MTEL Mathematics Foundations & Pedagogy Flashcards

A student solves 7 × 8 by thinking '7 × 7 = 49, then add 7 more = 56.' This demonstrates which mathematical practice?

Answer: Using known facts and decomposition strategies

The student uses a known fact and applies decomposition, demonstrating flexible, strategy-based mathematical thinking.

In mathematics education, the Concrete-Representational-Abstract (CRA) progression means:

Answer: Beginning with physical objects, then pictures, then symbols

The CRA sequence scaffolds learning by starting with manipulatives (concrete), moving to drawings (representational), and finally to symbols (abstract).

Which Massachusetts Curriculum Framework strand addresses students' ability to make sense of problems and persevere in solving them?

Answer: Mathematical Practice Standards

The Standards for Mathematical Practice, including MP.1 (make sense of problems and persevere), describe the processes and proficiencies central to mathematics education.

A teacher notices students can perform long division procedures but cannot explain why they work. This gap is between:

Answer: Procedural fluency and conceptual understanding

Students who can execute procedures without understanding concepts have procedural fluency without conceptual understanding, an important instructional gap to address.

The use of number lines to teach fraction concepts primarily helps students understand:

Answer: Fractions as numbers with magnitude and position

Number lines help students see fractions as numbers with specific positions and magnitudes, building conceptual understanding beyond part-whole models.

Which instructional strategy best supports mathematical discourse in a Massachusetts classroom?

Answer: Think-pair-share and structured math talks

Think-pair-share and math talks promote reasoning, justification, and communication, which are central to Massachusetts mathematics standards.