Mathematical Curriculum Links

We promised an entry on mathematical curriculum links, especially at the primary level. Since we live in Ontario we will highlight these, although I suspect that the expectations, especially in primary grades, are similar to other North American jurisdictions.

1. If you want a summary of the expectations in mathematics, here is my personal favourite. It is called Ontario Curriculum Tracking Templates. Click on the link, and you will see all the expectations in mathematics in point form for grades K through 8.

2. Here is the link to the Ontario Ministry of Education, Elementary Mathematics Curriculum, in pdf format.

3. Here is the link to the Kindergarten Curriculum into which mathematics is incorportated. It is also in pdf format although there is a plain text version available.

4. The Ministry of Education has exemplars on line. They are examples of children's work at the four different levels in the different strands. Here are links for grade one, grade two and grade three. Other grades are also available on this site.

5. The ministry has published an early math strategy in 2003 to encourage problem solving based mathematics and to promote cooperation and sharing amongst mathematics teachers in the spirit of the Japanese Lesson Study method of curriculum development. Here is the link. In 2004 the ministry published a similar documument for the junior grades.

6. E workshops: The ministry of education has hosted documents and on-line videos to explain different aspects of the curriculum in elementary schools. These include numeracy.

7. Illuminations: This is the National Council of the Teachers of Mathematics site. It is an American site, but it has numerous links and ideas for elementary mathematics teachers.

8. The Hamilton-Wentworth District School Board has a very good numeracy site. Stop and visit here for they have numerous resources for both parents and teachers. In particular I am impressed with the plans that they have for teaching mathematics for grades one through eight. These plans suggest what to teach each term, the big ideas that you can address in so doing and the related curriculum links. They also suggest what resources to use, such as the relevant chapters from common textbooks which is a great help in planning. Here are the plan for grade one, grade two and grade three. If you are a junior or intermediate teacher you will also find your grades there.

9. The Upper Canada District School Board maintains a site called Aftermath with many useful links for literature, curriculum, online resources and etc, although I have the impression that it has not been updated for a little while as there are some dead links.

10. Proteacher: This is a special portal and search engine for teachers. There also links to blogs, discussion boards and even online chats if you need support and ideas. It is used by English language teachers around the world.

Chess for Children

“Life is a kind of Chess, with struggle, competition, good and ill events”

Benjamin Franklin

This is the fifth in a series of entries on games for children. It concerns one of the great games of the world, Chess. Click here for an introduction to the history, rules, strategy and tactics.

Chess is a game that we have successfully taught to older primary children. The rules are simple enough that children in grade three can master them in two to three periods of instruction.

All games have some mathematical value. There have been many studies in recent years about the numerous the cognitive benefits of learning Chess. If you do a web search, you will find numerous entries and citations in this regard, so we won't bother doing this for you. Chess is easy to learn but difficult to master. There are numerous books on the subject. If you look in the children's section of your local library or bookstore, you will find books on this game for children.

Chess is a game that has numerous applications for mathematical thinking. In Canada, there is an association that promotes the game entitled, Chess'n Math Association. They claim that it teaches : "problem-solving from start to finish. It forces you to look ahead and anticipate. Skills we all need to succeed in life." If you want to teach the game, it is worth visiting and looking around. Follow the many useful links.

There is an organization in New York City called Chess in the Schools. They claim numerous benefits for Chess. For example:

"In 1991 and 1996, Stuart M. Margulies, Ph.D., a noted educational psychologist, conducted two studies examining the effects of chess on children’s reading scores. The studies demonstrated that students who participated in the chess program showed improved scores on standardized tests. The gains were even greater among children with low or average initial scores. Children who were in the non-chess playing control group showed no gains."

Almost every country in the world has a Chess federation. Since we live in Canada, we will link to the Canadian version. It is available in French and English. It provides a free training manual for teachers in pdf format that can be downloaded. Click here for the link.

Chess is a subject of great fascination for mathematicians. Many have tried to write a program that can beat the best chess players in the world, in the same way that the Chinook program at the University of Calgary has mastered the game of Checkers. Perhaps the most successful attempt has been the Deep Blue program developed by IBM which had considerable success against the famous Chess Grand Master, Garry Kasparov.

As with Checkers, there are Chess problems which would serve as a good way to study the game if there were no other players available, and these multi step problems serve as an excellent source of enrichment for gifted students. Here is one site, with hints, called Bruno's Chess Problem of the Day. There are other sites for problems on the web, and one can buy books of these in virtually any bookstore.

Like many of the other games mentioned in this blog, inexpensive versions are available in many stores. If you are on a budget, check your local second-hand stores or dollar stores. In a pinch, you can make a set out of paper or other easily available materials. There are Chess clubs in most major cities, and it is easy to form one in your school.

As with most games, there are online versions such as Yahoo Games just to name one, and inexpensive software or freeware versions available to download or purchase. Check online or at your local computer store.

Mathematics Software Recommended by Colleagues

Software is another way to learn and practise mathematics. Click here for a discussion about the history and value of educational software.

Here are some recommendations for software from colleagues on one of my favourite sites, Proteacher. To get imput I usually go to the Discussion boards and post a question and within a day, I usually have several answers. Click here for a link to the discussion boards.

