationship with nature. It can provide a calm and supportive environment that allows us time to think and recharge. But unfortunately as we are becoming more and more dependent on electronic stimulants we are running the risk of losing our understanding of this relationship.

I liked the point that Louv made about being in nature meant 'doing something, about direct experience - about about not being a spectator.' This inspires me to think about opportunities in the classroom for outdoor experiences to take place, which will truly and fully engage the learners.

I was also attracted to the fact that through a positive relationships with nature, students are catered to in a holistic sense.

Part 2: Why The Young (and the Rest of Us) Need Nature

Louv talked about a correlation between the rise of childhood obesity in America and a rise in organised sports. This draws a conclusion that an increase in sport isn't the solution to childhood obesity but he believes rather that more unstructured outdoor play provides the answer.

This part of the books presents anecdotes of how nature has supported people in their lives and how a higher contact with nature results in lower stress levels. There are also lots of studies which show that more time in green spaces reduces symptoms of ADHD in children.

Direct experiences with nature have been replaced by indirect technological experiences. People are more aware of environmental issues on a global scale rather than a local one.

It was interesting to read about what can be learned through building a tree house. Although building a treehouse may not be a logistical option in most primary schools there are a host of similar activities that could be used, which would provide children with authentic, direct, hands on, outdoor learning experiences.

Part 3: The Best of Intentions: Why Johnnie and Jeannie Don't Play Outside Anymore

This part of the book talked about the barriers to free creative play outdoors. The reasons it focused on were a lack of time - every minute being allocated to an organised activity, safety concerns and a lack of knowledge.

When Louv discussed that difference between free and organised outdoor play I found it interesting that he mentioned that usually people have fond memories of the free play activities but not the organised ones. Children also didn't see the organised activities as a form of playing, rather something they had to do.

Part 4: The Nature-Child Reunion

This part of the book discusses how parents can increase their child(ren)'s experiences with nature. Through viewing it as something that will support their development, modelling outdoor experiences, releasing fears about outside situations and encouraging safe independence.

Whilst this section was interesting, it is less informative for me to use in my practice. It may however, be useful to inform conversations with parents and families of students I teach.

Part 5: The Jungle Blackboard

Richard Louv discusses the fact that concept of environment based education is at least a century old. This is interesting as it shows that it is not a new fad. I have also been told by teachers who have more experience than me, that education cycles around the same approaches which can be seen in the fact that this is an old idea resurfacing in education today.

It talks a lot about place based education, which is a focus in teaching in New Zealand as a way to help students become more connected with their local and area and feel a strong sense of place. Through using this technique in schools in America it has shows to result in better achievement, attendance and behaviour.

Schools in Finland are regularly discussed these days and their educational approach appeared in this section of the book. Finland's techniques appear to be quite at odds with approaches in other countries, such as America, but seems to achieve remarkably high results.

This part of the book also discussed that schools need to provide natural green spaces to play in, not just manicured lawns and playgrounds. Natural and wild spaces provide students an opportunity to be creative in their play and to interact with nature in an organic sense.

Part 6: Wonder Land: Opening the Fourth Frontier

Humans have lost their ability to coexist with wilderness. This is an area that needs to be addressed if nature is to be successfully reintroduced into cities.

This part discusses the future in terms of green architecture and environmentally sensitive housing developments. This is an area of reconnection with nature that far surpasses my focus of this area.

Louv discusses that part of the problem for the disconnect between children and nature is to do with litigation. This is a particular problem in America, and whilst people are trying to come up with solutions to this problem, it restricts people's ability and willingness to be more proactive in providing natural outdoor experiences.

Cities used to be built with planning towards including natural spaces. Now population has grown but natural spaces haven't reflected this and no longer meet the requirements of the population they serve.

Part 7: To Be Amazed

The final part of this book talks about the intrinsic link between spirituality and nature. This connection provides a greater scope for engaging people with nature and becoming proactive about protecting and experiencing it.

Louv also discusses that the pace of progress will be slow but there will be progress and we need to persevere.

Opinions

More practical examples for use in classroom would be useful.

I need to find the balance between technology and nature in the classroom, as I believe both are important for equipping students to be successful in the world.

Good to start to develop my understanding of why outdoor learning is important.

How can outdoor learning be used to develop literacy and maths skills?

Google Educator

I'm very excited to announce that I am now officially a Google Certified Educator.

And here's the certificate to prove it!

The course required some self study, making sure I was comfortable with the different apps available from google and had a strong understanding of how to implement the different features to benefit my teaching practice.

Now I can't wait to get an opportunity to use these skills in the classroom to support students' learning and help connect them further with the wider world.