# When a Maths Curse is a Good Curse!

In one of my previous posts I wrote about the use of children’s literature to encourage rich mathematical investigations and improve student engagement with mathematics. One of my favourite books, Math Curse by John Szieska and Lane Smith, is described in the blog post as a great way to engage reluctant learners. Even better, Math Curse encourages children (and their teachers) to see the mathematics that is embedded in every aspect of our lives. In this post I am going to share some student work from a Grade 3 classroom. In this classroom, the teacher read the book to the students before challenging them create their own class maths curse. The children took their own photographs, and working in small groups, they came up with a range of mathematical problems and investigations, which they then gave to other groups to solve.

Here are some of the photos with their accompanying questions:

1. If one of the beyblades spins for 2 minutes and 31 seconds and the other one spins for 1 minute and 39 seconds what is the difference between the two times?
2. If one of the beyblades spins for 1 minute and 1 second and another spins for 78 seconds, which beyblade spun for the longest and by how long?

Hair:

1. If there are 31 people in the class (10 boys and 21 girls) and all of them have hair that is 30cm long. Half of the boys cut 10cm off their hair, the other half cut 20cm off their hair. How long is the classes hair now altogether? How long was it before? How much hair has been cut altogether?
2. Check your friend’s hair. Estimate how long it is when it is out, how long it is when it is in a ponytail, and how long it is when it is in a braid. List some different ways you could check if your estimate is accurate? What are the potential problems with your methods?
3. I’m 9 years old. I had really long hair for 6 years, then I cut it. How long did I have short hair for?
4. I have 5 friends that are girls and 2 friends that are boys. All 5 girls have hair length of 50cm. The boys both have different lengths of hair. The 1st boy has 30cm of hair, the second has 25cm of hair. What is the difference between the 1st boy and the girls and the 2nd boy and the girls?

Birthday Balloons:

1. Write down the dates of important celebrations. If you add all the dates together, what is the value of their numbers?
2. How many days are there in 6 years?
3. If everyone’s birthday occurred every three years (starting the year you are born) what years would your birthday fall on?
4. If Lisa and Jane went on a holiday every 2 months, how many holidays could they take in a year?
5. If you could rearrange the seasons, what months would you choose to be Spring? Why?
6. What is the most popular letter in the days of the months?
7. Why do you think there are 4 seasons in a year?

From Problem Solving to Problem Posing

What is the purpose of getting students to write mathematical problems? First of all, the problems give us good insight into whether students recognise mathematical situations, and whether they understand where, how, and what mathematics is applied in day to day situations. An added bonus is that the students are highly engaged because they have ownership of the mathematics they are generating, the topics they choose are of interest to them, and stereotypical perceptions of school mathematics are disrupted.

Student Reflection

The students who wrote the examples above completed a structured written reflection following the sequence of designing and solving each others’ maths curses. Here are some of reflection prompts and a sample of responses:

What did you enjoy about today’s learning?

“working with my team”
“working at the problems for a long time and then finally getting them after a long, hard discussion”

“solving questions that my friends wrote”

“I felt challenged and I learnt more about what maths is”

“working with my group, choosing our own questions and learning something new”

“I liked the chess card the best because we had to solve it together and use problem solving”

“having a go at tricky questions even if i got them wrong”

Did you learn anything new?

“how to work things out in different ways”

“not every question uses just one skill like addition, division, multiplication or subtraction”

“Maths is not always easy”

“how to work together”

“Everyone in the group has different responses so we needed proof to figure out the right one”

“It surprised me how hard my own questions were”

“I didn’t know that we could come up with so many interesting questions”
“I got a shock! We had to research to solve some problems, Adam even taught me how to add a different way”

“I got some questions wrong “

“It was hard but if we put our brains into gear we could figure it out”

“I was able to play while doing maths”

Using activities such as this provides multiple benefits for students. Contextualising the mathematics using students’ interests highlights the relevance of the curriculum, improves student engagement, and makes mathematics meaningful, fun and engaging!

# Setting up Your Students for Mathematical Success : Tips for Teachers

Many children begin the new school year with feelings of fear and anxiety. Will they like their new teacher or teachers? Will the work be difficult? What will the homework be like? As you prepare programming and planning for a new teaching year and new students, give some thought to the strategies and activities you and your students can do in the first few weeks of term to ensure everyone gets the most out of their mathematics lessons for the entire school year. Think about what you can do differently in 2017 to make your work more engaging for both you and your students. The following are some ideas to consider.

