|Doing Mathematics with Your Child (Kindergarten to Grade 6)
Today, critical thinking, problem solving, reasoning ability and ability to communicate mathematically are essential skills. These processes are the foundation of mathematics instruction in Ontario schools. “Doing Mathematics with Your Child” is a guide available for parents of students in Kindergarten to Grade 6. This guide offers ways to engage their child in thinking and talking about mathematics around the four strands: number sense and numeration, measurement, patterning and algebra, and data management and probability.
Please use the link below to access the guide in English and 13 other languages:
|Art and Math
Art and math have a lot in common with each other. In fact you can see the math in art and the art in math! Patterns, shapes, geometry, symmetry, spatial reasoning, proportional reasoning, etc… are all a part of the arts (visual art, music and dance), as they are of mathematics.
Some of what you see your child doing in school in the arts, is also an engagement with mathematical ideas at the same time! By blending mathematics and the arts, students learn in ways that are intellectual, emotional and physical. Children learn in many different ways, and research tells us that participating in the arts is one way that is very engaging for all of us.
A child stringing beads in a pattern on a string or creating a patterned bracelet is creating an understanding of patterning, although to them it may look simply like a pleasing design. When a child learns to play the piano, they are developing mathematical understanding of the relationships between scales, notes and chords. Symmetry can be seen in the symmetrical features of a butterfly or in a design when building. Children may notice patterns in wallpaper, tile tessellations on the floor or on a phone cover, rhythmic beats or repeated choreography in music videos or chords in a popular song. There is math everywhere!
How might you and your child notice and name the mathematics in the arts (visual, music and dance) that you encounter? Making the links helps deepen the understanding of both!
Interested in more?! Search on the internet for “golden ratio” to see an example of mathematics at work in nature and art!
|Communicating with Children Using Math Language
Talking About Math:
Talking about mathematics with your child – whatever his or her age – helps strengthen his or her mathematical reasoning and understanding. Some ways to keep the talk engaged and focused while you support your child include:
- Revoice - Repeat what you heard your child say, then ask for clarification (e.g., “So you are saying it’s an odd number?”).
- Repeat/Restate – Ask your child to restate your reasoning (e.g., “Can you repeat what I said in your own words?”).
- Reason – Ask your child to apply his or her own reasoning to someone else’s reasoning (e.g., “Do you agree or disagree? Tell me why.”).
- Adding On – Prompt your child to participate further (e.g., “What more would you add to that?”).
- Think Time – Wait several seconds (try five) to give your child time to think (e.g., “Take some time to think.”). You may be surprised by how hard it is to stay silent in that time!
We all use mathematics daily in what we do. Involve your child in using numbers to solve problems and make those everyday decisions with you. For example:
- “Do we have enough plates and utensils for all the guests coming for the birthday party?”
- “We are doubling this recipe. How much of all the ingredients will we need?”
- “We are fertilizing the lawn. The fertilizer bag covers three square meters. How many will we need?”
- “This store is selling the game you want for 20% off of $27.00. That store is selling the same game for $19.99. Where should we shop?”
|Growth Mindset in Math
In general, a growth mindset is the belief that intelligence and ‘smartness’ can also be learned and that the brain grows from experience and effort. The opposite, a fixed mindset, is the idea that you are smart, or you are not. In math, that translates into “some people are good at math, and some are not.” Did you know that praising efforts rather than intelligence or results can impact your child’s ability to persevere in challenges?! The goal is to have children thrive on challenges and see failures, not as a sign of low intelligence, but as a learning opportunity. Brain research tells us that making mistakes actually wires more connections into the brain! When a person has a growth mindset, they accept challenges, see their efforts as worthwhile, and are open to learning from mistakes. Students with a growth mindset achieve at higher levels than those with fixed mindsets. How can you help? Some simple ways:
- Adding “yet” when they claim they are “not good at this” (Respond: “You are not good at this yet.”)
