Using visuals is a well-known strategy
to teach emergent bilinguals (EBs). This study examined how preservice teachers
(PSTs) implemented visuals to help EBs understand mathematical problems and how
an innovative intervention cultivated PSTs’ capability of using visuals for
EBs. Four middle school mathematics PSTs were engaged in a field experience with
EBs to work on mathematical problems; during the field experience, the PSTs
received interventions. In one intervention session, the PSTs were asked to
make sense of a word problem written in an unknown language with different
visuals. After this intervention, they changed their use of visuals when
modifying tasks for EBs. The results suggest that immersive experiences where
PSTs can experience learning from the perspective of EBs helps PSTs implement
mathematically meaningful visuals in a way that makes mathematical problems
accessible to EBs.

Related MTE Podcast

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

Num & Ops Fractions

Mathematical Practices

Functions

Geometry

Measurement & Data

Ratio & Proportion

Algebra

Counting & Cardinality

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

Look for and make use of structure.

Model with mathematics.

Make sense of problems and persevere in solving them.

Interpreting Functions

Reason with shapes and their attributes.

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

Develop understanding of fractions as numbers.

Analyze proportional relationships and use them to solve real-world and mathematical problems.

Reasoning with Equations and Inequalities

Creating Equations

Understand ratio concepts and use ratio reasoning to solve problems.

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

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

Count to tell the number of objects.

K.CC.B.5, K.CC.B.4a, K.CC.B.4b, 4.NF.B.4a, 4.MD.A.3, 6.RP.A.1, 6.RP.A.2, 6.RP.A.3b, HSA-CED.A.2, HSA-REI.D.10, 7.RP.A.1, 1.G.A.3, 2.G.A.3, 3.NF.A.1, 3.NF.A.3c, 3.MD.A.1, 3.MD.C.6, 3.MD.C.5a, 3.MD.C.5b, 3.MD.C.7a, 3.MD.C.7b, 3.G.A.2, HSF-IF.B.4, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP4, CCSS.Math.Practice.MP7, 5.NF.B.3

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, Pre K to 2nd, 6th to 8th, 9th to 12th

Num & Ops Fractions

Mathematical Practices

The Number System

Geometry

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.

Look for and make use of structure.

Attend to precision.

Model with mathematics.

Make sense of problems and persevere in solving them.

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

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

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

Reason with shapes and their attributes.

Develop understanding of fractions as numbers.

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