1. Be a positive mathematical role model

I’m sure this won’t come as a surprise, but there are teachers in our schools who actually don’t like maths and don’t like teaching it. Why is this a problem? Student know! This knowledge perpetuates the common misconception that it’s okay to dislike mathematics, and worse still, it’s okay to be considered ‘bad’ at maths.  Unless the teacher is an award-winning actor or actress, it’s really difficult to hide how you feel about a subject – it’s obvious in body language, tone of voice and of course, the way you teach the subject and the resources you use. If you know someone like this, suggest they seek some support from a colleague or colleagues. Often the reason a person dislikes mathematics is related to a lack of confidence.

1. Get to know your students as learners of mathematics

The foundation of student engagement requires an understanding of students as learners, in other words, the development of positive pedagogical relationships (Attard, 2014). Positive relationships require teachers to understand how their students learn, and where and when they need assistance. It’s also important to provide opportunities for ongoing interactions between you and your students as well as amongst your students.

Another way to get to know your students as learners is to use existing data. For example, if your school takes part in external testing such as PAT, you can use this data as a guide. However, keep in mind that things change quickly when children are young – what they knew or understood three months ago may be very different after a long summer holiday.

A great activity to do in the very first few maths classes of the year is to ask your students to write or create a ‘Maths Autobiography’. If required, provide the students with some sentence starters such as “I think maths is…” “The thing I like best about maths is…” “The thing or things that worry me about maths is…” They could do this in different formats:

• In a maths journal
• Making a video
• Using drawings (great for young children – a drawing can provide lots of information)
1. Start off on a positive note

Have some fun with your maths lessons. I would strongly recommend that you don’t start the year with a maths test! If you want to do some early assessment, consider using open-ended tasks or some rich mathematical investigations. Often these types of assessments will provide much deeper insights into the abilities of your students. You can even use some maths games (either concrete or digital) to assess the abilities of your students.

A great maths activity for the first lesson of the year is getting-to-know-you-mathematically, where students use a pattern block and then need to go on a hunt to find other students who have specific mathematical attributes. Encourage your students to find someone different for every attribute on the list, and change the list to suit the age and ability of your students. For example, in the younger years you could use illustrations and not words. In the older years, you could make the mathematics more abstract.

1. Take a fresh look at the curriculum

Even if you’ve been teaching for many years, it’s always good to take a fresh new look at the curriculum at the start of each year. Consider how the Proficiencies or Working Mathematically processes can be the foundation of the content that you’re teaching. For example, how can you make problem solving a central part of your lessons?
Take a close look at the General Capabilities. They provide a perfect foundation for contextual, relevant tasks that allow you to teach mathematics and integrate with other content areas.

1. Consider the resources you use: Get rid of the worksheets!

Think about using a range of resources in your mathematics teaching. Regardless of their age or ability, children benefit from using concrete manipulatives. Have materials available for students to use when and if they need them. This includes calculators in early primary classrooms, where students can explore patterns in numbers, place value and lots of other powerful concepts using calculators.

Children’s literature is also a great resource. A wonderful book to start off the year is Math Curse by Jon Scieska and Lane Smith. Read the book to your students either in one sitting or bit by bit. There are lots of lesson ideas within the pages. Ask your students to write their own maths curse. It’s a great way to illustrate that mathematics underpins everything we do! It’s also a great way to gain insight into how your students view mathematics and what they understand about mathematics.

1. How will you use technology in the classroom?

If you don’t already integrate technology into your mathematics lessons, then it’s time to start. Not only is it a curriculum requirement, it is part of students’ everyday lives – we need to make efforts to link students’ lives to what happens in the classroom and one way to do that is by using technology. Whether it’s websites, apps, YouTube videos, screencasting, just make sure that you have a clear purpose for using the technology. What mathematics will your students be learning or practicing, and how will you assess their learning?

1. Reach out to parents

As challenging as it may be, it’s vital that parents play an active role in your students’ mathematical education. They too may suffer from anxiety around mathematics so it’s helpful to invite them into the classroom or hold mathematics workshops where parents can experience contemporary teaching practices that their students are experiencing at school. Most importantly, you need to communicate to parents that they must try really hard to be positive about mathematics!