- Ask questions that focus on their effort and choices and get them to reflect on satisfaction of that effort (e.g. What did you learn today? What mistake did you make that taught you something? What did you try hard at today?)
- Model this yourself as you share about your day
|Holiday Math: Take advantage of math in the world
Summer is a great time to learn how math relates to the real world. Math is everywhere!
Help your child prevent “summer learning loss” by taking advantage of the many great opportunities to practice math naturally!
Below are a few ideas to get you started:
- Cooking can involve weighing, measuring, ordering, estimating, adding, multiplying …
- Restaurants and shopping can involve money, number identification, estimating, adding, subtracting, division …
- Parties can involve matching numbers of people to plates, cutlery, area of tables, estimation,
- Trips can involve time, distance, budgeting, speed, evaluating various routes, license plate games (e.g. adding or multiplying the numbers on the plate) …
- Home projects can involve estimation, measuring, multiplication …
- Gardening can involve measuring, counting, area, division …
These ideas all demonstrate how much math is involved in our daily lives and will support your child in his or her basic computation and problem-solving skills in natural, fun and real ways.
|Homework Help for Students Grade 7 to 10
Homework Help is a free online math help resource for students in Grades 7-10. Homework Help provides free, live one-on-one tutoring from Ontario teachers Sunday to Thursday from 5:30pm – 9:30pm ET. The program is funded by the Ontario government and administered by TVO's Independent Learning Centre. To log in, students will need to register with their Ontario Education Number (OEN), found at the top of their report card near their name.
(Your child’s OEN never changes so any of their Ontario report cards will have it.)
Note: Homework Help is offered in English and is only available to students at publicly funded schools.
|Inspiring Your Child to Learn and Love Math
Inspiring Your Child to Learn and Love Math is a tool kit for parents developed by the Council of Ontario Directors of Education (CODE). This toolkit was created specifically for parents of children in the elementary grades in Ontario (Junior Kindergarten to Grade 8). The toolkit emphasizes the many ways in which parents’ help and support plays an important role in inspiring their children to learn and love mathematics. The goal of this resource is to provide parents with the most significant research-based information to help them be the best, most knowledgeable and most confident supporters for their child's mathematics education.
Inspiring Your Child to Learn and Love Math provides modules with simple, but effective methods and materials for parents to support their child’s math learning. It shows parents how to get involved in their children's learning, and offers guidance for working with students of different ages. This Parent Tool Kit was developed by experts in mathematics education, with input and advice from parents and students. When families and educators join together, students of all ages can experience greater success in their learning.
Parents and educators alike can use the Implementation Guide to host a parent engagement session, and give parents in their school communities information they need to help their children navigate the K-8 mathematics program.
The complete tool kit is available at:
|Learning to Count
When children are learning to count, they like to touch, point to and move objects as they say the number aloud – so encourage them to!
- Have your child count toys, kitchen utensils, items of clothing as they come out of the dryer, collections (such as stickers, buttons or rocks) and any other items your child shows interest in counting.
- Mix it up! Have your child count a set of objects but start at different places in the set (for example, start counting in the middle of the set rather than at the beginning). This helps to develop the idea that the counting of objects can begin with any object in a set and the total will still be the same.
- Sing counting songs and use counting in meaningful ways in games, such as Hide-and-Seek. Counting games, rhymes and songs exist in every culture. Some counting songs and rhymes help children to count forward and backward as well.
- Have your child skip count (counting by twos, fives or tens) to count larger groups of items quickly. Use such objects as blocks, pasta pieces, toothpicks or buttons.
- Develop your child’s awareness of the symbols used to represent numbers by making it a game. Look for number symbols in your home and neighbourhood: on the television remote, on the microwave, on the telephone keypad, in flyers and media, on signs and on team sweaters.
- Play a number version of I Spy. For example, “I spy something that has the number five on it,” or “I spy something in this room that there are three of.”
