Background
Curriculum in the area of Mathematics, is probably the most likely to send a shiver up your spine. However, the Math curriculum at our school is probably very unlike what you experienced as a student yourself.
At Our School, we have not adopted a single textbook series or program to meet the needs of our learners in Math. This is partially due to an understanding that students of all levels should be exposed to thinking creatively and flexibly about mathematical concepts and ideas (NCTM, 2000). We seek enriching mathematical opportunities because we know, “Failing to acknowledge and encourage the use of creativity in the classroom reduces mathematics to a set of skills to master and rules to memorize” (Mann, 2009). Therefore, teachers create opportunities for students to demonstrate flexibility of thinking; reasoning & proof; and divergent problem solving strategies.
ADOPTION
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The Math Committee, in partnership with the Director of Teaching and Learning, made the decision to move away from a mass adopted text series five years ago. Prior to this decision, all grade levels in the elementary school were utilized a program called, Everyday Math. There was a gradual shift away from textbooks, which led to a greater need for teaching to the AERO adopted Standards and Benchmarks. It also created a greater need for teachers to have a deep conceptual understanding of each benchmark themselves.
Five years later, teachers are consistently utilizing AERO benchmarks, their understanding of mathematical concepts, and student data to craft rich projects, lessons, and units of study. This also allows teachers to continually, “nurture children’s inborn instinct to question and problem-solve” (Early Math Collaborative, 2014). Thus, valuing inquiry, creativity, and flexibility of thought.
Five years later, teachers are consistently utilizing AERO benchmarks, their understanding of mathematical concepts, and student data to craft rich projects, lessons, and units of study. This also allows teachers to continually, “nurture children’s inborn instinct to question and problem-solve” (Early Math Collaborative, 2014). Thus, valuing inquiry, creativity, and flexibility of thought.
AERO STANDARDS & BENCHMARKS
The AERO Standards and Benchmarks are critical in developing the taught curriculum at Our School. Teachers continually build upon their understanding and application of the strategies, skills, and developmental understandings embedded in each standard and benchmark.
The following is an example of an overarching Standard, and the Benchmarks addressed in each grade level:
The following is an example of an overarching Standard, and the Benchmarks addressed in each grade level:
In this example, we are looking at the standard:
Students will understand and apply numbers, ways of representing numbers, relationships among numbers, and number systems
As you can see, this standard is broken down into benchmarks across several grades, starting in Kindergarten and continuing until grade six. Thus, as a third grade team of teachers sat down to plan their math unit, they would review the benchmark:
Apply models of multiplication (e.g. equal-sized groups, arrays, area models, equal “jumps” on number lines and hundreds chards) and division (e.g. repeated subtraction, partitioning, and sharing) to solve problems
And determine the important skills, concepts, and understandings their third grade learners must have to demonstrate mastery of this benchmark. This involves generating essential questions that students may need to grapple with as the develop this understanding; such as: How can we model our understanding of multiplication and division in different ways? Why do we use many strategies to multiply and divide (Why do we think flexibly?)? And, How can we prove a strategy is effective?
Teachers prepare projects, lessons, engagements and discussions that facilitate the opportunity for students to utilize a variety of tools, resources, models, and strategies to build their knowledge of a given standard & benchmark. Let’s take a closer look at how this might transfer into an elementary classroom.
Students will understand and apply numbers, ways of representing numbers, relationships among numbers, and number systems
As you can see, this standard is broken down into benchmarks across several grades, starting in Kindergarten and continuing until grade six. Thus, as a third grade team of teachers sat down to plan their math unit, they would review the benchmark:
Apply models of multiplication (e.g. equal-sized groups, arrays, area models, equal “jumps” on number lines and hundreds chards) and division (e.g. repeated subtraction, partitioning, and sharing) to solve problems
And determine the important skills, concepts, and understandings their third grade learners must have to demonstrate mastery of this benchmark. This involves generating essential questions that students may need to grapple with as the develop this understanding; such as: How can we model our understanding of multiplication and division in different ways? Why do we use many strategies to multiply and divide (Why do we think flexibly?)? And, How can we prove a strategy is effective?
Teachers prepare projects, lessons, engagements and discussions that facilitate the opportunity for students to utilize a variety of tools, resources, models, and strategies to build their knowledge of a given standard & benchmark. Let’s take a closer look at how this might transfer into an elementary classroom.
A DAY IN THE LIFE
Brian Jones is a grade two teacher, and has been preparing for the start of the Data Analysis & Probability Unit for weeks now. He has reviewed the standards & benchmarks, reflected on the grade level work from the year before, planned with colleagues, and given a pre-assessment to ensure that he is taking into account his students’ prior understanding. Based on this student data, Brian has learned that he can spend less time on the benchmark: Use tables, pictographs, and bar graphs to represent data, as most of his students have already demonstrated mastery of this benchmark. He will work in a small group with the students who do not have this understanding yet, rather than focusing on this concept as a whole class. However, he has also learned that the majority of his learners do not have an understanding of the following benchmark: Interpret data presented in circle, line, and bar graphs and answer questions about the displayed situation. Thus, has has planned more time with this focus accordingly.
Perhaps most importantly, Brian understands that his learners need to connect their understanding to authentic experiences, so Brian will not be making copies of worksheets with zoo animals and sports balls for the students to ask questions about. Brian will be pairing with the Science Coordinator at the school to develop a series of experiments for the students to develop and apply an understanding of Data Analysis and Probability. These experiments will all be centered around the topic, “Creating a School Garden” and the data students collect over the next six weeks will be utilized to make a recommendation about the potential for Our School to create gardens to produce food for school lunches and snacks.
The students will be engaged in real-world problem solving and application of their understanding of Data Analysis. Mr. Jones will be intentional about the mini-lessons he incorporates and the conversations he has with individual students. He will collect student data throughout the unit; including formative assessments to check for understanding of his grade level benchmarks. By the end of the unit, students will not only have a strong understanding of Data Analysis and Probability, they will also connect this understanding to the world around them. At Our School, this is just another example of bringing together relevant, meaningful and challenging curriculum while still allowing for the inquiry, creativity, and passion of our learners.
Perhaps most importantly, Brian understands that his learners need to connect their understanding to authentic experiences, so Brian will not be making copies of worksheets with zoo animals and sports balls for the students to ask questions about. Brian will be pairing with the Science Coordinator at the school to develop a series of experiments for the students to develop and apply an understanding of Data Analysis and Probability. These experiments will all be centered around the topic, “Creating a School Garden” and the data students collect over the next six weeks will be utilized to make a recommendation about the potential for Our School to create gardens to produce food for school lunches and snacks.
The students will be engaged in real-world problem solving and application of their understanding of Data Analysis. Mr. Jones will be intentional about the mini-lessons he incorporates and the conversations he has with individual students. He will collect student data throughout the unit; including formative assessments to check for understanding of his grade level benchmarks. By the end of the unit, students will not only have a strong understanding of Data Analysis and Probability, they will also connect this understanding to the world around them. At Our School, this is just another example of bringing together relevant, meaningful and challenging curriculum while still allowing for the inquiry, creativity, and passion of our learners.
references
Early Math Collaborative (2014). Big ideas of Early Mathematics. Upper Saddle River, New Jersey: Pearson.
Mann, E. L. (2009). The search for mathematical creativity: Identifying creative potential in middle school students. Creativity Research Journal, 21(4), 338-348.
NCTM- National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston: NCTM.
Mann, E. L. (2009). The search for mathematical creativity: Identifying creative potential in middle school students. Creativity Research Journal, 21(4), 338-348.
NCTM- National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston: NCTM.