Introducing Cat Maths cards activities, games and lessons

Why are the Cat Maths cards so amazing?

We were excited to take delivery of two packs of prototype Cat Maths cards. They look wonderful, and have given us the chance to try out various activities and games with children and teachers. This has confirmed our hopes that the cards are versatile, engaging and afford multiple learning opportunities in mathematics, including statistics. There are also a whole range of games you can play with them, appealing to different people. Children learn well in games, and these rich and varied cards allow for a wide range of games that teach concepts and skills through their mechanisms.

Some of the cards from The Cat Herder Games

Some of the cards from The Cat Herder Games

Cat Maths Cards

In a single set of Cat Maths cards there are 75 Cat cards with multiple elements. Each cat is one of six colours, tabby, white, tortoiseshell (or calico for our American friends), ginger, black and brown. There are male cats and female cats. Each cat lives mainly indoors or outdoors. They are different ages, between 1 and 20, and the birthday cake symbols are different colours for different age ranges. The cats can have one of four natures – playful, tough, sleepy and snooty. Each cat has between 0 and 4 toys, a combination of ball, mouse, post and wand. And each cat is named.

Along with the cat cards are twelve Attribute cards, which list the different things that the cats can be classified by. These are orange in colour, so I’m pretty sure they will be known as the orange cards. Similarly there are twenty-seven green Value cards that list the colours, habitats, natures, age ranges etc.

Ideas for activities

Organise and sort (individual, small groups, or whole class as groups)

Children love to organise, sort and order things. It is interesting that the first thing many children like to do is to put the cats in order of age. They can then be encouraged to think of other ways to sort or order – by colour, gender, number of toys etc. Ordering, looking for patterns and comparing are important mathematical skills. One five year old girl enjoyed turning over an orange card, arranging ten cat cards according to the attribute specified and then telling me what she had found out. She would happily have gone through all twelve orange cards if I hadn’t wanted to try out other activities.

A fun physical class activity is for each child to have one card, and they arrange themselves physically according the attributes on a turned over orange card. For example you turn over the Orange card and it says “Number of Toys” so the children organise themselves according to the number of toys their cat has.

Engrossed in the catsSorting game: Cat Herding.

This is the same as the Dragon Games event, Formations, which kids love. Each player starts with 3 cards, face down in front of them, hands off the table. Turn over an orange card and race to order your cats according to what the orange card says. You could be sorting by colour, age, name, nature etc. The first finished gets another cat to add to the herd. The winner is the first to nine cats. This appeals to older children, who are more competitive.

Counting

Children can count all of the different categories. Turn over a green card, and it might say “Playful”, so you count all the playful cats. Then turn over another green card – “Black” and you count the black cards. Children like to record their observations in sentences.

In a larger group, individual children or groups of children are given an equal number of cards. Turn over a green card and see which group has the most of that kind. For example the green card says “Mouse”, and the children count how many of their cats have a mouse, and decide who has the most.

Subtraction

Children or groups of children are given an equal number of cat cards. Turn over a green card, and they can choose one of their cats that has that characteristic to be “adopted”. Keep doing this until one child or group has managed to have all their cats adopted. Talk about how many you started with, how many have been placed, and how many are left. Discuss who has the most and fewest cats left. Children will start to work out a strategy to adopt out cats to maintain variety in the ones they keep, in order to increase their chance of winning.

Statistical analysis

At the early levels of school, the emphasis in statistical analysis is on answering statistical questions by sorting and counting. Each child can have their own investigation. Here is an example using the Statistical Enquiry Process:

Problem: I wonder if more of our cats are playful or snooty?

Plan: We will collect data on our twenty cats and see what natures they have.

Data: The children have twenty cat cards from which they can see what the nature is.

Analysis: The children count how many cats of each nature. They can put the information in a table or graph, or use the cards to make a picture graph.

Conclusion: We found that our cats are more likely to be playful than snooty. Seven of our cats were playful, whereas only three of our cats were snooty. There were also five sleepy cats and five tough cats.

This leads on to inference

Now this is what is really exciting: each group of children will have a different set of cards, and will get a different result. This helps them to get an intuitive understanding of variation and sampling at a young age. This does not happen if you only use one set of data, often generated from the children themselves, which is what commonly happens in Primary level statistical analysis.

Reading about these activities and games can be difficult, so we are making a set of really short videos to explain them all.

In the meantime, here is a video about the Cat Maths Kickstarter. We would love it if you could support us by pledging.

