Household Maths – real maths in the classroom

Back in the 90s, as a young teacher known for his knowledge in Maths, I developed a comprehensive Maths program based on the curriculum of the time. I personally had great success with the program, which I dubbed “Household Maths”, and with my support several teachers I worked with also followed the program enthusiastically. With little co-ordination or entrepreneurial skills, I even managed to sell a few copies of it. For various reasons I don’t ant to get into here, I was drawn away from using the program for many years, even though I still had a strong belief in its purpose and results. Now with a renewed push for purposeful Maths, I want to bring “Household Maths” back again.

I think the basic premise of the program and the majority of its content and curriculum base is still sound, 20 years after I first created it. However, to get it adopted today, I’ll need to link it to current curriculum documents. Before I do that though, I’d like to throw it out there to the teaching community and gauge whether it is worth the effort. As I have said already, I really have faith in this program but I’m not going to spend months rewriting it for the 21st century curriculum if others don’t share my enthusiasm.

What follows is the original introduction and program summary ( with some comments about how I would integrate new technologies, as is my want). I would really appreciate some critical feedback on what you think. Attached at the end is the PDF version of the whole program so that you can view it in its entirety.

 During my years involved in education, whether as a student or teacher, many teachers have made Maths such a boring subject. In turn, their classes have responded by being bored. Sheets and sheets of repetitive sums have done nothing other than keep the bright child occupied and the struggler frustrated. I have been guilty of this myself. The struggler learnt to hate Maths and the bright child just did the sums because they were easy.

I have always looked for programs that made Maths interesting for the children. Many books and programs have been released under the heading of “Real Maths”. Too many, though, are just a book of activities that are not related to each other and could be dealt with in a single session ,are part of a program that still had too many worksheets filled with monotonous equations or aren’t that real to the children, anyway.

Finally I’ve decided to do something myself . I thought to myself – When is Maths most useful and meaningful? The simple answer was in daily life at home. Maths is all around us in our house. Paying bills, going shopping, looking for bargains, building a house, developing the garden, planning holidays –  all of these tasks are Maths at work.

I wanted more than a book of activities to keep the children busy once or twice a week, though. I wanted my entire Maths program for the year to be a rewarding, interesting and entertaining learning experience based on Maths at home. Children love pretending to be adults. So this program was going to treat them like adults.

The key to it all was always going to be making it interesting and fun. When faced with a policy that says Maths must be taught for one hour a day, so many teachers decide to make a worksheet of equations with as many sums as they can fit on it to keep the children working for the hour. Of course what happens is that the bright children barely have to think and finish within twenty minutes while the strugglers get stuck on the first sum for twenty minutes and just know they’ll never finish in time. This only builds up their frustration and hatred towards maths while the bright sparks just confirm what they already know – they’re good calculators. But can they think? Have they been taught to think?

The Household Maths Program aims to teach the children to think about Maths, to use Maths and to realise Maths is a vital part of life. It is aimed at Upper Primary/Junior Secondary/Middle School classes because of the processes involved. If used by an enthusiastic teacher willing to be challenged by the work the children will produce, it will send out into the world students who enjoy Maths and are able to use it effectively. The teacher will have a lot of fun too.

SUMMARY OF PROGRAM

The Household Maths program is made up of  two components.

– Weekly activities including shopping for essentials, receiving pay, paying Bills and rent / loan instalments, petrol, Life’s Little Surprises and other weekly expenses decided upon by the “family” of the household.

– Major tasks incorporating many maths skills and running concurrently with the weekly tasks. These tasks can last from 1 – 2 days to 4 – 5 weeks or more .

The weekly activities are set out as follows:

A description of the household is given to each child. Six different households are included  in this  program to  provide  a  variety  of  environments in the classroom.( you can create more if you wish. )  The description covers the weekly / fortnightly pays  ( or unemployment benefits ) received by spouses, the number of children in the family, house payment situation ( rent, loan or fully owned ), bank balance, credit card allowance, number of cars and something the household is saving for. The children fill in the blank lines with the names, ages and birthdays of their “children”.

