One goal in teacher education is to prepare
prospective teachers (PTs) for a career of systematic reflection and learning
from their own teaching. One important skill involved in systematic reflection,
which has received little research attention, is linking teaching actions with
their outcomes on student learning; such links have been termed hypotheses. We
developed an assessment task to investigate PTs’ ability to create such
hypotheses, prior to instruction. PTs (N = 16) each read a mathematics lesson
transcript and then responded to four question prompts. The four prompts were
designed to vary along research-based criteria to examine whether different
contexts influenced PTs’ enactment of their hypothesizing skills. Results
suggest that the assessment did capture PTs’ hypothesizing ability and that
there is room for teacher educators to help PTs develop better hypothesis
skills. Additional analysis of the assessment task showed that the type of
question prompt used had only minimal effect on PTs’ responses.

Grades: 3rd to 5th, 9th to 12th, 6th to 8th, Pre K to 2nd

Num & Ops Fractions

Geometry

Mathematical Practices

The Number System

Use equivalent fractions as a strategy to add and subtract fractions.

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Reason with shapes and their attributes.

Develop understanding of fractions as numbers.

Look for and make use of structure.

Attend to precision.

Model with mathematics.

Make sense of problems and persevere in solving them.

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Compute fluently with multi-digit numbers and find common factors and multiples.

6.NS.B.4, 7.NS.A.1d, 1.G.A.3, 2.G.A.3, 4.NF.B.3a, 4.NF.B.3d, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP4, CCSS.Math.Practice.MP6, CCSS.Math.Practice.MP7, 3.NF.A.1, 3.NF.A.3c, 3.G.A.2, 4.NF.B.4a, 5.NF.B.3, 5.NF.A.1

More than ever, mathematics coaches are being called on to support teachers in developing effective classroom practices. Coaching that influences professional growth of teachers is best accomplished when mathematics coaches are supported to develop knowledge related to the work of coaching. This article details the implementation of the Decision-Making Protocol for Mathematics Coaching (DMPMC) across 3 cases. The DMPMC is a framework that brings together potentially productive coaching activities (Gibbons & Cobb, 2017) and the research-based Mathematics Teaching Practices (MTPs) in Principles to Actions: Ensuring Mathematical Success for All (NCTM, 2014) and aims to support mathematics coaches to purposefully plan coaching interactions. The findings suggest the DMPMC supported mathematics coaches as they worked with classroom teachers while also providing much-needed professional development that enhanced their coaching practice.

Grades: 9th to 12th, 6th to 8th, 3rd to 5th, Pre K to 2nd

Mathematical Practices

Look for and express regularity in repeated reasoning.

Look for and make use of structure.

Model with mathematics.

Construct viable arguments and critique the reasoning of others.

Reason abstractly and quantitatively.

Make sense of problems and persevere in solving them.

CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP2, CCSS.Math.Practice.MP3, CCSS.Math.Practice.MP4, CCSS.Math.Practice.MP7, CCSS.Math.Practice.MP8