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## Danger! Animals in the Mathematics Classroom

In our attempts to make a concept easier, we may hinder student learning.

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## Emphasizing the M in STEAM activities

Modifications to a first- and second-grade STEAM activity, Elephant Toothpaste, highlight ways to emphasize mathematical thinking by running multiple experiments, posing mathematical questions, and having students make both qualitative and quantitative observations. Contributors to the iSTEM department share ideas and activities that stimulate student interest in the integrated fields of science, technology, engineering, and mathematics (STEM) in K–grade 5 classrooms.

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## Investigating a Super-Bear

Three inquiry-based tasks highlight the planning, classroom discourse, positive results, and growth in one class's journey.

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## Problems

A monthly set of problems targets a variety of ability levels.

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## Threatened to extinction

Hundreds of species of animals around the world are losing their habitats and food supplies, are facing extinction, or have been hunted or otherwise negatively influenced by humans. Students learn about some of these animals and explore multiple solution strategies as they solve this month's problems. Math by the Month features collections of short activities focused on a monthly theme. These articles aim for an inquiry or problem-solving orientation that includes four activities each for grade bands K–2, 3–4, and 5–6.

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## LEGOs: Linking Units, Operations, and Area

Use those multicolored linking bricks to help students connect measurement with an understanding of number and operations as well as fractions.

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## Problems

A monthly set of problems is aimed at a variety of ability levels.

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## A Math Field Day: Embed Content with Play

Can you remember your typical elementary school field day? In this article, we provide details on hosting a mathematics field day, focused on embedding rich mathematics into authentic fun-filled field day experiences.

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## Problems

A monthly set of problems is aimed at a variety of ability levels.

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## Surveying Middle-Grades Teachers' Reasoning About Fraction Arithmetic in Terms of Measured Quantities

We report a novel survey that narrows the gap between information about teachers' knowledge of fraction arithmetic provided, on the one hand, by measures practical to administer at scale and, on the other, by close analysis of moment-to-moment cognition. In particular, the survey measured components that would support reasoning directly with measured quantities, not by executing computational algorithms, to solve problems. These components—each of which was grounded in past research—were attention to referent units, partitioning and iterating, appropriateness, and reversibility. A second part of the survey asked about teachers' professional preparation and history. We administered the survey to a national sample of in-service middle-grades mathematics teachers in the United States and received responses from 990 of those teachers. We analyzed responses to items in the first part of the survey using the log-linear diagnostic classification model to estimate each teacher's profile of strengths and weaknesses with respect to the four components of reasoning. We report on the diversity of profiles that we found and on relationships between those profiles and various aspects of teachers' professional preparation and history. Our results provide insight into teachers' knowledge resources for enacting standards-based instruction in fraction arithmetic and an example of new possibilities for mathematics education research afforded by recent advances in psychometric modeling.