Each child is given an exercise book or something similar. Each page in the book is to be divided up into four columns: income, expenditure, savings and balance. The children record all transactions in this book. An example of this transaction record is provided.

Provide each child with enough shopping lists to last the year out. ( master copy provided ). Each week the children will fill the list in and look through catalogues and dockets for prices to complete their weekly groceries. Get the children to plan a weekly menu to give them an idea of how much food they will need to buy their family.

A checklist of bills is provided to remind the children when they need to pay their bills. Set months for gas, electricity, water, council rates and phone bills are given by teacher. All other dates for bills are decided by children. Teacher gives bill totals to children. ( copies of services bills are provided in program. )

A record of credit card transactions is given to the children to allow them to keep  a record of what they have spent on their cards. Payment ( or part payment ) will take place at the end of each month.

A checklist of weekly expenses will be given to each child so that they can make sure they aren’t forgetting to do anything.

Each week the children will choose at random from a collection of cards called Life’s Little Surprises. On these cards are a selection of unplanned expenses and incomes such as fines, repairs, presents, updating, competition prizes, debts etc. Draw up a chart to record when these expenses will be paid.

The weekly tasks generally provide opportunities to use the four basic operations of addition,subtraction, multiplication and division and are fun and useful alternatives to pages and pages of drill worksheets.

NOTE: When I originally ran this program, all of these resources involved a lot of paper use. Today, with the advent of 1:1 laptop/iPad programs, all of these components could be implemented more effectively with technology. Google Calendar, the iPad Calendar or Edmodo’s calendar could be used to deliver or remind the students of all their bills and expenses. Databases, spreadsheet programs or iPad/iPod finance apps could be used to send scheduled bills or track expenses. Excel/Numbers/Google Spreadsheets could be used to record/check the weekly cash and credit card transactions. Users of interactive Whiteboards could hide the Life’s Little Surprises cards behind a graphic and the students could drag random expenses or incomes out on the board. 

New skills are taught and, more importantly, used through the Major tasks or integrated activities. It is important that new skills are taught in the context of how they can be used. There is no point teaching something like percentages as just a whole lot of unrelated numbers on a blackboard or worksheet. Children, especially those with a dislike for Maths, will see no use for them. Therefore, even at the teaching stage, the skills must be related to a useful purpose.

Just as important is to show how a variety of skills are needed to complete real life tasks. The integrated activities in this program involve the use of a number of skills. The age group this program is aimed at have many of these skills already so it isn’t that big a task to have the children working through these tasks. It is also easier teaching the new skills because the nature of the tasks gains and maintains the children’s full attention.

There are thirteen integrated activities in the program. Combined, they cover all the requirements of a Maths curriculum and will easily make up a year’s program.( Note: operations involving fractions may be found lacking in this program, mainly because it is hard to find a real life purpose for adding, subtracting and dividing fractions for the average person. They will have to be taught in a different context. )

Each activity is outlined in detail and the skills covered by it are included. Worksheets are occasionally included but the beauty of this program is that most of the resources are accessible to the children already and worksheets aren’t always needed. The materials required for each task are listed and most will be found in the home. Detailed lesson plans are also provided. Included is a checklist of skills that are taught through the program. You should find that everything in your school’s Grade 6 syllabus is included ( with the possible exception of some fraction work ). Use the checklist to record your students’ progress by ticking the box each time evidence of the skill being used is found. Space for comments is also provided.

TIMETABLING THE PROGRAM

 The general practice in schools is to allow approximately one hour a day for Maths. In doing so I would allow about 40 minutes for the main activity (10 minutes teaching and 30 minutes working on the task ) and the remainder of the time on individual household finance organisation.

I would begin most days with a few minutes for the children to carry out essential transactions , such as bill or loan payments and entering their pays into their accounts. Life’s Little Surprises is an activity the children looked forward to at the start of the week to see what was going to happen to them this time so I always timetabled it for Mondays. By the time they all chose the cards it took about 5-10 minutes . If they had the money, or it was a straightforward transaction such as a speeding fine, they often completed the transaction at this time. But often it required shopping around so having LLS on Monday gave them time for this.