- Ask for your child’s help to count items in your home. “I wonder how many chairs we have around the table? In this room? In the house?” Count windows, light switches, lamps or beds. You might record “how many” by using a combination of numbers and pictures.
|Literacy and Numeracy on the Fridge – Video Podcast
In any household, the refrigerator door attracts a lot of traffic. That makes it the perfect place to post puzzles for children. Being able to solve problems and communicate your thoughts are skills that everyone needs. In this video podcast, Simaya age 6, thinks aloud as she solves the puzzles by herself. Her mom, Caroline, encourages her daughter to experiment and take risks. Asking her a question such as, "Why did you choose to do that first?" helps Simaya adjust and clarify her thinking. http://www.edu.gov.on.ca/abc123/eng/podcast/onfridgePod.html
Mathies.ca, hosted by Ontario Association for Mathematics Education (OAME), is designed for Ontario K – 12 students and parents. This website includes games, learning tools, activities, and additional supports for students to explore, build and enhance their mathematical thinking. A parent ‘Frequently Asked Questions’ section includes: “How can I help with the learning of mathematics?”, “What mathematics activities can we do together?”, “What digital supports are available?” and “What additional support is available?”
|Math and Picture Books
Reading to your child is both a wonderful way to spend time together and also an effective way to engage your child in conversation. Students of all ages love stories and love to talk about stories. “Literature provides students with opportunities to make connections with their own lives, provides a context to think and practise mathematics, and enriches students’ view of the world of mathematics.” A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6.
Listed below are a few titles to begin the conversation about mathematics at home. These picture books are connected to several math strands of the Ontario mathematics curriculum from your child’s report card:
- Caps for Sale, by Esphyr Slobodkina (Number Sense and Patterning)
- The Doorbell Rang, by Pat Hutchins (Number Sense)
- Count to 10 with a Mouse, by Margaret Wise Brown (Number Sense)
- Is a Blue Whale the Biggest Thing There IS? by Robert Wells (Number Sense and Measurement)
- Actual Size, by Steve Jenkins ( Measurement)
- One Grain of Rice, by Demi (Number Sense and Multiplication and Division)
- Grandfather Tang’s Story, by Ann Tompert (Geometry)
- Stone Soup, by Heather Forest (Data Management and Probability)
If you and your child are more comfortable in a language other than English, then read to your child in that language.
Your local public library may be helpful in choosing books connected to mathematics.
The link below may also be helpful to access digital books online in a number of languages:
International Digital Library: http://en.childrenslibrary.org/
|The Ontario Mathematics curriculum on… A Balanced Approach
The Ontario Curriculum: Mathematics has been designed so that students build their understanding of mathematics as they progress from K to Grade 12. In designing lessons to help students achieve the curriculum expectations, teachers employ a balanced variety of instructional strategies including problem solving, direct instruction, investigation, assessment, and practice. An important goal of the curriculum is that students be able to apply the mathematics that they have learned in real-world situations. To find out more about the Ontario Mathematics curriculum, please go to www.mathies.ca. At this website, you will find a variety of games, learning tools, activities, and additional supports that have been specifically designed to help students to achieve the expectations in The Ontario Curriculum: Mathematics. There is also a Parents page that will provide more information on how you can help your child to succeed in the mathematics classroom.
|The Ontario Mathematics curriculum on… Math Skills for the 21st Century
The set of skills our children need today extends beyond the traditional paper and pencil calculation skills that dominated mathematics instruction that most parents remember. In addition to having a good understanding of number facts and the ability to work with numbers, there are other important skills such as reasoning, problem solving and the communication of mathematical ideas that are also essential in the twenty-first century. For example, students need experience with making estimates, deciding on and adjusting their strategies, persevering through to a solution, and justifying their thinking. The Ontario Curriculum; Mathematics, Grades 1-8 (2005) supports the development of this mathematical thinking in a way that is meaningful and relevant to students. The Ontario Curriculum: Mathematics, Grades 1-8 (2005) is available on the Ministry of Education’s website at http://www.edu.gov.on.ca/eng/curriculum.
