The "Next Generation Science Standards" ("NGSS") emphasize integrating engineering design into the science classroom (NGSS Lead States 2013). Inventing is an authentic and relevant classroom approach, regardless of content area, located at one end of a design continuum opposite from routine problem solving. Invention, at the…

The COVID-19 pandemic has led to an urgent need for engaging computational alternatives to traditional laboratory exercises. Here we introduce a customizable and flexible workflow, designed with the SARS CoV-2 virus that causes COVID-19 in mind, as a means of reinforcing fundamental biology concepts using bioinformatics approaches. This workflow…

Diagnostic labels for children with primary, or otherwise unexplained, language disorders range across settings and within the scientific literature. Among other problems, this lack of agreement creates difficulty with the successful employment of evidence-based practice. This article reviews the evolving terminology and addresses issues of…

Members of a third-grade class were involved in a heated discussion. They were using a fixed number of links to create fences for toy cows. The children could change the shape of the field produced by the links, but they could not add any links or take any away. Understanding the relationship between perimeter and area is a difficult concept for…

Students often have the misconception that mathematics involves reading the problem, staring at the page, and then writing down an answer. With more than twenty years of experience working with students in eighth-grade math through college calculus, the author has been increasingly interested in how she can foster problem-solving skills in her…

This article describes how fifth grade students participated in a place-based environmental education initiative in West Michigan that supports teachers who want to involve their students in citizen science by protecting local water resources. Every year, Groundswell works with about 100 teachers at 30 schools to engage students in citizen science…

Perovskite solar cells have garnered exponential research interest due to their facile fabrication, solution processability, and low cost. However, there have been limited efforts to integrate this class of materials into the undergraduate laboratory curriculum. Therefore, we designed an integrated laboratory experiment in our upper-division…

We describe three activities that help undergraduates (pre-service teachers) to develop scientific vocabulary on measurable attributes and units of measurement. Measurable attributes are important features in understanding a word problem and solving the problem. These activities help students comprehend word problems better by identifying…

Although traditional textbooks may not guide students through explorations or encourage group work, as many standards-based curricula do, virtually all textbooks contain mathematically accurate information and problems that, with adjustment, can be leveraged to support mathematical curiosity, reasoning, and discussion. Teachers who recognize rich…

In this article, the authors engage middle-grades students in a series of tasks to develop the mathematical idea of equal versus equivalent, culminating in a gerrymandering task with social, political, economic, and educational implications. The primary mathematical goals of this exploration were to involve students in solving real-world problems…

Rich mathematical modeling activities are crucial to giving students agency and making mathematics meaningful. Proportional reasoning and transitional algebraic reasoning are the primary topics in the prealgebra curriculum, so a need exists for meaningful modeling activities using proportional reasoning in addition to geometric modeling. In…

Gap reasoning is an inappropriate strategy for comparing fractions. In this article, Patrick Sullivan and Joann Barnett look at the persistence of this misconception amongst students and the insights teachers can draw about students' reasoning.

Differentiating instruction can be difficult, however, when higher performing students yearn to be stretched and lower performing students benefit from scaffolded support. One way to meet these students' learning needs and everyone in-between is to embrace the notion of novel exploration in support of critical school mathematics concepts. Novelty…

Working with language-independent logic structures can help students develop both inductive and deductive reasoning skills. The Japanese publisher Nikoli (with resources available both in print and online) produces a treasure trove of language-independent logic puzzles. The Nikoli print resources are mostly in Japanese, creating the extra…

The task shared in this article provides geometry students with opportunities to recall and use basic geometry vocabulary, extend their knowledge of area relationships, and create area formulas. It is characterized by reasoning and sense making (NCTM 2009) and the "Construct viable arguments and critique the reasoning of others"…