After this brief activity , I would go straight into the main activity – the integrated tasks on the following pages. It is important not to spend too much time at the beginning teaching because the children will lose interest. Plan carefully which skills you want to focus on and what that will allow the children to complete. Remember the tasks are not one day activities so the children don’t have to be finished. Once the children are engaged in the activity, you are now free to concentrate on the children who need extra teaching.

Allow about ten minutes at the end of each lesson for the children to use their checklists to see what weekly transactions they must complete. (e.g. petrol, newspaper, bill due,etc.) If they don’t have much to do, allow them to browse through catalogues to find bargains, extra items they have to buy because of Life’s Little Surprises or to start filling in their shopping list. This time may also be used by the slower children to complete work on the main activity without being seen not to have finished as much as the other children.

At times, you may feel that the children are not doing enough Maths. They may spend ten minutes looking through a catalogue and complete two equations. The thinking you have to develop is : have they successfully used maths skills in this situation? Yes! And that is what is important. A child who completes 25 equations on a worksheet and the child who has bought a lounge suite, paid a bill and put her pay into an account are doing the same thing. Except the second child knows why she is doing those sums and is using Maths.

This program is about quality learning not filling in the time with lots of irrelevant equations.
( Of course you should still allow time for drills / games in basic number facts such as times tables.)

INTEGRATED ACTIVITIES
The 13 tasks I planned are;
BUILD YOUR OWN HOME
DESIGN YOUR GARDEN / ENTERTAINMENT AREA
PLANNING A HOLIDAY
GET THE MET / UP,UP AND AWAY
THIS IS AUSTRALIA CALLING
ON SALE NOW
FAMILY FUN
PARTY TIME
I’M BROKE
COOKING UP A STORM
CLASSIFIED INFORMATION
ODDS ON
ELECTION TIME
Check out the PDF below for more detail.
Each task is outlined as follows:
PURPOSE OF TASK
MATHS SKILLS TAUGHT/DEVELOPED THROUGH THIS UNIT
PREPARATION / RESOURCES
TECHNOLOGY COMPONENT
WHAT TO LOOK FOR WHEN ASSESSING
DEVELOPMENT OF SKILLS THROUGH ACTIVITIES

With greater access to websites, programs and apps, many of the tasks would be easier to complete while still requiring the same level of mathematics skill. Online shopping and auction/advertising websites, measurement and money converters, recipe sites and apps, travel websites and apps, websites for utility companies, on line maps and world time clocks….. the list goes on… provide a wealth of content to be used in real life situations.

 

Would appreciate feedback on whether the program still has merit today. Here is the PDF of the whole program     householdmath

Maths Extension/Enrichment and Edmodo


Addressing the needs of all students in your Maths Classroom can be a real challenge. Do we stream based on ability? Do we use collaborative mixed ability groups? What’s the role of rich,open ended questions and differentiated curriculum? How do we pitch to the middle 50% but still cater for the upper AND lower 25%? It’s a challenge I’ve been grappling with for 25 years. Recently, I’ve been considering the use of Edmodo to provide access to extension and enrichment Mathematics opportunities for the more able students in the classroom. ( For those unfamiliar with Edmodo, click here for a description) This is my plan. I would be interested in feedback on its potential effectiveness before going further with it.

Identifying the target group
This is not a simple task. The standard method these days seems to be the standardized test. In Australia, we have NAPLAN, the yearly national assessment task targeting Years 3,5,7 and 9. Debating its merits here is not my intention today. I see its usefulness in quick identification of the higher achievers in a current group of students. I would then administer the next level test to these able students to gauge how far their abilities extend beyond the current class level. For example, after selecting a group in Grade 6 based on Grade 5 results from the previous year, I would give them the Year 7 test. Using data analysis, I’d identify their strengths and learning needs for future programming and targeted areas for extension and enrichment.

This would only be a starting point. Standardized tests are a narrow form of assessment that don’t necessarily identify fully the student’s need for extension in Mathematics. I’d continue to evaluate the children within and outside the extension group. I’m sure during the year I would identify children who could join the group for extension in specific areas they excel in. The beauty of using an open, collaborative, independent learning platform like Edmodo is that students can opt in and out of specific tasks or units of work.

