Instructional Design and Pacing Recommendations

It’s exciting and challenging to implement a new curriculum!  Our team has intentionally designed and customized every component of the Carnegie Learning's Texas Math Solution to support high quality mathematics instruction in grades 6-12 across the state of Texas.

With implementing a fully blended curriculum for the first time, many districts grapple with pacing decisions. This article provides insight into how you can prioritize key program components and fundamental mathematics concepts while simultaneously preserving the instructional design of the Texas Math Solution to give your students the most impactful learning experiences possible.

Instructional Design

What are the foundational instructional design principles embedded throughout the Texas Math Solution?

The Texas Math Solution has been strongly influenced by scientific research on the learning process and student motivations for academic success. Its guiding principles are active learning, discourse through collaboration, and personalized learning.

• Active Learning: The research makes it clear that students need to actively engage with content in order to benefit from it. Studies show that, as instruction moves along the continuum from entirely passive to fully interactive, learning becomes more robust. All of the Texa Math Solution activities provided for the classroom, and within MATHia, encourage students to be thoughtful about their work, to consider hypotheses and conclusions from different perspectives, and to build a deep understanding of mathematics.

• Discourse through Collaborative Learning: Effective collaboration encourages students to articulate their thinking, resulting in self-explanation. Reviewing other students’ approaches and receiving feedback on your own provides further metacognitive feedback. Collaborative problem-solving encourages an interactive instructional model, and we have looked to research to provide practical guidance for making collaboration work. The collaborative tasks within each lesson are designed to promote active dialogue centered on structured activities. 

• Personalized Learning:  One of the ways to build intrinsic motivation is to relate tasks to students’ existing interests. Research has proven that problems that capture student interests are more likely to be taken seriously. In the lessons, problems often begin with the students’ intuitive understanding of the world and build to an abstract concept, rather than the other way around. In MATHia, step-by-step examples guide students through sample problems, describing each step, rephrasing or redirecting questions, and honing in on the parts of the problem that may prove difficult.

Carnegie Learning’s instructional approach is a culmination of the collective knowledge of our researchers, instructional designers, cognitive learning scientists, and master practitioners. It’s based on both a scientific understanding of how people learn and a real-world understanding of how to apply that science to mathematics instructional materials. At its core, our instructional approach is based on three simple, key components:

• Engage: Activate student thinking by tapping into prior knowledge and real-world experiences. Provide an introduction that generates curiosity and plants the seeds for deeper learning.

• Develop: Build a deep understanding of mathematics through a variety of activities— real-world problems, sorting activities, worked examples, and peer analysis— in an environment where collaboration, conversations, and questioning are routine practices.

• Demonstrate: Reflect on and evaluate what was learned. Ongoing formative assessment underlies the entire learning experience, driving real-time adjustments, next steps, insights, and measurements.

What are the key program components in the Texas Math Solution? 

There is significant research on the benefits of learning collaboratively and, at the same time, individual practice is necessary for students to become fluent and automatic in a skill. A balance of these two approaches provides students with the opportunity to develop a deep conceptual understanding through collaboration with their peers, while demonstrating their understanding individually.

• Learning Together: Students learn together not only to develop math skills, but to learn how to collaborate, create, communicate and problem-solve. Our classroom activities emphasize active learning and making sense of the mathematics, and we ask deep questions that require students to thoroughly understand the material.

• Learning Individually: Through MATHia, students receive 1-to-1 adaptive math coaching, providing a personalized learning path and ongoing formative assessment. Students are not intended to learn individually in isolation without communicating with others. The idea is that learning is individualized for each student based on their performance. Even though students may start the same course together and follow the same sequence of content, they will have individualized pathways in terms of time, pace, number of questions, hints provided and performance.

Pacing Recommendations

When implementing a complete curriculum for the first time and need support in further customizing to fit the constraints of our district. Frequently asked questions include: 

How do we balance a full year of instructional materials with the reality of our school year calendar?

Planning is essential!  The Texas Math Solution is a complete curriculum, providing course materials for ALL users, therefore, the core content is scaffolded, on grade-level, and allows for extension. Our Texas-dedicated content development team was intentional in determining pacing for each lesson within the scope of a full 180-day school year in order to maintain a balance of Learning Together (textbook/ digital lessons) and Learning Individually (MATHia). 

When implementing the Texas Math Solution within the confines of your district’s school year, you will likely need to make additional pacing decisions. We recommend focusing your modifications at the lesson level to ensure complete coverage of the TEKS throughout the school year. For a variety of reasons (shortened school calendar, extended out-of-school time, missed instructional minutes each day), it may be difficult to do every problem on every page of every lesson, therefore thoughtful and intentional lesson planning is essential. 

