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• Subtest 2: III. Mathematical Processes

Mathematics (Grades 5–12) Subtest 2

Subarea III. Mathematical Processes

0014

Understand mathematical connections and communication.

• identifying connections between concepts and procedures in mathematics
• identifying connections between mathematics and other disciplines
• expressing and representing mathematical ideas and problems in a variety of formats (e.g., verbally, graphically, symbolically)
• identifying contributions to mathematics made by different individuals and cultures and the type of societal problems that gave rise to mathematical systems
• determining the strengths and limitations (e.g., mathematical fidelity, rounding error) of calculations performed with and of outputs of a variety of technologies (e.g., dynamic geometry software, statistical packages)
• demonstrating knowledge of the use of technology to examine, explore, and express mathematical concepts and to develop mathematical reasoning

0015

Understand the content and methods for developing students' content-area reading skills to support their reading and learning in mathematics.

• demonstrating knowledge of and the relationships between the key components and processes involved in reading (e.g., vocabulary knowledge, including orthographic and morphological knowledge; knowledge of academic discourse, including the syntactic and organizational structures used in print and digital academic texts; print processing abilities, including decoding skills; use of cognitive and metacognitive skills and strategies; fluency, including accuracy and word recognition)
• demonstrating understanding of the relationships between and among comprehension processes and other factors (e.g., students' motivation, interests, cognitive abilities, and background knowledge)
• demonstrating ability to plan instruction and select strategies to support all students' content-area reading (e.g., differentiating instruction to meet the needs of students with varying reading proficiency levels and linguistic backgrounds, identifying and addressing gaps in students' background knowledge, scaffolding reading tasks for students who experience comprehension difficulties)
• demonstrating knowledge of explicit strategies for facilitating students' comprehension before, during, and after reading content-area texts and for promoting their use of comprehension strategies (e.g., using textual features such as graphs and diagrams; identifying learned concepts that build within a chapter or across chapters)
• demonstrating knowledge of explicit and implicit strategies for promoting students' academic language and vocabulary development, including their knowledge of domain-specific vocabulary words
• demonstrating ability to plan instruction and select strategies that support students' reading and understanding of mathematics texts (e.g., asking students to translate between different mathematical representations, asking students to describe in words or sentences the relationship between symbols and the situation being modeled)