1. One member at Proteacher recommended a set of software from Scholastic called Fastmath. Here is what she said: "I don't know what you consider 'primary', but this is for grades 2+. Our kids BEG to get on it every morning, and their facts memorization has really improved. Everything is a game."

2. Another member suggested Zoo Zillions and Carnival Countdown. She said: "I use Carnival Countdown, Zoo Zillions and the other Edmark titles for practicing math skills in my classroom and we also have them in our lab. Kids can move at their own pace."

3. A third member of Proteacher recommends an online version called HeKko. It seems designed for California but might be worth a look for teachers in other jurisdicitions. Here is what she says: "There is an online site: http://www.hekko.com/ . You can enter the names of your children and make a class list. Each child moves at his/her own pace."

Checkers for Children

These young guys are playing checkers. I'm out there playing chess.

Kobe Bryant

This is the fourth in a series of posts on games for children.

The quote above suggests that Checkers (called Draughts in England) is a simpler than chess. However, it is a challenging game of strategy, with simple rules and few pieces that is easily taught to young children. You can purchase sets wherever games are sold. They are readily available for little cost. Typically you can find sets at most dollar stores which is a bonus for teachers or parents on a budget. If you are interested in arts and crafts, they can be made. Here is a link for an example of a printable version.

There are many variations in rules. Wikipedia has an detailed article with many suitable links. Click here to read this article. Since we live in North America we suggest that you teach the version of rules used by the American Checkers Federation. Here is a good link that explains the rules clearly.

There are extensive data banks of games so that you may study strategy. For interested or gifted children, there are sets of checker problems which are very challenging. To solve, the child must figure out the next several moves to win the game. Click here for an example from Checker enthusiast, Jim Loy.

Dice Games for Children

The dice of Zeus fall ever luckily.

Sophocles

This article is on dice games and it is the third in a series of posts about games to teach mathematics.

Dice are extremely old, dating back to antiquity. Their mathematical applications are obvious. They require counting and are ready made tools for teaching about solids and probability -providing that they have not been doctored that is. Wikipedia has an extensive article on the history, use and probability of dice if you would like further background. The article also has some excellent links. Just click here.

Here are links to dice games and their rules:

1. From Activity Village, a British site with activities for children.



2. From About.com, a collection of blogs about just about any subject under the sun



3. From Scholastic.com, a set of four dice games suggested by math guru, Marilyn Burns

Just a note in passing. Although dice are easy to purchase, if you need a substitute or do not have any on hand, you can make spinners out of paper, a paper clip and a pencil that will perform the same function. Click here for some spinner templates.

Domino Games for Children

This is the second in a series of posts about simple games for both parents and math teachers.

There are numerous versions of domino games. Go to Wikipedia for a short history and some useful links. Sets of dominoes can be found at toys, stationary, department and dollar stores. In a pinch, you could make your own out of paper and then laminate them for classroom use. Here is a link for printable ones.

1. Here is a simple introduction to dominoes for parents or teachers. This link gives the rules for a basic "draw" game. Needless to say there are numerous variations on the rules of dominoes. If you do not feel like reading, you can watch a video version of the rules for the draw game. If you are a teacher you could show this to your class as a quick way of demonstrating the rules. Click here. The video lasts about four minutes.

2. The NCTM has a set of lesson plans for using dominoes in the classroom on their excellent site entitled Illuninations. Click here for lesson plans using dominoes.

Card Games for Children

What we learn with pleasure, we never forget.

Alfred Mercier

One of our core beliefs as math teachers is that games teach mathematical thinking. A game is a dynamic problem. After each move, the player must adjust his thinking to achieve his goal. At times they can improve arithmetical ability too. Alot of games require counting. I personally learned to add quickly by playing Cribbage with my parents.

Games are an easy and fun way to improve your child's mathematical ability in addition to being just plain fun. Children will not realize that they are practising math and frankly won't care as long as they are having fun. If you are a parent, this is an easy way to spend some quality time with your child without spending much money.

This is the first in a series of blog entries here on simple games for both parents and math teachers. We are including games that require few materials, the kinds that can be found at home or are available cheaply at locations such as dollar stores.

Today I am going to concentrate on card games.

1. We live in Ontario so here is a plug for a local organization. The Ontario Association of Mathematics Educators designed a document for teachers called "Using Playing Cards in the Classroom" and is in convenient PDF form to save on your computer or to print out.

2. Here is a link to many useful card games for practising basic number facts from the schools in Granby, Connecticut.

3. Here is a link from a site called Crewton Ramone's House of Cards.  It has some useful videos and some good quotes about play.

4. Here is a fantastic collection of card games to teach different math skills from a group called The Positive Engagement Project.  The book is called Acing Math One Deck at a Time.

Teacher Resources for Using Literature in Mathematics Teaching

In addition to assisting teachers in using Literature in the teaching of Mathematics, parents may also find these books useful as resources containing good literature with which they may reinforce mathematics concepts with their children simply by reading and discussing the books.

