Introduction
There are four modules in the Introduction to the Revised Mathematics TEKS professional development. Each module is approximately three hours. Each module has three grade bands, each focusing on the TEKS for those grades.
Be sure to download the journal for your grade band below.
Note: Please download the latest version of Adobe Reader, which enables you to type directly into the PDF and save your work.
This is the last of four modules to introduce the revised mathematics TEKS. The four modules are
- Revised Math TEKS (Grades K–8) with Supporting Documents,
- Applying the Mathematical Process Standards,
- Completing the Gap Analysis, and
- Achieving Fluency and Proficiency.
This module reflects focused discussions of mathematics topics within each course.
Definitions
Watch the video and read the Merriam-Webster definitions for the terms below. Use the dictionary definitions to create your own definitions and record them in your journal.
Research Activity
Watch and video and download the research article. Read the research information and consider how it relates to your understanding of computational fluency, mathematical proficiency, and automaticity.
Conceptual Understanding
Watch the video and write your definition of conceptual understanding in your journal.
Watch the video and review the National Research Council definition of conceptual understanding below.
Conceptual understanding refers to an integrated and functional grasp of mathematical ideas. Students with conceptual understanding know more than isolated facts and methods. They understand why a mathematical idea is important and the kinds of contexts in which it is useful. They have organized their knowledge into a coherent whole, which enables them to learn new ideas by connecting those ideas to what they already know.
A significant indicator of conceptual understanding is being able to represent mathematical situations in different ways and knowing how different representations can be useful for different purposes.
Reflection Activity
- How is the National Research Council definition of conceptual fluency similar or different from your own?
- How is conceptual understanding different from mathematical proficiency?
Watch the video for a possible response.
Vertical Learning Progression Activity (Grade Bands)
Watch the video overview of the vertical learning progression activity.
Watch the video for your grade band for additional activity instructions and use the Texas Response to Curriculum Focal Points to complete the Vertical Learning Progression Recording Sheet in your journal.
Developing Mathematical Proficiency
Watch the two videos below and respond to the reflection questions in your journal.
Reflection Activity
- How does pairing a content standard with a process standard allow students to become mathematically proficient?
- Why is it important that the student expectations in the mathematical proficiency column be coupled with the process standards?
After you have finished recording your thoughts in your journal, watch the video below for possible responses.
Student Activities (Grade Bands)
Watch the appropriate video for your grade band, and explore the student activities in your journal.
Consider the following questions:
- How does the concept of addition build vertically?
- What might need to happen instructionally between each activity?
- How do these activities, collectively, help build computational fluency?
- How do these activities lead to student success on the state assessment?
Download the Fluency Activities Focusing on Addition Kindergarten—Grade 7 document to see where the activities you looked at in your journal build from or build to as students progress to grade 8.
Make-a-Ten Methods
How do these ideas build vertically?
Let's start in grades K–2 and look at some possible models of these ideas and how they connect to computational fluency.
Source: Beckmann, S. (2010). RtI for Elementary and Middle School Mathematics [PowerPoint slides]. Retrieved from Education Northwest.
Developing Fluency and Extending Beyond Whole Numbers
Studying basic facts by examining and using relationships among facts allows for "algebraic reasoning" including
- taking apart, working with pieces, and putting back together;
- thinking about the meaning of operations; and
- developing number sense.
How could we take the strategies from the Make-a-Ten methods and extend them beyond whole numbers?
Source: Beckmann, S. (2010). RtI for Elementary and Middle School Mathematics [PowerPoint slides]. Retrieved from Education Northwest.
Drill or Practice?
How do the activities that we just looked at compare with some of the more traditional paper and pencil activities? Look at the example for your grade band below.
Watch the videos, and consider how the provided definitions of drill and practice are reflected in the examples above. Record your thoughts in your journal.
Source: Van De Walle, J. (2004). Elementary and Middle School Mathematics Boston: Pearson
Case Studies
Watch the video instructions for your grade band and review the Case Study student work samples for Student A and Student B in your journal.
Record your observations, and respond to the following questions on the Case Study Recording Sheet in your journal:
- What evidence exists that indicates the student has computational fluency?
- What evidence exists that indicates the student has mathematical proficiency?
- What evidence is missing?
When you have finished, watch the Possible Responses video for your grade band.
What next steps might the teacher take to address computational fluency and mathematical proficiency?
Reflection
How are computational fluency and mathematical proficiency similar? How are they different?
Summarize your observations by completing the Venn diagram in your journal.
Conclusion
Thank you for participating in this module. Please consider continuing your professional development by accessing the other modules in the Introduction to the Revised Mathematics TEKS series.
- Revised Math TEKS (Grades K–8) with Supporting Documents
- Applying the Mathematical Process Standards
- Completing the Gap Analysis