The Edmodo Extension Maths Program
This is how I envisage setting up and running an Extension Program in Mathematics within the standard classroom environment.

First I would set up a Maths group for every student in the class. I wouldn’t want the Extension group to stand out from the crowd by having sole access to Edmodo for Maths. I would use this area to post problem solving tasks that the whole class could engage with, links to quality Maths sites that students could use to consolidate understanding in current units and revise past lessons as well. I would provide opportunities for discussion of strategies used, allow children to share their understanding, ask questions that both teachers and students could answer and share with the class. I’d allow for the possibility of using iPad apps like ShowMe or Explain Everything to post audiovisual explanations or lessons created by teachers or lessons. I would also post resources children could access to support them while working independently. The extension group could have a lead part in sharing their expertise with other classmates in this main Edmodo group. they could even create their own mini “Khan Academy”.

I would then create a subgroup within the main Edmodo group for my Extension/Enrichment group. I envisage this group being formed from able students across all classes in a particular grade level, possibly across several if there are able students in lower Grade levels who could qualify. I would plan for this group to access materials and concepts beyond what is available to the main group but accessible through the same platform as everyone else.

Obviously there would need to be some significant planning and negotiation with all class teachers to ensure this worked within their programs. consideration would have to be made about how these students would participate in both the extension sessions and regular class lessons. I see this happening in a number of ways.

Option 1. The students begin the lesson with the rest of the class. When they have received enough instruction on what is expected of them, they move on to completing required work for their class teacher independently, leaving their teacher to work with those who need support. When they complete the set task, they submit it on Edmodo through the assignment section and then enter their Edmodo Extension Sub group to collaborate on the higher level tasks assigned by me. They communicate with each other either personally if in the same grade or via posting their strategies, solutions, suggestions, questions, comments on Edmodo for the rest of the Extension group to respond to. Their work will be completed digitally and submitted through the Assignments section of Edmodo so that I can feedback and collaborate with them on the tasks.

Option 2. Alternatively, for one session a week, the group would meet with me and work on high level problem solving tasks and extension work related to the unit of work their class in currently involved in. Using online enrichment programs like the website nrich, the group would be collaborating on problems, sharing their possible solutions and strategies not only with each other but by submitting group or individual solutions on the nrich site for other like minded students to collaborate on through global forums. I envisage opportunities for the students to use technology such as screen casting computer programs or iPad apps I previously mentioned like ShowMe to record their solutions and strategies audio visually. Using a site like nrich, which would allow them to self select problems to solve would give them the freedom to challenge themselves both individually and in teams. It would also give them the option to opt in and out to return back to their class if they choose to.

Option 3. A third model could be a choice of making daily decisions to complete regular class work as homework and deciding to work in their extension groups or individually on Edmodo on a daily basis. As their test results would have already indicated in being selected for the program, they have most likely mastered the skills being taught in the regular class program and a simple completion of the tasks for homework would satisfy their class teacher’s need for evidence they have understood that area so they can report on it later in the year. This option fits a Personalized Learning model commonly encouraged in today’s schools and would allow the student to remain engaged in Maths at or beyond their level rather than going through the motions of completing simple tasks.

How Edmodo would help me implement this program

  • All links to nrich and teacher/student created work would be posted on Edmodo, with individual entries tagged or saved in libraries so that students could always have easy access to the tasks.
  • The collaborative nature of leaving instant comments and feedback allows the group to stay in contact with each other outside of school to continue their problem solving together. This could become engaging homework, with the teacher able to remain in contact and feedback on the work they post on Edmodo.
  • Each member of the group can work on their own problem solving and submit it to me or their teacher independently of the group for personal feedback before sharing with group if they choose to.
  • The function of the Assignment process in Edmodo allows for children to receive private feedback and allow the teachers to collect, collate and mark each submission, enabling effective assessment to occur at all points in the program. Teachers can submit rubrics and criteria for marking the work on Edmodo so the students know what is expected of them. I have had success with such use last year working with a Literature Circle group.
  • The fact that all students from the classes are also using Edmodo for their Math work as well means that all students can easily be given the opportunity to opt in to or out of the Extension group at any time without any extra planning or organisation by the teachers. I think this would be an important option as it would encourage other students to take on the challenge of extension tasks if they choose to.
  • Other teachers can be given co teacher status and become involved in the program, either as observers or contributors. This would allow for professional feedback on the suitability and effectiveness of the program.