These are just a few tips to begin the year with…my next blog post will discuss lesson structure. In the meantime, enjoy the beginning of the school year and:

### Engaged teachers = engaged students.

Attard, C. (2014). “I don’t like it, I don’t love it, but I do it and I don’t mind”: Introducing a framework for engagement with mathematics. Curriculum Perspectives, 34(3), 1-14.

# Using Children’s Literature for Mathematical Investigations

How often do you progress from problem solving to investigation-based work in your mathematics classroom? Have you ever considered using children’s literature in your mathematics lessons to provide an interesting and creative context for mathematical exploration?

The idea of investigation is fundamental both to the study of mathematics itself and also to an understanding of the ways in which mathematics can be used to extend knowledge and to solve problems in very many fields” (Cockroft, 1981, p.250).

Mathematical investigations move beyond problem solving, yet are not ‘project work’ They are inquiry based and support a constructivist approach to learning in which learners actively construct their own knowledge through reflection on physical and mental actions. During investigation-based work, learning is placed within a purposeful context that requires students to engage in mathematics by combining content knowledge with higher order thinking skills and creativity. Investigations provide insights into the work of mathematicians and mathematics as a career, as well as providing opportunities for students to adapt, modify, and build on prior knowledge (National Council of Teachers of Mathematics, 2000).

Children’s literature can provide a rich context from which to begin mathematical investigations. They provide opportunities for students to incorporate creativity into mathematics while creating links across other subject areas. Using literature as a stimulus for open-ended investigation can provide each student in the class an opportunity to achieve success, regardless of mathematical ability by creating a rich, shared context.

There are many children’s books that lend themselves to mathematical investigations- some are written with that purpose in mind, and others are books that were not intended for use as a stimulus for mathematics, but naturally lend themselves to mathematical exploration. Marston (2010) identifies three different types of mathematical picture books:

1. Explicit: books purposefully written for teaching and learning in the mathematics classroom, e.g. Counting on Frank (Clements, 1990) or How Big is a Foot? (Myller, 1962);
2. Percieved: books with incidental mathematical concepts as perceived by the teacher e.g. Goldilocks and the Three Bears; and
3. Embedded: books that have embedded mathematical ideas but written to entertain rather than specifically for teaching and learning e.g. Uno’s Garden (Base, 2013)

A good book to use as a stimulus for mathematical investigations is one that builds intrigue and excitement in your classroom. A good book will also include humour, whch is important if you want to engage reluctant learners. One of my favourite children’s books is Math Curse (Szieska & Smith, 2007) which describes a young child who gets a math curse after his teacher, Mrs Fibonacci, says “you know, you can think of almost anything as a math problem…”. The book encourages readers to see mathematics in almost everything they do, from waking up in the morning to catching the bus to school and sharing cup cakes with the class. Throughout the book the authors have placed interesting mathematical challenges mixed with lots of humour.

The best way to begin a mathematical investigation is to read the book, and then brainstorm possible mathematical questions that could be explored. Once students have had a chance to share their ideas, it is up to the teacher to facilitate how the investigation should progress. Students can form groups and select an area to investigate, or they can conduct an individual investigation that could be teacher guided. Perhaps a group could select more than one area to investigate.

Here is are some websites that list children’s literature suitable for use in mathematics teaching and learning:

http://everydaymath.uchicago.edu/teachers/k/literature-list/

http://literacy.kent.edu/Oasis/Resc/Educ/mathkidslit.html

http://www.the-best-childrens-books.org/math-for-kids.html

Base, G. (2013). Uno’s garden. Sydney: Penguin Books Australia

Clement, R (1990). Counting on Frank. Sydney: Collins

Marsten, J. (2010). Developing a Framework for the Selection of Picture Books to Promote Early Mathematical Development. In C. Hurst, B. Kissane, & L. Sparrow (Eds). In Shaping the future of education. Proceedings of the annual conference of the Mathematics Education Research Group of Australasia. Fremantle WA: MERGA

Myller, R. (1962). How big is a foot? New York: Bantam Doubleday Dell Publishing Group

National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: NCTM

Szieska J., & Smith, L. (1995). Math Curse. New York: Penguin