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In a Grade 6 mathematics classroom, a boy sat in the back of the room. He was unremarkable - quiet, and dressed as if he had come from a home with little money to spare on clothing. He did not utter a word during the entire class, but kept his head down and did every problem his teacher assigned. After the students left, an observer asked the teacher about him.

“He makes a perfect score on everything I give him. I don’t know what to do with him. I have been working so hard to bring the students who struggle along, that I really have not focused on him,” she said.

This is a common state of affairs in schools. Teachers, administrators, and parents spend most of their time, energy, and resources trying to bring struggling students up to grade level. This is an excellent goal, and one that should be in the forefront of our educational efforts. However, what if you were the parent of a child who is working above grade level? What if she is gifted in math? Is your child getting everything she can possibly get from the instruction she receives in school?

That is the beauty of the Algo Club. The learning activities are designed to meet students where they are - to challenge each student to extend their mathematical abilities in content, problem solving, reasoning, and communication. Students who have struggled in mathematics learn from the multiple opportunities to interact academically with the session facilitators and their peers, and students who are very proficient in mathematics are challenged to think and work at a higher level. Don’t all of our children deserve this type of individualized learning?

In a recent professional development session about journal writing in mathematics classes, a kindergarten teacher noted, “I don’t know what to do with my students and their math journals. They are too young to be able to communicate anything on paper.”

Although the teacher recognized that communication is an important tool for identifying, articulating, and extending children’s thinking about mathematics, she did not consider that oral discussion is one effective mode of mathematics communication. In this way, children learn how to reflect on their understanding – both the mathematics content and their own thinking processes. Students should be encouraged to communicate their mathematical thinking in many ways – through words (spoken and written), pictures, and symbols.

In early years, children may communicate their mathematical understanding on paper through symbols they make up on their own, or they may use symbols that they have seen, but use them incorrectly. This is perfectly developmentally appropriate; over time, children learn to use appropriate mathematical conventions and language.

As parents, you may find many, many opportunities for developing mathematical communication skills in your child. When going out for pizza, you could ask questions like, “Why do you think this pizza is cut into 8 slices? What would happen if the baker had cut it into 12 slices?” When going to the bank, you could ask your child to time how long you stand in line. “Why do you think it will be that amount of time? What could make that amount of time in line last longer? What could make it shorter?”

The best way to improve children’s written depictions of their thinking is to simply “turn them loose”, and let them try! Be accepting of unconventional representations, and ask your child to explain orally what they did on paper. Before you know it, they will be communicating – through both spoken and written means – with ease.

Have you ever heard a young child question his or her parent about how things work, or why things are the way they are? Why is the sky blue? How did someone build that skyscraper? Why is that boy so tall? Although a barrage of questions can be annoying at times, when doing mathematics with children, questions that begin with “why” and “how” should be commonplace. Consider this scenario:

A child is classifying whether shapes are polygons or not polygons. He studies the definition of a polygon: a flat, closed figure with at least 3 sides. In his “polygon” pile, he places a triangle, a square, and a pentagon. In the “not a polygon” pile, he places a circle.

What questions might you ask? To promote this child’s reasoning and his ability to prove his answer, you might ask:

• Why is the triangle in the “polygon” pile?
• Why is the circle in the “not a polygon” pile?
• How did you figure that a pentagon is a polygon?
• How are triangles, squares, and pentagons alike?

When a child answers questions such as these, it requires him or her to observe patterns, use vocabulary, consider definitions, evaluate attributes of objects, and justify why things are the way they are.

One challenge for adults working with children to increase these higher-level thinking skills is the realization that the development of mathematical reasoning often requires that the child first obtain an incorrect answer. As a parent or a teacher, it is difficult to not “jump in” and show the child his or her error. The adults’ role, however, should be to encourage the child to examine his own thinking and discover the incorrect reasoning when it happens.

A couple of weeks ago, a Grade 4 student brought home the following problem in her math homework:

Four runners were preparing to race. Before the race, each runner shook hands with the others. How many handshakes were there in all?

The child’s grandmother, who usually helps with homework after school, could not figure out how to help the Grade 4 student. The child’s mother couldn’t figure it out either. She exclaimed, “When did kids start doing problems like THIS in elementary school?”

In recent years, there has been a focus on developing problem-solving abilities in children, through the use of both traditional problems and non-traditional problems. Many parents are familiar with traditional problems like this: I had $1.30. I spent $0.75 on the way home. How much money did I have left? They are able to help their children with a problem like this by pointing out the “key words” – have left. “Have left” means that you subtract.

Often, the key word method of problem solving is effective. The words “in all”, for example, typically mean to add. However, look back at the handshakes problem. The words “in all” are there in the question. The only number that appears is ‘four’. So, what should the child add?

Instead, let’s focus on teaching our children problem solving strategies that work across both traditional and non-traditional problem types. Useful problem solving strategies like drawing a picture, making a table or chart, and using guess and check (previously called ‘trial and error’) help children make sense of problems and determine the correct answers. Through the Algo Club, children are provided with logic puzzles, brainteasers, and games in an effort to promote such higher-level thinking and problem-solving strategies.

By the way, how did you figure out the answer to the handshakes problem? I made a type of chart. First, I designated the runners as Runner A, Runner B, Runner C, and Runner D. Runner A shakes hands with B, C, and D, which is 3 handshakes. Runner B then shakes hands with C and D (he has already shaken hands with A, so he doesn’t do that again), which is 2 handshakes. Runner C shakes hands with D (she has already shaken hands with A and B), which is 1 handshake. Runner D has already shaken hands with everyone, so she takes her place at the starting line. The answer: 6 handshakes.

The next time you are at the park or playground, notice the children at play. A group of children in the sandbox push trucks up and down a ramp. They learn that if they push the truck with the perfect amount of force, it jumps the ramp and lands exactly in the centre of the sandbox. Under the trees, some children are doing the long jump, and measuring by walking heel-to-toe who jumped the longest distance. In a house across the street, a girl is putting together a jigsaw puzzle, and her little brother is building a city with blocks.

Although they are playing at different activities, all of these children have one thing in common: they are developing mathematics skills. The children on the playground are learning about measurement and distance, and the children in the house are developing spatial sense by determining how things fit together.

Parents can begin helping children develop spatial sense early in a child's life, and this is best accomplished through play. Toys that involve movement (for example, trains and cars), toys that involve building and fitting things together (like blocks and puzzles) and art activities that involve cutting and putting the pieces together to make something else all serve as excellent developers of early math skills and spatial sense.

Although workbooks and web-based programmes are very popular and promoted by some curriculum developers and mathematics programmes, there is no substitute for children having real experiences manipulating tangible shapes. This early play allows children to later visualize shapes and the movement of them mentally, and this aids in geometry learning. It is much easier for children to develop such skills when they are young, as it is more difficult to learn those skills later.

Now, you can register your child for the Algo Club online! We are introducing the Algo Club online registration form. Please visit our registration information page to see further details.

Our staff members are all excited about welcoming your child to the Algo Club. The first class will start on the week of September 13th!

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