Most primary teachers think of problem solving, one of the four mathematics proficiencies where children inquire into real world problems or solve open tasks.
However mathematical reasoning, the fourth proficiency in the mathematics curriculum, is often overlooked by primary teachers but fits very neatly with creative and critical thinking.
Expressing the common property or pattern noticed is generalising.
You might use an open problem such as “A rectangle has a perimeter of 24m. Find as many different rectangles as you can.”Along with questions and prompts to elicit students’ understanding of area, perimeter, rectangles and squares as they develop a range of examples that fit the constraint you can also use analysing and generalising prompts.
Generalising involves identifying common properties or patterns across more than one case and communicating a rule (conjecture) to describe the common property, pattern or relationship.
In order to generalise students need to first analyse the problem to notice things that are the same or different, notice things that stay the same and things that change, or order examples to notice patterns.
Some will claim they've never used a bit of their algebra but they're talking in terms of actually using algebra to do simple day-to-day math functions.
Mentally, people use algebra everyday and probably aren't even aware of it.
For this problem we are looking for students to form a rule, part of the early algebra curriculum.
When students form conjectures about common properties or relationships, the challenging prompts for students is “Why does your rule work?