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Posted in New material | Tagged , , , ,

Evaluating mathematical games

It is the start of the school year in the northern hemisphere and the mathtwitterblogosphere (#mtbos) is full of ideas, and requests for ideas, for games that will help make learning in mathematics more fun.

At StatsLC we are releasing The Dragon Games, which is a collection of four different games, and a set of cards and accessories that can be used for an almost infinite number of games. We are also gearing up for a Kickstarter campaign for The Cat Herder Games for younger children.

My thoughts have turned to what makes a good mathematics game.

Candy cereal and pseudo-educational games

Educational games are a mixed bag. Some pseudo-educational games are like sugar-filled cereal. They pretend to be educational, just as the cereals pretend to be healthy. And just as candy cereals propose to be part of a healthy breakfast, the pseudo-educational games can offer to be part of a worthwhile educational programme. However, these games may have little benefit in terms of learning, and take up valuable learning time. There are many pseudo-educational games, particularly related to mathematics, and though most of them are not actually harmful, many are a waste of time. How much better to use games that are like a nutritious and tasty breakfast, being both educational and fun!

Why use games

People want to spend more time doing something if it is fun and rewarding and they feel as if they are making progress. Some games make practice or drill more palatable, some teach through the game mechanics, and some games can simulate real-life processes and decision-making

Considerations

  1. Games need to be fun.

It seems obvious that games should be fun, but sometimes that part gets missed out. The fun aspect should form part of a game evaluation. Of course fun, like beauty, can be in the eye of the beholder. Many children do like simple roll-and-move games like snakes and ladders, which adults might find boring. Snap and memory are very simple games, that can be played with any kinds of cards that pair, and these are fun for a certain age-group. Conversely, fun does not have to be easy. Struggle is good for learning and for satisfaction. It helps for a game to be easy to learn, especially in a classroom.

  1. Basic educational games can provide practice opportunities that lead to fluency.

There are things in mathematics that require practice. It is vital for children to have their number facts at their fingertips, and have confidence in their recall. Just as a good grasp of vocabulary helps in acquiring a new language, having automaticity in recalling the basic addition, subtraction, multiplication and division facts helps enormously in later mathematics learning. When I talk with Secondary school teachers, one of the main things they would love their students to have on arrival is knowledge of the basic facts.

In earlier times, these facts were drummed into pupils with drill and stick. This almost certainly contributed to undesirable outcomes such as antipathy towards mathematics and believing that being a mathematician is about speed of recall. But my mother’s generation sure could add, subtract, multiply and divide!

Games that require matching, such as memory, snap and happy families (Go fish) are useful mechanisms for reinforcing basic facts. However these are low-level games, as the mechanism is independent of the concepts being taught. A disadvantage of this kind of game is that the mechanism rewards speed or location memory. It does not develop understanding, though in my experience fluency can help understanding. We need to be careful about the use of speed in games. This works for some children, but not for others. In mathematics there is a place for automaticity, but there needs to be understanding as well.

  1. Games that involve mathematical thinking are a higher level of game.

Say, for example, we are trying to reinforce the names and properties of different geometric shapes. One way to do this is to have sets of cards with information about each shape, and use them in a game that references this information. This helps to teach properties and terminology in an abstract way. A higher level approach is to have a game that applies the properties of the shape in a meaningful way, perhaps filling a space or completing 360 degrees.

Another example is the game “How Close to 100” proposed by Jo Boaler in “Mathematical mindsets” that actively uses multiplication to draw arrays and label the number of squares occupied. This requires active application of multiplication in a way that a game of snap with question and answer cards does not.

We are developing Cat cards as a younger version of the Dragonistics Data cards. One class activity or game is called Cat Adoption. Pairs of children sit in a large circle on the mat, each pair with a whiteboard or paper and pen. Each pair of children is given a number of cat cards – say 10. The teacher turns over a criterion card, which might say “Playful”. This means that all the cats that are playful can be placed for adoption, by putting them in a separate adoption pile. Each pair of children then performs the subtraction on their whiteboard or paper and holds it up for the teacher to see. This is repeated until one pair of children has placed all their cats for adoption. This game gives practice at subtraction, at the same time as reinforcing the mechanism of subtraction. It also gives practice at representing an operation in two ways – with the cards and using mathematical notation.

Some of the cards from The Cat Herder Games

Some of the cards from The Cat Herder Games

  1. It is preferable to have control of error.

Self-correcting games reduce the likelihood that players will reinforce wrong facts. Having visuals that allow for self-correction make it easier for children to play without adult intervention. This is also where computer games have an advantage as they can provide instant feedback about incorrect responses.