These are my initial thoughts and obviously this kind of radical change to the status quo of primary schools as I have experienced them would involve leadership, class teacher, parent and student discussion. I need to think through this more and would appreciate feedback from others on how they have managed the needs of the more able students in their classrooms. I would really appreciate readers leaving a comment and contributing to the conversation of extending and enriching the learning of the able mathematician.

The iPad and Maths – Are we there yet? Pt 2 (non Math apps do the job?)

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Can ubergeeks like me find Mathematical applications in the non Maths apps on the iPad? Skitch app and Leaning Tower of Pisa meets angle measuring

My last post focused on the state of apps related to Numeracy education and concluded that the iPad has a fair way to go in how it is being utilized to develop number skills through the current crop of Maths applications. On the whole, there are too many apps focused on rote learning and simple number facts and equations. Having said that, I actually believe the iPad has much to offer teachers and students in Mathematics. However, don’t go looking for the apps in the Education section of the App Store.

I’ve always been a big proponent of making Maths real in the classroom. Yes, every teacher out there wants to make Maths interesting and relevant for their students but sometimes this just comes in the form of “Real life Maths” textbook problems. The danger of Apple’s foray into textbooks on iPads is that we will continue to get the traditional textbook experience with the bells and whistles of interactivity and ‘magic tablet dust.’ The good news from my perspective is that the iPad already is ready to replace textbooks and make Maths an engaging real world experience. What it takes of course, as I have been pushing in this blog since its inception, is quality teaching practice coupled with great, easily accessible technology. And it comes not from Maths apps but the already available, successful apps across all walks of life in the App Store.

Screencasting/Whiteboard apps
Whether you choose Explain Everything, ShowMe, Educreations or ScreenChomp (depending on price, features or usability), using these apps to record children’s learning is a killer feature of the iPad for me. Yes, we can sit them in front of Khan Academy or YouTube and get them to watch someone else teach them how to do Maths but any good educator knows that students learn more by participating in the teaching and learning process rather than being passive receptors of information. With these apps, children can record visually and with audio the strategies they use to solve equations, real problems, geometric tasks, statistics, virtually any Maths task and share with others in the classroom.

If you are lucky enough to have access to an AppleTV and a full set of iPads, the whole class can switch from one student’s iPad screen to another to participate in an engaging real time discussion without waiting for their turn on the interactive whiteboard. Their recordings can be saved and posted to blogs or other online options to share with outside audiences, with possibilities of feedback or collaboration.

This kind of use of the iPad would do far more for developing deep understanding and granting access to authentic assessment than any textbook. It would also encourage the less confident students to share their knowledge without getting up in front of the class. You could just watch their recordings and comment later.

Drawing Apps
Doodle Buddy is a popular app already being used by many students for a variety of reasons. It has many possibilities in the Maths Classroom. Younger students can create pictographs by using the stamp tools to record their survey results. It can then be used to develop more “mathematical” visual representations by drawing around those pictures to make column graphs. The app comes with special backgrounds, one of which is a dot grid. Students could use this to draw paths following directions, create shapes and angles and use it to create line graphs as well.

A more complex drawing app is iDraw. This application can be used for shape exploration using its tools to create transformations through rotations, reflections and resizing. Scale concepts can be introduced and area and perimeter explored through drawing plans of houses, gardens, playgrounds and the like.

iDraw

Further engagement could take place through a specific house design app called Home Design HD, which not only gives you a wide range of tools for precision drawing and measuring of house plans but also converts the plans into 3D models.

