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SummerUpRole of the Instructional StaffDr. Kimberly Samaniego
Balancing Conceptual and Procedural Knowledge
Math is unique among subjects: it builds on itself
When students do not understand a key concept early on, they cannot apply it with precision years later
UCSD math professors site lack of conceptual understanding as an obstacle for students seeking STEM degrees and/or careers
Math is the “Achilles’ Heel”
The Problem with Teaching Procedures without Conceptual Understanding As kids move along the pipeline...early
leaks turn into gushers
Often the problem begins in earlier grades (3-5) with fractions, ratios, and proportions
Leaks in the Math Pipeline K-14
Lack of support for difficult transition from concrete to abstract reasoning leads to over-reliance on procedural teaching
Surviving students lack options as they struggle with heavy concepts & procedures in Algebra 2…
The struggle continues resulting in low math placement into college math
3-5 6-8 9-10
11-12 College
Students & teachers struggle with fractions/ratios and proportions
The Myth of the Flat Curriculum
Topics-based instruction teaching procedures
Many curricula are created for ease of coverage
Not all topics are weighted equally
Not all ordering is aligned to promote conceptual development
“the most important things that every student needs to know”
Define the “most important things that every student needs to know to be successful in the next level”
Give these “things” a name like the “Big 10”
Create exit level assessments around the “Big 10” (skills for skills tests)
Organize instructional activities around the “Big 10”
Reasoning and Sense Making
Reasoning and sense making must become a part of the fabric of the high school mathematics classroom” (NCTM, 2009, p.14).
Two key changes in practice must occur:
1.Provide students with opportunities to engage in solving worthwhile mathematical tasks (cognitively demanding or high-level)
2.Support students’ engagement with such tasks without taking over the thinking for them
(Peg Smith, University of Pittsburg)
Task Development
Identify a mathematical task that is aligned with the lesson goals
Design tasks that lay a conceptual foundation which later builds to procedural development for mastery of the skill
Make sure the task is rich enough to support discussion, promote reasoning, and provide opportunities for students to show their thinking
(a cognitively challenging mathematical task)
Use Standards for Mathematical Practice as a guide
ActivityWork with your table-mates to
collaboratively define the “most important things that every student needs to know to be successful in the next level”
Use the SCOUT course content outline to guide your thinking
Use the Algebra II Overview from CCSS framework
Differentiated Instruction
Recognize that all students have prior experiences (not blank slates)
Make connections between what students know and tease out what they do not know or have misconceptions about (never assume that they know nothing)
Use MDTP data to define whole class strengths and weaknesses to assist in organizing the course topics (pre-teaching, re-teaching, tasks)
Ideas for Differentiating Instruction
Use MDTP data to determine small group instruction for deeper teaching and acceleration
Create individualized learning plans for each student
Create monitoring strategies and formative assessments to inform student progress (competency-based)
Revise learning plans daily based on student understanding and demonstrated mastery of the content
Utilization of Instructional Staff Engage in a conversation prior to the start of
the course to create a common understanding about:◦ The goals of the course◦ How students are assessed◦ Everyone’s instructional roles
Meet regularly to discuss instructional plans and duties for the day ◦ Whole class instruction – what are the instructional
aids doing during this time?◦ Small group instruction – who, what, and when?◦ 1-1 instruction – who, what, and when?
Meet to discuss the strategies for instruction