  1. The extraneous activities must not be a distraction.

In some on-line games, students are rewarded for progress by improving their avatar or similar. This seemingly harmless reward can provide a distraction from the task at hand. I recently saw a game on a hand-held device that required the student to tip the device as well as recall numerical facts. The operation of the device provided a barrier and distraction.

  1. Games teach other skills

Games can teach how to win and lose graciously, play fair, and let others take turns. These are important life skills, that are included in the Key Competencies of the NZ curriculum. Some children do not have opportunities to play games and learn these skills at home, so it is important to provide these opportunities at school.

Games are great

It is a natural thing for children and adults to want to play. If we are going to help children learn through play, we need to make sure the games we provide are fun and teach the desired lessons.

The Dragon Games and The Cat Herder Games

At Statistics Learning Centre we are committed to helping all teachers to teach statistics, and all learners to understand statistics. In addition we aim to help families and children to have fun together in learning mathematics and statistics. Our game The Dragon Games has already proved popular. In October 2016 we are running a Kickstarter campaign for our new resource, The Cat Herder Games. We hope you can be part of developing this versatile resource and game combined.

Posted in Ask for help, Game | Tagged , , , , ,

Why Kickstarter crowdfunding, and how you can help

Strengths and weaknesses

Here’s the thing:
We at Statistics Learning centre are really good at making high quality resources, and teaching people about statistics and maths. (See this recent post on our impact)
We are not really good at marketing our products and services so that lots of people know about them and we get enough money for the company to be sustainable.

Ralph Waldo Emerson said, “build a better mousetrap and the world will beat a path to your door.” I don’t know if this was ever true, but it sure isn’t true now. You can have the best product in the world, but if people do not know about it, the path to your door will remain unbeaten.

I believe our NZStats online courses are the best available for learning the NZ statistics curriculum. Even our competitors have admitted that. But we are a little social enterprise and what you see is what you get. It is difficult to convince teachers that students will be better off using our materials, when many of them are so busy they don’t even have time to give the materials a free trial. Maybe we should have spent more time on marketing.

Dragonistic Data cards and Cat Herder cards

These colourful and inviting cards are used for teaching statistics and mathematics.

These colourful and inviting cards are used for teaching statistics and mathematics.

Lately we have discovered something else we are really good at. We have developed the idea of multivariate data cards into a versatile resource that engages young students and helps them understand implicitly about population, sample and variability. Not only have we developed the idea, but we have turned it into a high quality reality in the form of our Dragonistics data cards. And then we have come up with a set of games you play with cards that helps develop mathematical skills. These are very exciting! Teachers and kids who use them are loving them, but we do need to get the word out better.

An example of the cat cards, with multiple pieces of information

An example of the Cat Herder cards, with multiple pieces of information

We are now creating for a younger age group and making cat data cards that are just so beautiful and clever it is hard to imagine any child or primary school teacher resisting them. These cards will also have multivariate data, with inbuilt relationships, and accompanying attribute cards and criteria cards, that will make a fantastic set for learning, playing and creating games. We believe they will be even more versatile than regular playing cards, with the advantage of so many more ways of grouping and sorting.

Crowdfunding

But the problem is, we have not been very good at getting the word out. And this is why we are turning to crowdfunding. Over the years we have helped thousands, maybe even millions of people to learn and teach statistics. Most of the time this has cost them (or you) nothing, or very little. So now we are setting up a Kickstarter campaign so you all can help us back. Kickstarter is the largest crowdfunding platform, and has a big following of supporters in games, which is why we have chosen it.

This is how crowdfunding works
1. We set a target amount – what we need to accomplish our project, which in this case will be manufacturing and bringing to market our Cat Herders game and game developers kit. At present we think the target will be $20,000NZ.

2. We decide on incentives for supporters to contribute towards our campaign. The most obvious incentive is a copy of the final product, and the pledge amount would be around the retail price of the set of Cat Herder cards. But there are other rewards as well, to encourage and thank for greater contributions. Supporters could donate copies to the schools of their choice. Or they could pay to have naming rights of one of the cats. Or even have our talented cat artist draw their pet. We may offer handmade plushies of our delightful cats. Or supporters can just contribute to help make the world a better place.

3. We launch the campaign and encourage the community to contribute to make it happen. If we reach our target amount, the money is credited to us and we go ahead, manufacture Cat Herders and send out the rewards. If we do not get to our target, no one pays anything, and Cat Herders remains just a wonderful idea. What we really hope will happen is that we will exceed our target and be able to produce even more great resources.

Our plan is to have our campaign in October this year (2016). We need to build our community in the meantime, which is where you come in.