MathStart books, created by Stuart Murphy, tell stories every kid can relate to and enjoy, while helping them understand that math is much more than a school subject—it’s all around us and in everything we do!Each book in the MathStart series includes suggestions for group or individual exercises that reinforce math concepts presented in the story, easy-to-do activities, and a bibliography of children’s books that feature similar math concepts.

A great series, available for ages 3 and up. Visit these websites to learn more:

Visit HarperChildrens.com

Visit stuartjmurphy.com!

Literature-Based Math Activities: An Integrate Approach/Grades K-3 (Instructor Books) (Paperback)by Alison Abrohms (Author)

Math and Literature, Grades K-1 Marilyn Burns and Stephanie Sheffield

Math and Literature, Grades 2-3 Marilyn Burns and Stephanie Sheffield

Math Through Children's Literature: Making the NCTM Standards Come Alive (Paperback)by Kathryn L. Braddon (Author), Nancy J. Hall (Author), Dale B. Taylor

Teaching Math with Favorite Picture Books (Grades 1-3) (Paperback)by Judy Hechtman (Author), Deborah Ellermeyer (Author), Sandy Ford Grove (Author)

How to Use Children's Literature to Teach Mathematics (Nctm How to-- Series) (Paperback)by Rosamond Welchman-Tischler (Author)

Math And Nonfiction: Grades K-2 (Math and Nonfiction) (Paperback)by Jamee Petersen (Author), Marilyn Burns (Introduction)

Meeting the Math Standards with Favorite Picture Books: Lessons, Activites, and Hands-On Reproducibles That Help You Teach Essential Math Skills and Concepts (Paperback)

Useful Math Websites

Useful Mathematics Websites Recommended by Colleagues

1. Kid’s Place Brain Teasers
Three different challenging problems a week.
On the negative side, there are no flashy graphics. It is more likely to appeal to adults than to children.

On the positive side, this site has a new brain teaser each week. One is for grades 3-4, 5-6 and 7-8. Each problem comes with a set of hints. There is a link to the archive of past questions.

2. Math Cats
For primary and junior grades. Deals especially with problem solving and games.
From the NCTM journal, Teaching Children Mathematics for 2003

"The Web site at www.mathcats.com offers playful explorations of mathematical ideas that will pique students' interest... The most powerful part of the Web site... is the interactive applets that help students explore mathematics in a way that develops understanding..."

For a full review from Education World, click here. More reviews are available here.


3.Mr. Nussbaum
A variety of math games to reinforce basic computational skills.

On the negative side, the graphics on the free site are relatively simple.

On the positive side, there are a variety of activities to support fluency of basic facts. If you want your child to practise traditional algorithms for addition, subtraction, multiplication and division, the “Draggable Math” game is a good place to start. Its use of columns would be good for a child who had fine motor problems too.


4. PrimaryGames.com
Over 50 math games for grades PreK to grade 4. Many games in other subject areas too.

Click here to see how to use each math game.

On the negative side, there are lots of banner ads.

On the positive, the site is colourful, clearly organized and comprehensive. I especially appreciated the curriculum guide for the mathematics activities. See the Education World review here.

Websites with listings of Children's Literature relating to Mathematics

As the lists of children's books pertaining to the various mathematics strands cited on this blog are FAR from comprehensive, here are a few sites you may wish to visit to get more ideas:

The Upper Canada District School Board has a site called Read Any Good Math?
It has a list of books, songs and even poems about mathematics divided into the various strands.

Books by Marilyn Burns
http://www.marthalakecov.org/~math/burnsbooks.htm

A listing of Greg Tang's books: A New Approach to Math
http://gregtangdev.com/

Math Literature Connections
http://www.mathwire.com/literature/literature.html

Geocities: Books on Numbers
http://www.geocities.com/teachingwithheart/booksonnumbers.html

Christchurch City Library: Children's Picture Books that teach Mathematics concepts
http://library.christchurch.org.nz/Learning/MathsInPictures/

The Children's Literature Nook Presents: The Top 100 Children's Books: Math
http://www.geocities.com/heartland/estates/4967/math.html

Math Literature
http://home.nyc.rr.com/teachertools/mathliterature.html

Math and Literature
http://home.att.net/~cattonn/math.htmlhttp://home.att.net/~cattonn/math.html

Carol Hurst's Children's Literature Site
http://www.carolhurst.com/subjects/math/math.html

Mathematics and Children's Literature
http://illuminations.nctm.org/LessonDetail.aspx?id=U83

Mathematics is Elementary, Suggested Children's Literature
http://www.ait.net/products/mathematics/booklist.htm

Mathematics and Children's Literature
http://www.sci.tamucc.edu/~eyoung/literature.html

Math and Literature Idea Bank
http://www.mathcats.com/grownupcats/ideabankmathandliterature.html

Children's Literature in Mathematics Instruction
http://falcon.jmu.edu/~ramseyil/mathpict.htm

Math in Children's Literature
http://literacy.kent.edu/Oasis/Resc/Educ/mathkidslit.html

Mathematics & Children's Literature
http://www.nea.org/webresources/mathreadinglinks.html

Teaching Mathematics with Children's Literature
http://fcit.usf.edu/math/resource/bib.html