Math Curriculum Planning, Implementation & Support
Mahesh C. Sharma with Bob Stanton
Narrowing the achievement gap among different student populations at schools, reaching state, national and international mathematics standards, and realizing the potential of each child is my mission. This is my goal:
To provide access for children to meaningful mathematics in meaningful ways with lasting impact.
Providing broader access to quality mathematics for all students is a very important goal with many related tasks. With that being said, let’s not forget that only “the most important goals” are truly worth pursuing. It is my firm belief, based on many years of involvement in teacher training and working with both children and adults in many settings and countries, that our Vermont teachers given the right training, well-defined goals, and the right tools are capable of implementing instruction that will help schools realize these important goals and objectives. I am equally confident that Vermont children given the right instruction and supportive environment—can reach these student-centered goals. I have seen that with proper and timely feedback and with a taste of success, children strive to reach high expectations in mathematics. They want to succeed and we know that success is the greatest motivator for any individual, whether an administrator, a teacher or a child. There are the three key players in this mathematics improvement endeavor: the administrators, teachers and children.
In order to achieve the desired outcome, the ‘systems change model’ that LAPDA has developed includes three distinct components: Thoughtful planning; high quality professional development; and the creation and sustaining of a robust feedback loop. The LAPDA approach for working with schools and school districts combines elements of ‘top down’ and ‘bottom up’ strategies for bringing about and sustaining meaningful instructional change in mathematics instruction and learning.
As part of the ‘top down’ strategic efforts, the central emphasis focuses on securing and maintaining the engagement of the school/district leadership team so that they understand and commit to the coherent general principles of mathematics curriculum and instruction improvement for all. Research has clearly demonstrated that a mathematics curriculum that has breadth and depth in content and process results in deeper student understanding of concepts and their connections; emphasizes high levels of mathematical thinking and reasoning; and has high expectations of mastery of meaningful mathematics content as described in Core Mathematics Curriculum (Sharma, 2008).
The central tenet of the ‘top down’ (Phase one) effort is for the leadership team to grapple with the following questions and to come to a deep understanding of these embedded principles:
What is ‘good’ mathematics content? What are the key developmental milestones in mathematics learning and mastery? What are non-negotiable skills at each grade level that each student should master and the teacher should focus on? What are the characteristics of a mathematics way of thinking and reasoning? How is a mathematical way of thinking developed? How do children learn—conceptualize mathematics ideas, acquire fluency in mathematics language, and master skills and procedures of mathematics? What is the definition of ‘knowing’ a mathematics idea, skills or procedure? Are there consistent language and conceptual models for key mathematics content across grade levels? Why do children experience difficulty in learning mathematics? What are the implications of learning problems/disabilities in mathematics? What does an effective and productive mathematics lesson looks like? What should we look for in a mathematics lesson? How do we support teachers and children in learning mathematics?
The ‘bottom up’ strategy embraces these foundational change principles:
The core unit of change in instruction and achievement centers on what occurs at the school house level. The “Taught Curriculum” is what happens in the mathematics classroom each day and that means the teacher is the implementer of the curriculum. If robust and rigorous instruction is to be provided, the principal and teachers must be willing to explore the answers to the following questions:
Do the teachers have the requisite skills to implement the intended curriculum? Do they know the skills that are non-negotiable for each child to master at each grade level? Do they have the ‘pedagogical content knowledge’—content mastery, skills, strategies, models, sequence of content development, the language, the questioning process, and materials, to be able to implement that curriculum which includes the skills, procedures and concepts?
Teachers will need focused professional development and feedback to become adapt in instructional practices that support the following goals:
Emphasis on the key components of mathematics ideas—linguistic, conceptual and procedural; mastery rather than exposure—reinforcement of previously learned skills, mastering new skills appropriate to the grade and age level, and introducing new skills as the ground work for the future using models that will be followed later; rich and diverse language usage and powerful questioning techniques; emphasis on developing reasoning, thinking, and problem solving; multiple entry points, multiple solution paths, and multiple modes of demonstrating competence—a focus on concrete grounding of mathematical ideas through the use of materials progressing from intuitive to concrete to pictorial to abstract to applications to communication of mathematics ideas; a rich flow of communication between students and teachers and among students.
In order for meaningful change to occur and be sustained, there has to be ‘real buy in’ and commitment to the improvement agenda from both the top and the bottom of the implementation pyramid which includes the central office leadership team, the principal of each school, and the teaching staff, including regular and special education teachers.
This translates into the following:
A clear focus on content-based professional development, ongoing teacher support, ongoing curriculum development and/or revision, and alignment of student assessment with instructional practice. It requires high quality professional development that focuses on mathematics content (developmental milestones), pedagogical content knowledge (Didactic instruction, Socratic questioning, and Expert coaching), and provides models of effective teaching (presentation of model lessons that demonstrates the presence of key components of mathematics, levels of knowing and differentiation of instruction).
Our recommended planning and implementation process includes the following:
1. LAPDA staff will conduct a full day planning meeting with our prospective mathematics implementation districts as the first step in the improvement process: (We currently have five implementation districts)
• AM meeting with the district leadership team to include Superintendent, Curriculum Director, Special Ed Director, All Principals, & Math Teacher Leaders
• PM meeting with Curriculum Director, Math Teacher leaders and Math Curriculum Committee/District math team (usually a team that includes several math teachers)
• During Phase One, Mahesh will do a quick walk through in three “typical classrooms” one elementary, one middle and one HS (ninth grade) Algebra class to conduct a “dip stick assessment/gain perspective” on the current state.
• Based on this intake information, Bob & Mahesh will help the district to map their “current state” in mathematics as the first step in their mathematics improvement plan.
2. First orientation workshops targeted for all math teachers (Organized by levels K-5, 6-12)
• Workshop #1: K-5 teachers and all Special Educators that work at this level (Mahesh and Curriculum Coordinator will determine the workshop focus depending on what other training they have already received)
• Workshop #2: Grade 6-12 and Special Educators who work at this level. (Mahesh and Curriculum Coordinator will determine the workshop focus depending on what other training they have already received)
3. First series of “Clinical Rounds” days typically 3 days total (i.e. “job embedded” PD)
• K-5 focus: Mahesh will conduct a public pre-conference with a volunteer host teacher from the target grade level. All teachers at that grade level (and “invited others”) will observe the pre-conference and the demonstration lesson that follows in the host classroom. Mahesh will conclude this “Clinical Rounds” process with a public post conference with the volunteer host teacher and all invited others.
• Grade 6-8 (i.e. Middle school): See Clinical Rounds process outlined above.
• HS (focus will be on 9th grade with Algebra as the content) See Clinical Rounds process outlined above.
4. Follow up planning meeting with Curriculum Coordinator, Math Teacher Leader and Math Curriculum Committee
• This could be a half-day session with another Clinical Rounds session (PM) built into the planning day
• Debrief Year #1
• Plan Year Two PD
5. Develop a process to create and utilize ongoing impact data for analysis and feedback for continuous improvement at the systems and school house level.
• LAPDA will coordinate and facilitate this entire process for all Implementation Districts. As LAPDA Executive Director, Bob will attend the district leadership team meeting and as many other district based meetings as deemed appropriate. Mahesh will be working as a Contracted Consultant though LAPDA.