With the Skitch app, students can import pictures then use annotation tools to divide them into grids to make arrays, plot a path on a map screenshot, annotate graphs, draw angles on an image then measure with a real protractor. They can use this for real trigonometry problems instead of detached examples from textbooks.

Video Apps
Children can become engaged in sharing their Maths understanding by making learning videos with iMovie, recording entire lessons with concrete materials as support for presenting what they have learnt.

iMotion HD is a time lapse/stop motion animation app that could be used to record shape transformations made with real materials then played back and slowed down to discuss the transformations as they happen. Time lapse photography with this app could be used to record experiments related to measurement and time relationships then played back at different speeds to explore how long it took for ice to melt, for food to cook or a snail to travel over a certain distance. Possibilities are endless for authentic learning here.

Navigation Apps
Imagine exploring average speeds by looking over the results of a car trip, run or walk recorded with an app like MotionX GPS. The app can present its findings in graphs showing distances, elevations, speeds and maps (with wifi). By looking at the break up of the distances travelled and the time taken, engaging authentic discussions can take place about what caused the fluctuations in times taken to travel certain distances, differences in elevations and how that affected the journey, all real life applications of Maths. At a simpler level pedometer apps can be used just to track distances and times on shorter walks around the school to support earlier estimations of distances/lengths

Other Measuring Apps
The Theodolite app mimics the function of a real theodolite and can be used for real angle readings to determine the height or distance away from an object. Just like my earlier Skitch example, this could be use for practical applications for geometry and trigonometry that written problems in a textbook can’t compete with.

Clinometer, Gigantic Compass, Multi Protractor and the Best Ruler are tools that can replace traditional tools for measuring angles, directions and lengths while also providing quick reference to real numbers that can be used for relevant equations. Clock Pro HD provides a range of time recording tools that can be used for many tasks in a creative Maths environment. There are a range of conversion apps that can be used to support work in measurement tasks.

Wolfram Alpha is a workhorse app (Google on steroids)  that can do just about everything in Mathematics information that will support  all areas of Maths. Just read the description on the store to find out more. Here’s a detailed review from YouTube

Cat Physics

Games
Use physics based games like Angry Birds (does anyone need a link for this!?!), Cat Physics, PocketTanks and Super Stickman Golf to explore the use of angles then apply them to the creation of real life models. YouTube already has examples of Angry Birds Physics lessons here. The beauty of Cat Physics is that it shows the path after completing each level so you can actually measure the angle you used and then try out the real model you build. Pocket Tanks actually gives you the angle you are using. Playing these games can inspire students to test out other real applications for angles like golf club design, ramps, pinball machines, mini golf courses and so on.

Yahtzee, Monopoly and Solitaire games all have great possibilities for developing number concepts. There are also dedicated dice and decision making apps like DiceBag, Wheel of Chance and Undecided that can be used to enhanced Probability lessons.

Maths is all pervasive in our lives. So are iOS devices, be they iPods, iPhones or iPads. All it takes for the iPad to become an essential tool in the Maths Curriculum is creativity in finding Maths in our daily lives and using the related apps available. So while I bemoaned the lack of creativity in Numeracy related apps in my last post, I finish this entry confident and excited about how the iPad can make Mathematics an exciting experience for students across all grade levels. A lot of what I have mentioned here may not be staring at you in the face when you look at your country’s Curriculum standards or national standardised tests. But I don’t mind that. Get kids doing real maths, make the links to what the Education Departments want and it will all take care of itself. Be brave, but above all, be creative and real.

This is by no means an exhaustive list of apps or ideas. I would like to hear from others how they have used apps in Maths lessons. I haven’t mentioned spreadsheet/graph making apps like Numbers or Office like apps because we’ve been using them for years. I’m looking for something new.

The iPad and Maths – Are we there yet? Pt 1

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My last two posts on iPads and good teaching have focused on teaching and learning writing. Now I’m moving on to my favorite subject as a teacher – Mathematics.

I love Maths – both learning and teaching it. For those who don’t know me ( which is obviously most of you reading ), I am a Primary ( Elementary ) School teacher but I have spent most of my 25 year teaching career also tutoring High School Maths on the side, supporting many children who have missed out on understanding important Mathematics concepts.

