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Elliott, Rebekah; Brunner, Megan; Stoddard, Elyssa; White, Jenny – Mathematics Teacher: Learning and Teaching PK-12, 2022

Mathematics teachers are increasingly being called to integrate mathematical modeling into their course sequences and curriculum (NCTM 2018; NGA Center and CCSSO 2010). Mathematical modeling is a dynamic cycle calling teachers to engage in complex instructional work that advances students' mathematical knowledge and reasoning. The modeling cycle…

Descriptors: Mathematical Models, Mathematics Instruction, Instructional Design, Mathematics Skills

Huang, WenYen – Mathematics Teacher: Learning and Teaching PK-12, 2022

The study of mathematics is often described as the science of patterns (Resnik 1981), and the cognitive tasks involving the search, recognition, and assessment of patterns are fundamental to learning mathematics. Patterning activities lead students to a better understanding of dependent relations among representations, create a transparent way for…

Descriptors: Mathematics Education, Mathematics Skills, Pattern Recognition, Mathematics Activities

Lucenta, Amy; Kelemanik, Grace – Mathematics Teacher: Learning and Teaching PK-12, 2022

Students often look to the standard algorithm, which requires rewriting the task, regrouping tens to create enough ones to subtract, and other opportunities to make errors. However, when the authors apply structural thinking, the resultant strategy is an efficient and elegant shortcut and even brings a positive connotation to the word…

Descriptors: Mathematics Education, Mathematics Instruction, Teaching Methods, Computation

White, Dorothy Y. – Mathematics Teacher: Learning and Teaching PK-12, 2022

Every student has mathematical strengths beyond knowing basic facts, solving problems quickly, or showing work clearly. In this article, the author presents Smiles as an "on-ramp" task that supports students working together by unveiling and leveraging mathematical strengths. Nielsen describes on-ramp mathematics tasks as scaffolds that…

Descriptors: Mathematics Skills, Cooperative Learning, Problem Solving, Puzzles

Jones, Stacy R.; Gomez Marchant, Carlos Nicolas – Mathematics Teacher: Learning and Teaching PK-12, 2022

In this article, the authors present a composite counter-story of seemingly innocent encounters between a teacher and Raza learners for educators to grapple with color-blind and race-neutral practices when working with Raza learners. The authors offer entry points and questions to reflect on the intersection of race, language, and learning…

Descriptors: Story Telling, Language Usage, Spanish Speaking, Educational Practices

Sigmon, Miranda L.; Ming, Kavin; Herring, Daniel – Mathematics Teacher: Learning and Teaching PK-12, 2022

Disciplinary literacy involves reading, writing, speaking, listening, and thinking in the context of specific disciplines. Word sorts are a way for students to acquire and examine vital features of mathematics vocabulary as they process and organize new content-specific ideas. Addressing disciplinary literacy (i.e., literacy skills specific to…

Descriptors: Discussion (Teaching Technique), Vocabulary, Mathematics Instruction, Academic Language

Wares, Arsalan – Mathematics Teacher: Learning and Teaching PK-12, 2021

Many mathematics teachers and students are familiar with the typical "box problem." In this type of problem, one takes a rectangular (or a square) sheet of paper and cuts out four squares from the four corners of the sheet and then folds the four strips up to form a box. Math problems like this are seen in middle school, high school,…

Descriptors: Mathematics Instruction, Teaching Methods, Manipulative Materials, Mathematical Concepts

Rumack, Aaron M. – Mathematics Teacher: Learning and Teaching PK-12, 2021

Reading mathematics problems can frustrate students to the point of shutting down. Although Pólya's four-step plan is a well-known problem-solving framework, the author's students benefited from a more concrete and detailed approach: chunking the reading. In this article, the author describes an approach to problem solving used with eighth-grade…

Descriptors: Word Problems (Mathematics), Content Area Reading, Cognitive Processes, Problem Solving

Davis, Jon D. – Mathematics Teacher: Learning and Teaching PK-12, 2021

In this article, the author presents a set of design principles that were used to construct and refine a lesson involving the TI-Nspire handheld graphing calculator through multiple enactments in high school algebra classrooms to assist students in constructing a deeper understanding of systems of linear inequalities, a high school algebra content…

Descriptors: Technology Integration, Mathematics Instruction, Algebra, Instructional Development

Jones, Joshua – Mathematics Teacher: Learning and Teaching PK-12, 2021

Despite the importance of artificial intelligence in our daily lives, it has yet to be integrated into K-12 classrooms in a meaningful way. This article explores a lesson in which geometry students use Euclidean distance to implement a functional machine learning algorithm in Google Sheets™. The assignment requires students to apply the distance…

Descriptors: Geometry, Mathematics Instruction, Artificial Intelligence, Geometric Concepts

Livers, Stefanie D.; Bennett, Victoria Miller – Mathematics Teacher: Learning and Teaching PK-12, 2021

Within a single internet search, thousands of results occur when looking for a lesson or mathematics activity. However, the results are not all of good quality. In this article, the authors present a mathematics lesson planning protocol (MLP[superscript 2]) to help process the search results and offer experiences of teachers using the protocol.…

Descriptors: Mathematics Instruction, Teaching Methods, Lesson Plans, Planning

Dick, Lara K.; McCulloch, Allison W.; Lovett, Jennifer N. – Mathematics Teacher: Learning and Teaching PK-12, 2021

Eliciting and using student thinking (NCTM 2014) is a foundational pedagogical skill that informs the decisions teachers make during instruction. It informs the questions teachers pose, the focus of small-group and whole-class discussions, and even the small adjustments teachers make during a well-planned lesson. To use student thinking to…

Descriptors: Mathematics Instruction, Educational Technology, Technology Uses in Education, Thinking Skills

Brand, Sarah; Jung, Hyunyi; Dorlack, Ashley; Gailliot, Samuel – Mathematics Teacher: Learning and Teaching PK-12, 2021

Most children, when presented with the option between two drink items, will choose the one with "more." But what exactly do children consider when they recognize one object as having more than another? Is it the perceived surface area or volume of an object? Depending on children's cognitive development, the aspect of measurement on…

Descriptors: Mathematics Instruction, Mathematical Concepts, Mathematical Models, Grade 6

Manousaridis, Tracy – Mathematics Teacher: Learning and Teaching PK-12, 2021

Students thrive when presented with tasks that are approachable, challenging, and interesting. Remembering to challenge all students is essential, not just those who excel in mathematics; teachers need to open the door to meaningful mathematics for every learner. In this exploration into subtraction patterns, teachers will see how curious young…

Descriptors: Mathematics Instruction, Grade 3, Elementary School Mathematics, Inquiry

Ahrendt, Susan; Monson, Debra; Cramer, Kathleen – Mathematics Teacher: Learning and Teaching PK-12, 2021

In grade 3, students are expected to be able to represent a fraction on a number line by first identifying the interval from 0 to 1 as the unit and by partitioning the unit as needed on the basis of the denominator. This task extends these grade 3 fraction goals stated in the Common Core State Standards for Mathematics (NGA Center and CCSSO 2010)…

Descriptors: Elementary School Mathematics, Mathematics Instruction, Grade 3, Fractions