The most important two beliefs that I hold to be true about learners…

### Nobody is more mathy* than anyone else.

* Mathy is that thing we apply to certain students who are doing well in math; and not-mathy is its antonym, students we deem as unable to do math.

#### Learners either love math or do not yet realize they love math.

Learners either love math or do not yet realize they love math. Math is everyone and when we look at the Masters of Math, we find they come from all backgrounds and are just like each and every one of us.

Kloosterman (1994) believes that if teachers expect students to learn math, they then have the responsibility to show them that they too can learn mathematics. “Beliefs have a connection to the student’s view of himself and others as learning mathematics.” (Wester 2015)

The only thing that impedes a love for math is a lack of differentiated learning in the classroom. When students tell me, “I do not like this subject…” what I hear is “There is something I do not understand about this subject and it makes me feel uncomfortable.”

Sometimes a learner needs a scaffold; from an aide, a peer, a teacher or caregiver. The learner still wants to be in control of the problem, but needs help over a hurdle or perhaps an impedance (i.e. a pre-cursor that was not well understood by the learner or perhaps never even taught.)

The teacher has to be mobile and available to all. You correct the learner as they go along, not after. (Ashton-Warner 1963)

Learners enjoy being stretched out of their comfort zone. Learners may be drawn to tactile learning experiences (e.g. acting out the problem, drawing a picture) and some will easily begin the crossover to high-order methods (e.g. factor trees, functions, substitutions). A learner is only ready for high-order methods after having made enough progress on the more tactile and visual approaches. Learners need that repeated hands-on play with a problem to build the references in their mind needed to handle the more abstract methods of problem solving.

#### Learners in middle school are at a critical juncture in their mathematical education and must be given highest attention to.

“They are forming conclusions about their mathematical abilities, interest, and motivation that will influence how they approach mathematics in later years.” (Protheroe, 2007)