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## Challenging but Achievable Math for Young Children

Learning trajectories help teachers challenge children at just the right level for their best learning.

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## Five Core Routines for Teaching Mathematics Outside

Integrating mathematics and nature offers students benefits for physical and mental health and enriches their learning.

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## Developing Preservice Teachers’ Understanding of Area Through a Units Intervention

Preservice elementary teachers (PSTs) often enter their teacher preparation programs with procedural and underdeveloped understandings of area measurement and its applications. This is problematic given that area and the area model are used throughout K–Grade 12 to develop flexibility in students’ mathematical understanding and to provide them with a visual interpretation of numerical ideas. This study describes an intervention aimed at bolstering PSTs’ understanding of area and area units with respect to measurement and number and operations. Following the intervention, results indicate that PSTs had both an improved ability to solve area tiling tasks as well as increased flexibility in the strategies they implemented. The results indicate that PSTs, similar to elementary students, develop a conceptual understanding of area from the use of tangible tools and are able to leverage visualizations to make sense of multiplicative structure across different strategies.

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## Bridging Modeling and Environmental Issues

The Great Pacific Garbage Patch activity involves an urgent environmental issue that students can discuss. It engages students in the interpretation of visual data, measurements, units, and the area of regular and irregular figures.

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## Five Rs to Promote Equitable Norms and Culture

As mathematics teachers, we establish several norms, expectations, rules, and daily routines that result in culture building. Hence, in my classes, I decided to center the norms and culture building around five Rs: (1) rigor, (2) relevance, (3) responsiveness, (4) relationship, and (5) responsibility. Using these five Rs provided a norm to engage in our mathematical activities and reflections and established the expectation that everyone would contribute to mathematics teaching and learning (Boyce et al. 2021). Thus, this reflection describes how articles published this year (2021) in Mathematics Teacher: Learning and Teaching PK–12 (MTLT

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## Non-Euclidean Geometry Lesson Promotes Mathematical Reasoning

A two-day lesson on taxicab geometry introduces high school students to a unit on proof.

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## Building Powerful Mathematical Thinkers with dINBs

The Teaching for Robust Understanding framework facilitates online collaborative problem solving with digital interactive notebooks that position all students as doers of mathematics.

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## Empowering Latinx Families to Help Children with Mathematics

An innovative program addresses the digital divide with short, engaging videos modeling mathematic activities sent to families through a free mobile app.

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## Facilitating Student-Created Math Walks

An example of an after-school club activity gives educators some tools and suggestions to implement such an approach in their schools.

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## Puddle Play!

For the Love of Mathematics