How to help

We have some wonderful friends who really want us to succeed in this endeavour.
Here is how you can help:

  • “Like” our Facebook page, and share messages such as this with others.
  • Do similar things on Twitter, Pinterest, Youtube, WordPress or whatever social media you participate in.
  • Talk to people in real life (IRL as it as known) about our project. If you know a primary teacher or a parent of young children, make sure they know about Cat Herders. If you know a media person – tell them.
  • Give us suggestions on how else we can get the word out.
  • Follow this blog!

And when we launch our campaign, please support us so we can continue to make high quality and engaging resources to help people understand statistics and mathematics.

Posted in Ask for help, Game, Information | Tagged , | 2 Comments

One thing at a time

The idea of multi-tasking is appealing. We want to be able to do things all at once as we have so much to do. Like a buffet, we pile things onto our plate, not wanting to miss out on anything. But really we need to do one thing at a time, eat one thing at a time.

At Statistics Learning Centre we aim to help all teachers to be more confident and empowered in teaching statistics and mathematics. We have lots of ideas, and draw on the ideas and research of people such as Jo Boaler (Mindsets in Mathematics), Carol Dweck (Mindsets) and Brown, Roediger and Daniel (Make it Stick). There are so many ways to improve things. There are thousands of teachers in New Zealand alone, teaching hundreds of thousands of students, in thousands of hours every year. They can’t possibly all be good hours. How can it be made better?

And I guess it can’t all be made better, not quickly.

I love Twitter as a quick way to connect with educators all over the world. Though the discussions can be ragged and confusing as tweets of 140 characters fly through the ether, the overall feeling is of support, encouragement, humility and vision. I would suggest following #MTBoS (Math Twitter blogosphere) and #mathchat #Mathschat and #mathschatnz. There is also a wonderful group of educators who meet each morning at 6:30am for a quick pick-me-up before school –  #BFC630nz. Follow me at @RogoNic to get connected to a whole heap of great teachers.

I had been feeling that anything we do is pretty pointless when stacked up against all that could be done. Then on Twitter last night I read the tweet: “[Change] is hard, but it starts with changing one person. One mind. One idea.” Thanks @mattoman71 . It was what I needed to hear.
It starts with changing one person. One mind. One idea.

We can not expect it all to happen at once. Many teachers are so busy with so many demands on their time and energy – so many curriculum areas, so many children. I don’t think you want to think about it too hard or you would give up. So it comes back to little things – lots of little things.

So we can provide ideas and support to help teachers, one idea, one teacher, one class at a time. And that is all we can do!

Posted in Statistics Learning Centre, Teaching | Tagged , , , ,

Symbiosis between teachers and resource providers

Trade stands and cautious teachers

It is interesting to provide a trade stand at a teachers’ conference. Some teachers are keen to find out about new things, and come to see how we can help them. Others studiously avoid eye-contact in the fear that we might try to sell them something. Trade stand holders regularly put sweets and chocolate out as “bait” so that teachers will approach close enough to engage. Maybe it gives the teachers an excuse to come closer? Either way it is representative of the uneasy relationship that “trade” has with salaried educators.

Money and education

Money and education have an uneasy relationship. For schools to function, they need considerable funding – always more than what they get. In New Zealand, and in many countries, education is predominantly funded by the state. Schools are built and equipped, teachers are paid and resources are purchased with money provided by the taxpayer. Extras are raised through donations from parents and fund-raising efforts. However, because it is not apparent that money is changing hands, schools are perceived as virtuous establishments, existing only because of the goodness of the teachers. This contrasts with the attitude to resource providers, who are sometimes treated as parasitic with their motives being all about the money. It is possible that some resource providers are in it just for the money, but it seems to me that there are richer seams to mine in health, sport, retail etc.

Statistics Learning Centre is a social enterprise

Statistics Learning Centre is a social enterprise. We fit in the fuzzy area between “not-for-profit” and commercial enterprise. We measure our success by the impact we are having in empowering teachers to teach statistics and all people to understand statistics. We need money in order to continue to make an impact. Statistics Learning Centre has made considerable contributions to the teaching and learning of statistics in New Zealand and beyond for several years. This post lists just some of the impact we have had.  We believe in what we are doing, and work hard so that our social enterprise is on a solid financial footing.

StatsLC empowers teachers

Soon after the change to the NCEA Statistics standards, there was a shortage of good quality practice external exams. Even the ones provided as official exemplars did not really fit the curriculum. Teachers approached us, requesting that we create practice exams that they could trust were correct and aligned to the curriculum. We did so in 2015 and 2016, at considerable personal effort and only marginal financial recompense. We see that as helping statistics to be better understood in schools and the wider community.

