Rigor in the 6–12 Math and Science Classroom

A Teacher Toolkit

Barbara R. Blackburn, Abbigail Armstrong

• Publisher: Routledge
• Year: 2018
• ISBN:
  9781351708593
• Edition: 1
• Topic: Education
• Subtopic: Education General

Learn how to incorporate rigorous activities in your math or science classroom and help students reach higher levels of learning. Expert educators and consultants Barbara R. Blackburn and Abbigail Armstrong offer a practical framework for understanding rigor and provide specialized examples for middle and high school math and science teachers. Topics covered include:

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• Creating a rigorous environment

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• High expectations

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• Support and scaffolding

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• Demonstration of learning

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• Assessing student progress

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• Collaborating with colleagues

The book comes with classroom-ready tools, offered in the book and as free eResources on our website at www.routledge.com/9781138302716.

1

Introduction

Rigor has been an area of increasing focus in education. However, when you talk with teachers and leaders, everyone seems to have a different understanding of what rigor means, especially what it looks like in the classroom. In this chapter, we’ll look at why rigor is important, the misconceptions related to rigor and a clear definition of rigor.

The Call for Rigor

In 1983, the National Commission on Excellence in Education released its landmark report A Nation at Risk. It painted a clear picture: test scores were declining, lower standards resulted in American schools that were not competitive with schools from other countries and students were leaving high school ill-prepared for the demands of the workforce. “Our nation is at risk … The educational foundations of our society are presently being eroded by a rising tide of mediocrity that threatens our very future as a nation and a people.” More than 30 years later, similar criticisms are leveled at today’s schools.

New Calls for Rigor

Since A Nation at Risk was released, the call for more rigor has only increased. The Condition of College and Career Readiness (2011), a thorough report from the ACT, has reinforced the lack of preparedness by high school graduates for college and for the workforce. In 2010, the Common Core State Standards (www.corestandards.org) were created to increase the level of rigor in schools. Other recently revised state standards similarly reinforced the need. Rigor is at the center of these standards, and much of the push for new standards came from a concern about the lack of rigor in many schools today, as well as the need to prepare students for college and careers.

Despite these efforts, results indicate a further decline in the progress of American students compared to that of other nations.

Most recently (2017), the Pew Research Center released information that the academic achievement of students in the United States lags that of students in many other countries. As they point out, “Recently released data from international math and science assessments indicate that U.S. students continue to rank around the middle of the pack, and behind many other advanced industrial nations” (www.pewresearch.org/fact-tank/2017/02/15/u-s-students-internationally-math-science/).

Scores on the Program for International Student Assessment (PISA)
Subject	Ranking	Score Compared to Highest Score
Math	38 out of 71	470 compared to 564
Science	24 out of 71	496 compared to 556

Source: www.pewresearch.org/fact-tank/2017/02/15/u-s-students-internationally-math-science/

Based on data from the 2015 Trends in International Mathematics and Science Study (TIMSS), students in the United States have shown improvement in mathematics and science scores from 1995 to 2015. The most significant gains occurred with students who were in the 75th (High) and 90th percentiles (Advanced). These students consistently scored about the national benchmark averages. However, students who scored in the 25th (intermediate) and 10th (low) percentiles scored significantly lower than the average internationally. Only 37% of eighth graders have moved beyond basic mathematics knowledge facts or performing tasks beyond the low application level. The United States ranked tenth in international comparisons for mathematics.

The data is slightly improved for science scores. 49% of eighth-grade students scored at the intermediate and low levels of science benchmarks, which means they had basic knowledge of the sciences and could apply that knowledge but had not moved past communicating that knowledge in abstract situations. However, the United States ranked eleventh in international comparisons.

Percentage of Eighth-Grade Students Meeting TIMSS Benchmarks in 2015
Advanced	High	Intermediate	Low
Students can apply and reason in a variety of problem situations, solve linear equations and make generalizations.	Students can apply their understanding and knowledge in a variety of relatively complex situations.	Students can apply basic mathematics knowledge in straightforward situations.	Students can apply basic mathematics knowledge in straightforward situations.
10%	37%	70%	91%

TIMSS Science Data (2015)
Advanced	High	Intermediate	Low
Students communicate understanding of complex concepts related to biology, chemistry, physics and Earth science in practical, abstract and experimental contexts.	Students apply and communicate understanding of concepts from biology, chemistry, physics and Earth sciences in everyday and abstract situations.	Students demonstrate and apply their knowledge of biology, chemistry, physics and Earth science in various contexts.	Students show some basic knowledge of biology, chemistry, physics and Earth science.
16%	51%	81%	95%

Source: https://nces.ed.gov/timss/

Key Shifts in Standards

The Office of Vocational and Adult Education (OVAE) wanted to create a stronger link between adult education, postsecondary education and work. To do so, they evaluated the Common Core State Standards, which had been created based on a broad range of research and with wide input from stakeholders. Then they determined which of those essential skills were most relevant for post–high school plans. Finally, they shared the results in Promoting College and Career Ready Standards in Adult Basic Education. They noted three key shifts related to mathematical thinking.

Mathematics
Delving Deeply Into the Key Processes and Ideas Upon Which Mathematical Thinking Relies
Shift	Explanation
Focus: Focusing strongly where the standards focus	Focusing deeply on the major work of each level will allow students to secure the mathematical foundations, conceptual understanding, procedural skill and fluency and ability to apply the math they have learned to solve all kinds of problems—inside and outside the math classroom.
Coherence: Designing learning around coherent progressions level to level	Create coherent progressions in the content within and across levels so that students can build new understanding on previous foundations. That way, instructors can count on students having conceptual understanding of core content.
Rigor: Pursuing conceptual understanding, procedural skill and fluency and application—all with equal intensity	Conceptual understanding of key concepts, procedural skill and fluency and rigorous application of mathematics in real-world contexts.

Next Generation Science Standards

Similarly, there are concerns in science. The Next Generation Science Standards, written by forty members from the group of twenty-six lead state partners, are based on the National Research Council’s Framework for K–12 Science Education. The standards were written in response to four concerns.

Four Concerns

• 1. Reduction of the United States’ competitive economic edge
• 2. Lagging achievement of U.S. students
• 3. Essential preparation for all careers in the modern workforce
• 4. Scientific and technological literacy for an educated society

The standards reflect seven shifts from earlier standards. Each of these reflects an increase in rigor.

Shifts to Increase Rigor

1. K–12 science education should reflect the interconnected nature of science as it is practiced and experienced in the real world.
2. The Next Generation Science Standards are student performance expectations—NOT curriculum.
3. The science concepts in the NGSS build coherently from K–12.
4. The NGSS focus on deeper understanding of content as well as application of content.
5. Science and engineering are integrated in the NGSS from K–12.
6. The NGSS are designed to prepare students for college, career and citizenship.
7. The NGSS and Common Core State Standards (English language arts and mathematics) are aligned.

Source: www.nextgenscience.org/sites/default/files/Appendix%20A%20-%204.11.13%20Conceptual%20Shifts%20in%20the%20Next%20Generation%20Science%20Standards.pdf

Myths About Rigor

Now that we have discussed why rigor is important in the math and science classroom, let’s look at misconceptions...

Table of contents

• Cover
• Half Title
• Series
• Title
• Copyright
• Dedication
• Contents
• eResources
• Meet the Authors
• Acknowledgments
• Preface
• 1 Introduction
• 2 Creating a Rigorous Environment
• 3 Expectations
• 4 Support and Scaffolding
• 5 Demonstration of Learning
• 6 Assessment
• 7 Collaborating to Improve Rigor
• Bibliography