TExES Core Subjects EC-6 Mathematics (902)

CPA Approach

Concrete, Pictorial, Abstract

• Children first need hands-on experiences (manipulatives like counters, base-10 blocks)

• Then, move to pictorial representations (drawings, diagrams)

• Only after that should you teach abstract concepts (symbols, equations)

Ex: Don’t teach 7 + 5 = 12 before letting kids group 7 and 5 counters.

Piaget’s Stages of Cognitive Development

• Sensorimotor stage (birth to 2 years)

• Preoperational stage (2 to 7 years)

• Concrete Operational stage (7 to 11 years)

• Formal Operational Stage (11 to adult)

Preoperational Phase

The second stage of Piaget's theory of cognitive development, occurring from ages 2 to 7, where children begin to engage in symbolic play and learn to manipulate symbols, but do not yet understand concrete logic.

Concrete Operational Phase

Students think in more rational terms or more “operational thinking”. Students still need to have an object in front of them in order to be able to think logically about it.

Formal Operational Stage

Students no longer need a physical object in front of them to be able to think about it abstractly and they are able to use symbols.

Manipulatives

Physical objects used in teaching mathematics to help students understand concepts through hands-on experience.

Ex: Beads, Cubes, Base-ten blocks, Calculators, Video Games, etc.

What are the 5 major shifts in math classrooms according to the Professional Standards for Teaching Mathematics?

• Classroom as a math community (not just individuals)

• Students justify answers with logic/evidence (not just rely on teacher)

• Reasoning over memorization

• Problem solving over answer-getting

• Making connections (not isolated procedures/concepts)

Bloom’s Taxonomy

Remember, Understand, Apply, Analyze, Evaluate, Create.

Formative assessment

Used for developing instruction, what the student currently knows or still needs to learn.

Summative Assessment

Occurs at the end of the learning process and is typically graded.

Formal Assessment

Systematic, pre-planned data-based test that measure what and how well the students have learned the material. Determines the student’s proficiency. Usually used for a grade.

Ex: Standardized test (STAAR)

Informal Assessment

Easily incorporated in the day-to-day classroom activities and measure the student’s performance and progress.

Ex: Asking the class or the individual student questions

Norm-referenced Test

Shows how a student preforms relatively to his or her peers.

Criterion-referenced Test

Assess a student’s knowledge of certain skills and criteria.