|The Ontario Mathematics curriculum on… Number Facts
The curriculum has been designed to foster not only skill with operations such as adding, subtracting, multiplying, and dividing, but understanding. For example, when students are learning the skill of multiplication, they learn that 3 × 5 represents three groups of five and the fact that multiplication is repeated addition, e.g., 3 × 5 = 5 + 5 + 5. They also learn how multiplication and division are connected and will come to understand, for instance, that “If I know that 3 × 5 = 15, then I also know that 5 × 3 = 15, and that 15 ÷ 3 = 5, and finally that 15 ÷ 5 = 3. When students see multiplication only as strings of facts, they do not understand these connections which are important for them when they go on to study more advanced mathematics topics such as algebra and proportional reasoning. The Ontario Curriculum: Mathematics, Grades 1-8 (2005) is available on the Ministry of Education’s website at http://www.edu.gov.on.ca/eng/curriculum.
|Partnering with Your Teen in Mathematics
Partnering with Your Teen in Mathematics Grades 7 to 12 is a resource for parents, guardians, caregivers and other family members to support the development of their teen’s mathematical abilities. The document addresses key aspects of understanding of the adolescent learner, different ways of learning, engaging in conversations with your teen, and supporting mathematical thinking, learning and work habits. For the document, click here.
Consider the following examples…
You are planting trees in a straight path of your backyard. You plant a tree and then every 10 metres along the path plant another. If the path is 40 metres, how many trees will you need to plant?
How will you pack all those different sized boxes in the van so you only need to make one trip?
That couch you noticed in the store is perfect for the basement family room but, will it fit down the stairs?
Now ask yourself: what skills do I need to solve the problems? What do I see or visualize helping me in solving the problems?
This is the first of a two part series that will highlight what spatial reasoning is and why it is important.
What is Spatial Reasoning?
Spatial thinking, or reasoning, involves understanding and remembering the location and movement of objects and ourselves, either mentally or physically, in space. There are a number of sub skills and concepts that are interrelated among each other. It also includes being able to show and communicate thinking in a variety of ways.
Visualization is the ability to see images in your mind and to remember what you see when it is out of view (visual memory). Spatial Visualization involves using our imagination to rotate, change, create, organize, and retrieve mental images.
Both of these concepts are important in the development of spatial reasoning.
Why is Spatial Reasoning Important?
Research has shown strength in spatial reasoning abilities is related to success in mathematics. Spatial Reasoning, although it is an important part of geometry, is a process that enhances learning and communication across all math strands and all grades.
November’s issue will spotlight key concepts and ways to promote spatial reasoning for all ages of our students.
Spatial Reasoning – Key Concepts and Ways to Promote it With Our Students (Part 2)
Whether our K-12 students are learning science, mathematics, art, physical education, or literacy, spatial thinking skills are important. As our students are engaged in tasks that allow them to “create, build, compose, perform, model, represent, shift, manipulate, diagram, move, visualize, scale, compare” they are filled with opportunities to engage in using spatial reasoning skills.
The diagram below outlines the number of concepts included in spatial reasoning.
Paying Attention to Spatial Reasoning K-12
Ways to Promote Spatial Reasoning for Students K-12:
We know spatial reasoning is important and can be improved with a variety of activities across all ages. Studies have shown that improvements in one area of spatial reasoning will often transfer to other types of tasks.
Below are some examples of ways spatial reasoning can be promoted in the home environment:
- Visualization skills:
Provide opportunities for your child to use their visualization skills to better understand solutions to problems. Try asking your child to explain what they are seeing in their mind or what they visualize when solving a problem.
- Emphasize spatial language:
Model the use of spatial words in the home environment. For younger children, this language will include words related to location, distance, orientation and direction (i.e. left, right, over, under, above, below, parallel, tall and short). For older children this language will include geometrical rotations (i.e. rotations, translations, and transformations)
- Provide playful opportunities for your child to exercise their spatial reasoning:
There are many activities children can engage that require spatial reasoning. Some examples are jigsaw puzzles, many board games, block- playing with geometric shapes.
