Teachers assigned to teach STEM in an integrative way may or may not be dealing with deficiencies in their content knowledge. Regardless, asking them to teach STEM in an integrative way without adequate background is likely to create new knowledge gaps and challenges and intensify the challenge of finding qualified teachers for mathematics and science classrooms. Much can be gained in support of the teaching and learning of mathematics through connecting and integrating science, technology, and engineering with mathematics, both in mathematics classes and in STEM activities.

Engineering design, for example, offers an approach that nurtures and supports students' development of their problem-solving abilities, a top priority for mathematics teachers. The design process both reinforces and extends how students think about problems and offers tools that can help students creatively expand their thinking about solving problems of all types—the very types of problems and issues that students are likely to encounter in both their personal and professional lives.

Teaching mathematics well is an important component of a comprehensive STEM program. There is more to mathematics, however, than being part of STEM. The mathematics that students learn in school includes content and thinking that can be used as tools for tackling integrative STEM problems. But it also includes content that might be considered "just math" or might be connected to non-STEM disciplines.

Problems involving mathematical models of finance might or might not connect to science S or engineering E and might or might not involve in-depth uses of technology T.

Likewise, art might be integrated into a mathematics lesson that does not involve either science or engineering. Mathematics goes beyond serving as a tool for science, engineering, and technology to develop content unique to mathematics and apply content in relevant applications outside of STEM fields.

The standards describe a strong, balanced, comprehensive foundation in mathematical knowledge, thinking, and skills that is reflected in mathematics standards from across the states. Essentially every state includes attention to the kind of mathematical thinking, processes, and practices that students should develop as part of their balanced mathematics experience.

Thus, there is strong professional guidance, as well as policy direction, for the mathematics that should be taught at each grade level.

Further, in Principles to Actions: Ensuring Mathematical Success for All , NCTM has developed a set of eight teaching practices that describe the nature of effective mathematics instruction. These practices paint a picture of an interactive classroom in which students are engaged in working through rich tasks—sometimes struggling productively as they tackle challenging problems—with the teacher guiding classroom discussion focused on students' thinking and monitoring student learning throughout the process.

Professional recommendations for the teaching and learning of mathematics include offering students challenging, engaging, and relevant problems consistent with STEM recommendations from the public and private sector.

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## Kentucky Family Math Resources

Teaching mathematics and science well, according to these recommendations, can help students develop creativity, reasoning, and problem-solving skills that align with the goals of STEM programs. Bybee, R. Dugger, W. Larson, M. Math education is STEM education! Honey, G.

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## Mathematics Mastery

National Council of Teachers of Mathematics Principles and standards for school mathematics. Reston, VA: Author. Principles to actions: Ensuring mathematical success for all. Catalyzing change in high school mathematics: Initiating critical conversations. National Research Council A framework for K—12 science education: Practices, crosscutting concepts, and core ideas. National Science Teachers Association The Next Generation Science Standards.

Position Statement. Next generation science standards: For states, by states. Patrick, L. OK Math. Pelesko, J. STEM musings.

## 37 Classroom Rules for Student Success | Prodigy Math Blog

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### How to create classroom rules

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Figuring out interesting problems and solving puzzles makes challenging math fun. Challenging problems and puzzles in Beast Academy foster flexibility and perseverance, helping students develop the skills needed to tackle tough problems in any discipline. Each Beast Academy lesson presents a few basic mathematical concepts, then guides students through applying these concepts in new ways. Students learn by making connections and developing insights that help them understand challenging concepts on a deep level.

More Than Just Arithmetic. The Joy of Problem Solving.