Students often have trouble expanding their understanding of notation. – as ‘take away’ = as ‘equals’ i.e. the answer.
Do I say “minus” or do I say “negative”?
Some students interpret 3n as meaning “thirty something”.My students arrive from a large number of feeder schools and almost all of them have little or no understanding of correct mathematical notation. It is easier for me to deal with the student with no understanding of notation than to deal with the many incorrect conventions some students use.
My students need to be able to write their work correctly, so they can record their mathematical thinking correctly. For example, I have noticed that students don’t know how to use the equals sign correctly. They use it to form ‘running arithmetic sentences’. They may solve a problem like 4 x5 + 6 as 4×5=20+6=26.
How do we know algebraic notation is challenging for our students to learn?
We assess our students with a Prerequisite Knowledge Diagnostic Test.
Here is a series of three consecutive problems that Anna addressed with a small group of students in her Year 9 classroom. Notice how the students are struggling with gathering like terms, understanding when the negative sign means “negative” or “subtraction”, and finally struggling to understand exponent notation.
- Anna: Small Group Teaching Part 1 Notation, Gathering Like Terms
- Anna: Small Group Teaching Part 2 Notation, Negative or Subtraction?
- Anna: Small Group Teaching Part 3 Notation, Confusion about Exponents
So what have we done to help our students understand algebraic notation?
We have changed the way we approach our teaching by:
- Showing students how algebra is everywhere in our lives
- Establishing what each student understands through assessment
- Promoting algebraic thinking with rich and meaningful contexts
- Demonstrating the benefits of rigour and correct use of vocabulary
- Building a “toolbox” of knowledge and skills that students can use appropriately and efficiently