We, at Statistics Learning Centre, grasp at opportunities to teach teachers how to teach statistics better, to empower all teachers to teach statistics. Our workshops are well received, and we have regular attenders who know they will get value for their time. We use an inclusive, engaging approach, and participants have a good time. I believe in our resources – the videos, the quizzes, the data cards, the activities, the professional development. I believe that they are among the best you can get. So when I give workshops, I do talk about the resources. It would seem counter-productive for all concerned, not to mention contrived, to do otherwise. They are part of a full professional development session. Many mathematical associations have no trouble with this, and I love to go to conferences, and contribute.

I am aware that there are some commercial enterprises who wish to give commercial presentations at conferences. If their materials are not of a high standard, this can put the organisers in a difficult position. Consequently some organisations have a blanket ban on any presentations that reference any paid product. I feel this is a little unfortunate, as teachers miss out on worthwhile contributions. But I understand the problem.

The Open Market model – supply and demand

I believe that there is value in a market model for resources.  People have suggested that we should get the Government to fund access to Statistics Learning Centre resources for all schools. That would be delightful, and give us the freedom and time to create even better resources. But that would make it almost impossible for any other new provider, who may have an even better product, to get a look in. When such a monopoly occurs, it reduces the incentives for providers to keep improving.

Saving teachers’ work, and building on a product

Teachers want the best for their students, and have limited budgets. They may spend considerable amounts of time printing, cutting and laminating in order to provide teaching resources at a low cost. This was one of the drivers for producing our Dragonistics data cards – to provide at a reasonable cost, some ready-made, robust resources, so that teachers did not have to make their own. As it turned out we were able to provide interesting data with clear relationships, and engaging graphics so that we provide something more than just data turned into datacards.

Free resources

There are free resources available on the internet. Other resources are provided by teachers who are sharing what they have done while teaching their own students. Resources provided for free can be of a high pedagogical standard. Having a high production standard, however, can be prohibitively expensive for individual producers who are working in their spare time.  It can also be tricky for another teacher to know what is suitable, and a lot of time can be spent trying to find high quality, reliable resources.

Teachers and resource providers – a symbiotic relationship

Teachers need good resource providers. It makes sense for experts to create high quality resources, drawing on current thinking with regard to content specific pedagogy. These can support teachers, particularly in areas in which they are less confident, such as statistics. And they do need to be paid for their work.

It helps when people recognise that our materials are sound and innovative, when they give us opportunities to contribute and when they include us at the decision-making table. Let us know how we can help you, and in partnership we can work together to improve statistics education for all.

What do you think?

(Note that this post is also being published on our blog: Learn and Teach Statistics and Operations Research as I felt it was important,)

Posted in Statistics Learning Centre | Tagged ,

Impact

Statistics Learning Centre is a social enterprise empowering all teachers to teach statistics and all people to understand statistics.

So far…

Our video, Understanding the p-value has received more than 300,000 views

Our video, Understanding the p-value has received more than 300,000 views

Through our videos, we at StatsLC have helped more than a million people to understand statistics better, and continue to do so. Some of our videos can be seen on our YouTube Channel.

Through our on-line resources we continue to help many teachers and students in New Zealand to teach and learn statistics. Statistics is the second largest subject, after English, in the final year of secondary schooling in New Zealand.

Through the blog, Learn and Teach Statistics, we have helped and continue to help thousands of people to think again about ways of teaching statistics.

The Dragon Games, a family game of four events is due to be released in September 2016.

The Dragon Games, a family game of four events is due to be released in September 2016.

Through professional development sessions in schools and at symposia and conferences we have helped empower hundreds of teachers to teach statistics.

Through our Dragonistic data cards, and free supporting resources, posters and lesson plans, we aim to help many more teachers and students understand statistical concepts through hands-on activity. These resources are available on our shop.

Through our games, starting with The Dragon Games we aim to help families and children have fun together away from screens, with games that teach as well as being fun. Our next project has the working title of Cat Herders.

Through our fundraiser scheme, we aim to help schools have more resources.

Through our Kickstarter project, Cat Herding, we aim to connect with many of the people we have helped over the last five years, and help them to help us help others.

Through this blog, we are reaching out to connect with our community who have benefited from our work so we can all help each other.

Through our continued efforts and existence we intend to provide socially responsible data and resources to educate citizens about important things such as conservation, medical screening, health choices and road safety.

We hope you can help us. Please click on the Follow button, to be part of our community.

Posted in Statistics Learning Centre | Tagged , , , , , , , , , | 4 Comments