Transform Your 6-12 Math Class

Digital Age Tools to Spark Learning

Amanda Thomas

• Publisher: ISTE
• Year: 2019
• eBook ISBN: 9781564848048
• Topic: Education
• Subtopic: Education Technology

Through detailed lessons and examples, discover how to integrate technology in 6-12 math to amplify and enhance your mathematics teaching and drive student learning.

Instead of drill-and-practice apps and worksheets, what if technology enabled exploration of math concepts? Instead of screens for disconnected individual learning, what if technology fostered mathematical discourse and collaboration? Instead of a one-size-fits-all approach to teaching mathematics, what if we used technology to differentiate to meet students’ diverse needs?

Technology has the power and potential to support the teaching and learning of math content at all grade levels, but the presence of technology is insufficient unless it’s paired with effective teaching practices and meaningful content. This book poses and unpacks the above questions and many more, with examples that illustrate how to integrate technology in the 6-12 math classroom, highlighting opportunities to transform mathematics teaching through strategic technology use.

The book:

• Illustrates two contrasting examples in each chapter, including transcripts of sample class conversations, mathematical tasks, illustrations of student work and reflection and discussion prompts.
• Features discussion of research-based ideas relating to the contrasts presented in the chapters, encouraging readers to connect what they learn from the specific cases with the research on these topics.
• Covers a variety of mathematics content areas such as functions and algebraic thinking, geometry and measurement, and data and statistics.
• Provides strategies for implementing the concepts in class, with ideas and examples of tools based not on how they look but what they can do in your mathematics teaching.

Today’s technology offers more possibilities than ever for supporting students in mathematics. This book draws upon the latest research in technology and math education, while providing tools to incorporate effective strategies into curriculum right away.

Audience: 6-12 educators

CONSIDERATIONS AND CHALLENGES FOR INTEGRATING TECHNOLOGY IN MATH TEACHING

How technology is integrated into one’s teaching practices

is connected to the models of teaching and approaches to

learning that are employed.

THIS CHAPTER INCLUDES overviews of relevant considerations and challenges for integrating digital tools into math instruction in Grades 6–12. These considerations and challenges include a working definition for school math as a socially-constructed endeavor, including equity and access to cutting-edge technology, 1:1 technology initiatives, curriculum resources, and personalized learning. The chapter concludes with a discussion of standards that frame technology and math in secondary classrooms.

What Is School Math?

To many, math is a set of numbers, symbols, formulas, and rules. Others might think of school math in terms of subtopics such as arithmetic, geometry, algebra, and statistics. Mathematicians tend to focus on such things as patterns, structure, logic, proof, modeling, and abstractions. Math content standards have defined specific math learning expectations, as well as standards for math practice that articulate mathematical ways of thinking.

This book draws upon the National Research Council’s conception of mathematical proficiency as described in the 2001 book, Adding it Up: Helping Children Learn Mathematics. This vision of learning math consists of five interwoven, interdependent threads: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. Success in school math has often overemphasized procedural fluency; hence the interpretation of math as numbers, symbols, formulas, and rules. Although being fluent with procedures and algorithms is important, so too are understanding the underlying concepts and connections, formulating problems and choosing useful strategies to solve them, justifying and adapting logical reasoning, and approaching math as a subject worth learning. Technology can and should support all strands of math proficiency, but a quick glance at the market for math apps reveals an abundance of drill and practice applications that emphasize procedural fluency. There are far fewer apps that help develop other strands of proficiency. Although a drill and practice app might be easy to pick up and play, many of the apps that support deeper reasoning and conceptual understanding are most valuable in combination with interesting math problems. Considering all strands of math proficiency can help you, the teacher, make more effective technology choices for your students’ learning needs.

Math Learning Is a Socially Constructed Endeavor

When we interpret math proficiency as a combination of procedures, concepts, strategies, reasoning, and disposition, developing math proficiency becomes more complex than numerical problems with multiple-choice answers. Traditional models of teaching math have included teacher-centered classrooms where students sat in rows of desks, listened and watched dutifully as the teacher demonstrated how to carry out a procedure, practiced the procedure with the teacher as a class, and then completed independent practice exercises that mimicked what the teacher modeled. This paradigm of instruction is sometimes referred to as gradual release, or I do, We do, You do, and tends to align with behavioristic transmission of knowledge from teacher to student.

More contemporary models of math teaching center students in their own learning and emphasize procedural fluency in connection with other strands of math proficiency. Rather than asking students to reproduce a demonstration done on the board, teachers monitor and support students as they grapple with challenging math tasks. Facilitating classroom discussions that elicit students’ ideas and reasoning builds shared knowledge of concepts, strategies, and procedures. Partner and group work allow students to communicate mathematically and strengthen individual understanding through peer interactions. This model of teaching often employs a reverse gradual release, or You do, We do, I do, and facilitates classroom interactions that are more consistent with constructivist or sociocultural theories of learning that emphasize active learning in social contexts. How technology is integrated into one’s teaching practices is connected to the models of teaching and approaches to learning that are employed.

Equity and Access to Technology and Math

It is not enough for some, or even most students to learn meaningful math and to have access to educational technology. Patterns of inequities disproportionately impact girls, children with special needs, and students from racially, ethnically, and linguistically diverse backgrounds, depriving them of rich learning opportunities. For example, diverse students tend to be overrepresented in “low” math tracks where they are too often met with low expectations and procedurally focused math that is not built on a foundation of conceptual understanding. Here, too, there are often fewer resources and less-experienced teachers.