Maths involves an incredibly diverse range of processes, ideas, skills and concepts. Both children and teachers alike enter into Maths teaching and learning at different levels, depending on their personal experiences, successes and challenges with the subject. Over the years I’ve been involved in the conversation about teacher-led process/algorithm based teaching which I ( along with the parents of our children we teach) experienced as a child vs a more student centred, understanding and multiple strategy based learning approach more prevalent today.

The challenge facing us is that, while education training is rightly focused on the latter approach, the traditional process system still holds sway in many homes and can sometimes be a fallback for teachers who are unsure in Maths. It is also, in my experience, very much the default teaching method in many secondary/high schools in my part of the world. I won’t get into the pros and cons of the two models – that’s for a later post. This post I again focus on where the iPad (and other iOS products) sits in the world of Maths Education and whether, along with good teaching practice, it can have an impact in developing skilled mathematicians of the future.

The state of Maths apps on iPads at the moment
There’s a lot of potential in the apps available on iOS devices for Mathematics but overall I think they fall a little short of what I would like. Many of the apps are more directed towards the traditional memory/algorithm/procedural methods of teaching or drill practising of number facts and operations. I think where they may fall down is in the fact that the app developers are not necessarily involved in education and are basing their app concepts around traditional Maths they were exposed to.

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Maths Bingo

The number fact/ 4 operations apps serve their purpose of consolidating learning and improving automatic recall but they don’t necessarily support the initial teaching and learning required to develop understanding of concepts.
Here are some examples of apps in this category.
Drill/Number fact games
Freefall Maths – drill practice drag and drop
Factor Samurai– focuses on recognizing prime and composite numbers in a Fruit Ninja style game
Painless Algebra – practises +/- rules in operations
Maths Bingo – a popular app focusing on calculation involving the four processes at different levels of complexity
Math Hero – equations needing order of operations to solve in a game setting
Math Mago – a large grid of numbers 1-9 to eliminate by solving 2 number equations. At least there is more than one answer and it makes you think about which numbers to choose so you have options left. Sort of open ended but still just basic equations.
Math Kid – more number facts to solve but at least you get a visual aid to support your thinking after a few seconds instead of just timing you out. An improvement on others above in terms of mathematics teaching an learning.
Operation Math – lots of engaging bells and whistles based around secret agent missions but behind it all jut another number fact time limited practice app.

Procedure based apps
Fraction Basics – provides step by step instructions for working with fractions and the four operations as well as steps for working out equivalent fractions and improper/mixed numbers
Mathboard – a very popular app that has strengths. It generates equations involving all operations for solving at different levels and provides support in how to calculate the answer if the student can’t solve it. I would love this app if the solutions provided were a range of mental and written strategies rather than just the vertical algorithm. Again for those comfortable with this as the one method for solving equations, it is a winner. For those wanting more than that, it falls short.
YourTeacher.com and Khan Academy apps – two apps for the latest trend in Maths Ed – Flipped Teaching. Again I applaud these apps for the step by step support for children to follow to achieve success. The down side for me is the one solution fits all approach without involving the children in the discussion. At the end of the day, they tell the student what to do, but tend not to ask why.
Algebra Touch – a nice app that allows you to manipulate numbers by clicking and dragging, splitting them into simplified forms to aid in solving algebraic equations. Requires discussion to develop understanding of what is actually happening but the interactivity has potential.

They are all Fun games or sound step by step procedural apps for practising newly developed skills, monitoring progress or challenging students to improve. However, the games don’t teach or develop new understanding and the procedure apps don’t give scope to different strategies that may be better options. Some may argue that these apps enhance the users’ number knowledge through practice and repetition. This may be the case for some like myself who responded well to this method when I was in school. However, just as many of my friends and colleagues past and present have not developed the same understanding and find themselves relying on written methods they can’t necessarily apply mentally or to complex problems they have not exposed themselves to since college. Drill and practice 20 years ago has not developed their permanent understanding. This is why I support a more multiple strategy/understanding based model.