- Using technology:
Digital technology allows students to manipulate and see space and spatial relationships. Some examples include: GIS, GPS, Google Earth, and any tools that allow students to manipulate and rotate objects that is not possible with a paper and pencil.
|Thinking Tools for Mathematics
Mathematicians create models with objects and drawings as they are exploring patterns and thinking their way through problems. In the same way, students of all ages (and their educators) model mathematical concepts to not only share their thinking, but to help them to do the actual problem-solving. In school, we often call the objects used ‘manipulatives’ or ‘thinking tools.’ Classrooms have some very specific manipulatives for use, but a ‘thinking tool’ can be any object that helps to share or clarify a mathematical idea. These visual models of mathematical ideas allow us to organize our thinking, solve problems, and make connections from the concrete to the abstract. They also support and enhance our ability to solve problems with others, talk about, write and demonstrate our thinking. As students are exploring and investigating through models and drawings, they are building their knowledge and solving problems, moving towards a deeper understanding. They are making connections between what they know in all areas of mathematics and how they see mathematics in their world. Math becomes understandable, engaging and relevant.
You can support your child to use objects and sketches as ‘thinking tools’ to problem-solve when they do math at home:
- “What might help you to think through this problem?”
- “Try showing this with objects or a sketch.”
- “Can you show me what you are seeing in your mind?”
|Understand Numbers with Your Child
Research tells us that in mathematics, higher achieving students have a stronger flexibility and understanding of the relationships between numbers. In classrooms, educators are working with students to build skills with understanding and connections, to help develop their sense of number as well as learning and remembering facts. This helps them when problem-solving.
Think about knowing 4 + 7 = 11 simply as a memorized fact.
Now think about knowing that 4 + 7 = 11 because it is a 3 + 7 and 1 more (linked to knowing that 10 is an important number).
The understanding of this relationship can help a student to think flexibly about 64+27.
In the same way, it can be thought about as 60 + 20 + the 10 (that was made by the understanding of 4+7) and 1 more = 91
As a parent, you can support your child in thinking flexibly about how numbers are related:
- What other numbers or facts is this connected to?
Example: 6 + 7=? This is like the double I know of 6 + 6 and then 1 more.
- What do you know that might help you get there?
Example: 7 x 4 =? I remember that 5 x 4 = 20, so then I have to add on two more 4’s, which is 8, to get 28.
- What is another way that you can know that?
Example: 4 x 25 =? I can think about money and know that 4 quarters is $1.00, so 4 x 25 = 100
|Wrong Answers, Great Learning
Thomas Edison said that he did not fail at making the light bulb one thousand times, but rather that "the light bulb was an invention with 1,000 steps."
"I've missed more than 9,000 shots in my career. I've lost almost 300 games. 26 times I've been trusted to take the game winning shot... and missed. I've failed over and over and over again in my life. That is why I succeed." (Michael Jordan)
Making mistakes is a natural part of all learning. Those who we consider to be "great" are clear that mistakes lead to learning.
The latest research on mathematics shows that mistakes are a very important part of learning math! When a person makes an error in math and they have the opportunity to learn from it, they actually develop a much stronger understanding. In fact, the research states that students learn more from making mistakes than from getting all the right answers. When your child makes an error, it offers insight into what understanding your child has about a mathematical idea. It allows parents and teachers to talk to the child about what they know, and ask questions to stretch their thinking around where they are currently developing their understanding. Parents can ask "How do you know that? What was your thinking here? Is there another way you could solve that? How did you think about X (an element they may be missing or have misunderstood)?" This conversation helps to develop the crucial skills of reasoning and communication and is therefore more helpful than simply showing a child how the math is done.
When you support an attitude that values learning from mistakes, you are telling your child that mistakes are a valuable and natural ingredient in learning and lead to deeper understanding. Research shows that this attitude supports stronger achievement!