Likewise, students often do not have equitable access to technology resources and technology-rich learning activities. Achievement gaps on national and international assessments, patterns of enrollment in remedial college math courses, and interest in STEM majors and careers, provide further evidence of these inequities. When considering how to integrate technology into math teaching and learning, it’s not enough for some students to have access to tools and practices that can transform learning. Instruction should be designed so that each and every student has an opportunity to engage, participate, and develop a positive identity as a math learner.

1:1 Technology Initiatives

Student access to technology devices can be a major barrier for technology integration in math, or any subject. Many schools have been gradually transitioning from dedicated rooms for computer labs to mobile computer/tablet carts, and other options. Recently, we’re seeing more 1:1 devices for each student. In some cases, students are issued their own laptop or tablet for an entire school year, or across multiple years. Other options include 1:1 computers that are kept in classrooms for use when teachers and students choose to use them, which is seemingly more common in elementary classrooms. Bring-your-own device (BYOD) initiatives encourage each student to bring their personal computer, tablet, or smartphone. BYOD devices that differ from student to student introduce new challenges for you, the teacher, who must plan across platforms. Overall, ubiquitous access to devices could expand the possibilities for what you and your students could accomplish.

Curriculum Resources

The widespread availability of online open educational resources (OERs) offers a number of advantages for schools, teachers, and students. Especially for schools already investing in 1:1 technologies, free OERs offer significant cost savings over printed textbooks and curriculum materials. Many OERs are customizable for teachers, so you can sequence, add, or omit online content to meet your instructional goals. For students, an obvious benefit of online curriculum resources is convenience. Instead of remembering and transporting multiple books, one digital device can house a wealth of resources. In addition to providing online resources, digital platforms enable teachers, or groups of teachers, to create their own curriculum resources. Digital instructional materials and OERs could democratize access to the creation, customization, and consumption of curriculum. But it’s important to note that you, the teacher, must also become a careful curator and cautious consumer of online curriculum resources. In math, for example, comprehensive, coherent, standards-aligned, research-based curriculum materials require many years and a wealth of expertise to develop. Furthermore, free resources often do not go through the same vetting processes as traditionally-published materials.

Personalized Learning

The ISTE Standards for Educators specify that to personalize learning experiences, one should “Capitalize on technology’s efficiencies and functionality to meet students’ individual learning needs.” Few would argue the value of this goal, which sounds a lot like using technology to differentiate instruction. A related idea, sometimes used synonymously with “personalized learning,” is “individualized learning.” Individual learning programs allow learners to progress through lessons and complete assessments at their own pace. For more than half a century, individualized learning has been tried in classrooms with and without digital technologies. Some of these early individualized learning efforts were called programmed instruction, a term coined by the well-known behaviorist, B.F. Skinner. Modern, technology-based individualized instruction programs may include adaptive assessment, multimedia content, and voluminous data points. One must question whether or not they are substantively different from programmed instruction. When personalized learning manifests as programmed instruction, teachers must grapple with managing dozens of students, each working on different material at different times, and subject matter becomes reduced to a series of skills-based inputs and outputs. This is hardly the conceptually rich, inquiry-based, authentic learning that you wish to promote. On the other hand, you can and should use technology to create, adapt, and personalize learning experiences in ways that meet students’ diverse needs and identities.

Cutting-Edge Technologies

Coding tools, robots, drones, AI, 3D printers: new technologies present new opportunities! Embracing cutting-edge tools can be exciting and valuable for both you and your students. As some early adopters and innovative educators jump at the chance to incorporate the latest technologies, many have wrestled with how new tools could fit in with existing practices, curriculum, and standards. In addition to practical constraints of time, planning, and access to cutting-edge devices, other factors that impact teaching with new technologies include beliefs, knowledge, and attitudes about technology. Additional variables include subject matter and teaching methodologies. To realize the potential of innovative technologies for teaching and learning math, support is required when first learning how to incorporate new tools in combination with effective teaching practices.

Standards for Technology and Math

Technology integration and math teaching are guided and influenced by a variety of standards. The ISTE Standards for Students, Educators, Education Leaders, and Coaches (iste.org/standards) provide a framework for digital age learning across all disciplines. In math, the Common Core State Standards for Mathematics (corestandards.org/Math) have been adopted in 47 U.S. states and territories since 2010. In 2014, the National Council of Teachers of Mathematics (NCTM) released Principles to Actions: Ensuring Mathematical Success for All. These cross-cutting principles and effective teaching practices are helpful for implementing rigorous math standards (nctm.org/PtA). The Standards for Preparing Teachers of Mathematics (amte.net/standards), released in 2017 by the Association of Mathematics Teacher Educators (AMTE), descr...

Table of contents

• Cover
• Title Page
• Copyright
• About ISTE
• About the Author
• Acknowledgments
• Dedication
• Contents
• INTRODUCTION
• 1 CONSIDERATIONS AND CHALLENGES FOR INTEGRATING TECHNOLOGY IN MATH TEACHING
• 2 MOVING FROM GIMMICKS TO TOOLS FOR TEACHING RICH MATH
• 3 MOVING FROM INDIVIDUALIZED INSTRUCTION TO TECHNOLOGY FOR COLLABORATIVE LEARNING
• MOVING FROM ASSESSING WHAT STUDENTS KNOW TO ELICITING HOW STUDENTS UNDERSTAND
• 5 MOVING FROM TEACHER-CENTERED TO STUDENT-CENTERED INSTRUCTION
• 6 MOVING FROM TECHNOLOGY FOR ITS OWN SAKE TO TECHNOLOGY FOR RICH MATH LEARNING
• 7 A TOOL FOR INTEGRATING TECHNOLOGY IN YOUR MATH CLASSROOM
• REFERENCES
• ISTE STANDARDS
• INDEX