ACE Mathematics Newsletter
3 - 8 Mathematics | DEC 2018 YEAR 3: VOL. 1
In this Edition:
Mathematics Instructional Block: Aggressively Monitoring
Instructional Resources: 4th Six Weeks Instructional Planning Calendars & 4th Six Weeks Common Assessment Exemplars
Instructional Trends in Mathematics: Teaching Towards Conceptual Understanding
Upcoming PD: Math Team Thursday
Announcements: ACE Website
- Raises the accountability factor in students.
- Teachers are able to receive and provide real-time feedback about errors and misconceptions.
The intent is to check students' independent work to determine whether they are learning what you are teaching.
· Create & implement a monitoring pathway:
o Create a seating chart to monitor students most effectively.
o Monitor higher achievers first then proceed to struggling students.
· Monitor the quality of student work:
o Check answers against your exemplar.
o Track correct and incorrect answers to class questions.
· Pen in Hand: mark up student work as you circulate.
o Use a coding system to affirm correct answers.
Cues students to revise answers, using minimal verbal intervention. (Name the error, ask them to fix it, tell them you will follow up.)
When reviewing the Instructional Planning Calendars, pay close attention to the proposed unpacking of the targeted standards that support teaching using a conceptual trajectory of content development. Note the instructional resources section for suggested strategies, manipulatives, and anchor charts to incorporate into instruction. The links below can be used to access the grade-specific calendars.
4th Six Weeks Common Assessment Exemplars: We have developed 4th Six Weeks Common Assessments Exemplars for your reference. These tools are available on the ACE website under Teacher Portal tab, and are recommended as a framework for specific strategies to be incorporated during instruction as you address those targeted SEs.
Instructional Trends in Mathematics
Teaching Towards Conceptual Understanding
For decades, the major emphasis in school mathematics was on procedural knowledge, or what is nowadays commonly referred to as procedural fluency. Rote learning was the norm, with little attention paid to understanding of mathematical concepts. Rote learning is not the answer in mathematics, especially when students do not understand the mathematics. In recent years, major efforts have been made to focus on what is necessary for students to learn mathematics, what it means for students to be mathematically proficient. To be mathematically proficient, a student must develop:
- Conceptual understanding: comprehension of mathematical concepts, operations, and relations
- Procedural fluency: skills in carrying out procedures flexibly, accurately, efficiently, and appropriately
- Strategic competence: ability to formulate, represent, and solve mathematical problems
- Adaptive reasoning: capacity for logical thought, reflection, explanation, and justification.
Conceptual understanding is at the forefront for students to become mathematically proficient, since it allows students the opportunity to apply and possibly adapt some acquired mathematical ideas to new situations. Students demonstrate conceptual understanding when they provide evidence that they can recognize, label, and generate examples of concepts; use and interrelate models, diagrams, manipulatives, and varied representations of concepts; identify and apply principles; know and apply facts and definitions; compare, contrast, and integrate related concepts and principles; recognize, interpret, and apply the signs, symbols, and terms used to represent concepts. Conceptual understanding reflects a student’s ability to reason in settings involving the careful application of concept definitions, relations, or representations of either.
To assist our students in gaining conceptual understanding of the mathematics they are learning requires a great deal of planning and execution, it involves using our classroom resources (textbook, supplementary materials, and manipulatives) in ways we had not anticipated or thought of before. If we want to achieve superlative results we may need to be open to challenge our way of thinking and be willing to embrace newly developed instructional strategies based on the latest breakthroughs in neurosciences.
At ACE we will learn and support each other as we build our capacity in teaching conceptually. Getting students to use manipulatives to model concepts, and then verbalize their results, assists them in understanding abstract ideas. Getting students to show different representations of the same mathematical situation is important for this type of understanding to take place. Getting students to use prior knowledge to generate new knowledge, and to use that new knowledge to solve problems in unfamiliar situations is also crucial for long-term sustainable conceptual understanding to emerge. This will also sharpen students' complex problem solving skills which ranks 1st as the top-targeted skill by employers by 2020.
Upcoming Professional Development
ACE Website: www.acedallasisd.com
Please visit our revamped Teacher Portal tab on the ACE Website where you will have access to a wide variety of instructional resources and planning tools to create great lessons for our scholars. Instructional Planning Calendars, Common Assessment Exemplars, TEKS Differentiation Tools, Routines, Anchor Charts, and Problem Solving Protocol resources are available for your implementation.