Having said that, I can still see a place for the apps mentioned above. The immediacy of results gives feedback to the students and shows gaps in their ability they can work on. These apps could be used as a tuning in session to introduce strategies to make playing them easier and improve mental calculations. However, you can do that with an interactive whiteboard and computer or web based software. I’m looking for innovation that makes the use of the iPad better than previous technology. For many years there have been websites offering fun ways to practise number facts and operations without showing great improvement in student understanding. Either these sites haven’t been used enough because of lack of computer access or the method of drill games is not effective. We need to find new ways to use technology with Maths Education

The procedural apps can be effective if followed up with discussion to ensure the students have developed understanding, not just followed steps. These apps could easily be improved if they included a range of strategies. One app that does that is School A to Z, although I’m not sure it is available outside of Australia, as it is developed by the NSW Education Department. It includes instructions for a range of computational strategies based on Australian methods and curriculum standards. I would love to see more apps being developed by actual education experts rather than just app developers who like Maths their way.

Mathemagics

Another app I love because it presents a strong mathematical strategy focus in Mathemagics. Its main purpose is to present a wide range of mental calculation strategies. It provides the methods and tricks and then allows you to practise them within in the app.

Open ended apps
There are a range of apps that allow for more open ended problem solving. These apps allow for critical thinking to take place, for choices to be made. They offer problems with multiple solutions and allow opportunities for students to choose the operations they need to solve the problems. As a result, conversations can take place between users to discuss how best to solve the equation.

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Aydox

Examples of these apps include;
Aydox– a challenging mental arithmetic game that involves strategy, thinking ahead, multiple calculations to think of possibilities. This is the type of Maths App that can encourage a lot of mathematical thinking. At its simplest level, it can be used to create equations that equal or nearly equal given numbers on the matrix. At the highest level complex thinking takes place to try to score the lowest possible score.

3D Math – basic equation creation involving problem solving and critical thinking. It allows you to alter your initial choices and think about the possibilities in front of you to solve the problems. It is time based which still makes it difficult for weaker students to engage in.

Number Pyramid – involves finding missing numbers using operations and partial answers in a pyramid format
24 Challenge Lite -based on the 24 game, using numbered playing cards to find equations that equal 24 using four numbers and any of the 4 operations.

Manipulative Apps
This is where the iPad’s touch interface should excel. Apps where users can drag and drop objects to sort, count, group, divide, increase, decrease etc, should be n abundance. Again though, I haven’t found a massive range of apps to mimic the interactive features of electronic whiteboards or websites like NLMV. There seems to be toomuch of a focus on number facts on the iPad. Nevertheless, here is a sample of apps that fit the description.

Virtual Manipulatives – an app that lets the user drag and drop fractional parts representing decimals, fractions or percentages.
Number line – allows the user to place whole and decimal numbers on number lines
Motion Math HD – physically manipulate by tilting iPad a fraction in a ball to land on a blank number line in its estimated position. Fractions are presented as decimals, percentages, fractions and visual models. Quite engaging and challenging, developing visual estimation of fractional size.

SketchPad Explorer

SketchPad Explorer – offers a range of manipulatives in Number and Geometry. Potentially a very good app if more variety added.

Think 3D – in the app, the user gets to explore and build 3D objects, rotating the shape for different views.

Montessori Place Value – Students can move place value cards around to create 4 digit numbers or less

These are the kinds of apps I want to see more of on the iPad. It sells itself as a magical touch device. It should be full of possibilities for building, altering, creating. Its features shouldn’t be wasted on just pushing numbers to answer simple number facts.

As there are over 1/2 million apps in the App Store, I’m sure there are hidden gems I haven’t discovered. I would love to hear from others out there on the Net about Maths apps they have found useful. If you want to agree or disagree with me about the current crop of apps I’ve discussed here, I’d appreciate any comments.

In my next post I’ll discuss Maths reference apps, the role of screen casting apps in Maths and how to use apps not specifically labelled as Maths apps to enhance the Maths program. I’ll also look beyond Number and talk about apps for other areas of Maths.

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