The Texas Math Solution includes a full set of customized instructional materials, and facilitation notes, but does not provide scripts or detailed lesson plans for teachers. Teachers still should be planning with their students in mind, because they know them best. 

1. Teach with the end in mind. Understand the Big Picture of the course first, lay out the modules on a year-long calendar, then narrow in your focus to understand the topics within a module. Finally, dive into a topic to plan each lesson. 

• Texas Math Solution Course Overviews.
• Budgeting Your Year

2. Do the MATH! It is essential that you understand how the math develops within a topic before you start teaching the topic. Looking at each lesson in isolation, or day-by-day, often results in over-teaching a lesson and missing out on opportunities to make connections to prior or future learning that will support students as you move forward. Lessons within the Texas Math Solution are intentionally sequenced within each topic to build students’ understanding of the mathematics throughout the entire topic.

• Topic Internalization Process

3. Use the Lesson Internalization Process and study the TEKS to understand what students must know and be able to do and, when planning for each lesson, carefully consider the pacing. If a lesson states 2 days for pacing, plan for how you will teach the content in those 2 days even if it means you might have to cut some questions here and there to make it work. If you know you must take longer than the allotted 2 days, then understand that means you will have to give up that extra day from somewhere else in your year-long plan. Also, use MATHia data to understand your class progress and position in the course sequence. It is okay for students in MATHia to be ahead, right on pace or behind the content of the Learning Together lessons. But if a majority of your class is ahead of the content, can you shorten the pace of the lesson? If a large majority is far behind the current lesson content and they have been using MATHia consistently, should you slow down and address key concepts shown as unmastered by the majority of the class before moving on?

• Lesson Internalization Process 
• Prioritize activities that introduce key terms and have worked examples, generally those are essential concepts that should be focused on regardless of time limitations. 
• As a lesson progresses, and for longer lessons (3+ activities), you will notice some activities are just additional practice or application or are meant for extension. When looking to find additional instructional time, consider whether these activities are “nice to haves” but not “must haves” for some or all of your students. Can you assign parts of these activities to different student groups, or allow students to choose from a selection of questions or activities? 
• Quick Tips for Pacing 

4. Remember that MATHia helps students master the content at their own pace.

• Review the MATHia table of contents for your course(s) to identify the mathematics concepts that students will continue to focus on in their Learning Individually time. Continue moving forward with your instructional plan for the year, knowing that students will engage again with content in MATHia. 
• MATHia Table of Contents 

How do we teach everything without cutting standards and without cutting MATHia? 

1. Study the TEKS and prioritize key mathematics concepts as you plan. 

2. Layout topic pacing guides on a calendar to understand the yearly plan.

3. Determine where time is needed. 

4. Do not waste instructional time. If you take extra days on something, then revisit your plan and adjust based on taking extra days. You will not have time to have 1 full review day before each assessment and 1 full day to review assessment data and do corrections following each assessment. If you do this for every topic assessment, including mid-topic assessments, that would be on average an additional 36 days!

5. Trust that MATHia, when used consistently, allows students to master  skills at their own pace. Teachers should monitor student MATHia usage and progression and make connections between the concepts/skills they are learning in the text with MATHia.

How can ESC, district, and school leaders support teachers with making year-long pacing decisions?

The most important thing you can do as a district or school leader is provide time for your teachers to plan together. In the same way that collaborative learning is impactful for students, collaborative planning for teachers provides additional insights and clarity on key concepts, supports aligning on pacing “must-haves” versus “nice-to-haves,” and holds teachers accountable for moving through their year-long plans. 

• How can you provide common time for grade-level teacher cohorts to plan together throughout the year?
• Are teachers meeting weekly on campus? 
• Is it possible for teachers to meet once each grading period as a district or regional cohort with the support of math coaches/specialists or lead teachers? 

What are important considerations for teachers as they make day-to-day pacing decisions?

As you do the math and grapple with the most important concepts in each topic, you will notice that we generally begin with a more visual/concrete approach before moving to a more symbolic/abstract approach. As you prioritize content, we encourage you not to cut the visual/concrete in favor of jumping to the algorithms, shortcuts, or more abstract thinking only. This leads to learning misconceptions and, research states that, students who confuse concepts or rules do not have solid conceptual understandings to fall back on. Invest your time in building a strong foundation of conceptual understanding first so that your students can later make sense of the mathematics as they learn more abstract concepts.

Webinar Recording

Carnegie Learning hosted a Texas Math Solution webinar on Instructional Design & Pacing Recommendations. Watch Kasey Bratcher (Senior Vice President of Professional Learning), Sami Briceño (Senior Custom Publishing Content Lead), and  Julie Stowell-Moss (Manager of School Partnerships in Texas) as they discuss the instructional design of the Texas Math Solution and answer Texas educators' questions about pacing!