Embedded Files
Communication: The student uses math vocabulary, provides evidence to support ideas, helps others, and asks others for evidence.
Communication is a vital skill in all areas of life, and mathematics is no different. However, there are specific ways mathematicians communicate their thoughts and ideas. At TASIS, we help our students to use correct mathematical vocabulary, provide evidence through verbal, written, or illustrated explanations, and encourage them to ask others for evidence as they are working together.
Mathematical Vocabulary
Mathematical Vocabulary
In our math program, there is a lot of reading, writing, and talking about math. In order to read with understanding, explain something on paper or in a discussion, students must know the correct mathematical vocabulary used in any given unit.
For example, read the following scenario:
Bia has 15 apples. Nadya has 18 apples.
Any of the following questions may be asked (vocabulary words in bold):
How many apples do they have altogether?
What is the total amount of apples the girls have?
What is the sum of the apples the girls have?
With these questions, students need to use their knowledge of vocabulary to understand that they are supposed to use addition to solve the problem, even though it doesn't tell them explicitly to add.
Alternatively, the following questions may also be asked for the same scenario:
How many more apples does Nadya have than Bia?
How many fewer apples does Bia have than Nadya?
What is the difference between the girls' amount of apples?
With these questions, students would use subtraction to solve the problem.
The vocabulary words may also appear in directions, as follows:
Simplify the expression.
24 – 3 × 6 + 8
To solve this problem, students would need to know what simplify and expression mean. In this case, it means to combine the terms in the number statement, in the correct order, to obtain a single number:
24 – 3 × 6 + 8 = 24 – 18 + 8 = 6 + 8 = 14
Providing Evidence
Providing Evidence
Without evidence, or proof, mathematics would not work. Thus, we place a lot of emphasis on explaining thinking, using three primary methods:
Verbal: Students discuss how they arrived at their solutions by talking through their process, with teacher prompts to provide more information as needed."Six plus seven equals thirteen. I know that six plus six equals twelve, and seven is one more than six, so one more than twelve is thirteen."
Written: Students write out each step of their solution, showing their calculations and identifying important pieces of information. A lot of teachers call this "showing your work". It is expected that students show their work, even if they can make a calculation mentally (e.g. if a student can multiply 4 × 27 mentally, they should still write out
4 × 27 = 108 within their solution to show how they are getting the 108). See the Showing Work in Math slideshow below for examples of written work at each grade level.Visual: students show their thinking using physical manipulatives like base ten blocks, counters, connecting cubes; drawings like bar models or direct representations of a problem; or diagrams like tally charts, graphs, or shapes annotated with their dimensions (see the Visualization page).
Working with Others
Working with Others
It is also important for mathematicians to collaborate with others. Not only can collaboration help us ensure our answers our correct, it can help us better understand concepts because we have to communicate about them. When collaboration is appropriate, students can help each other by explaining their thinking (using mathematical vocabulary). Students should not provide the answer (unless they are checking their answers), but help others understand the process to get to the answer. Students should also develop the habit of asking others for proof, as it encourages the other person to verbalize their problem-solving process and provide evidence for their solutions.
Communication Tips
Communication Tips
The student textbooks contain the important vocabulary and definitions within each chapter. The back of the textbooks also have a glossary with all vocabulary terms that appear within the book. Talk to your child's homeroom teacher if you do not have access to the student textbook.
A Maths Dictionary for Kids is another great resource for looking up math vocabulary words.
When talking about math, use the correct terms and make sure the student is also using the correct terms. For instance, if a problem involves fractions, make sure you and the student are using words like numerator and denominator, rather than "top number" and "bottom number". Consistent, gentle reminders like "what is the mathematical word for the top number?" can help students get into the habit of communicating with math vocabulary.
When solving problems, ensure the student is drawing bar models whenever appropriate, and writing out the steps used to solve the problem. As problems increase in complexity, keeping track of the steps used to solve it becomes increasingly important.
Asking, "How do you know that?", or "What is your evidence for this answer?" can be good ways to encourage explaining thinking. This also gives an opportunity to the person asking the question to see if the student understands the mathematical concept(s) involved in the problem.
Page updated
Report abuse