Our Vision of Excellent Math Instruction: ECE (Grades K-2)
In our mathematics classrooms, we strive to build mathematically proficient students prepared to enter 3rd grade with the necessary knowledge and skills
to then meet the demands of college and career and apply mathematics in the real world. In our classrooms:
Students focus on the most important content. Rather than racing to cover as many topics as possible, we slow down and go into depth on the most important math concepts on
students’ path to college and career readiness. Doing so will gives our students the time and space they need to build an enduring understanding of the content we cover.
Students build number sense. We develop students’ understanding of our number system so that they are able to fluidly apply numbers in more complex situations later in their
schooling. We draw connections within and between topics so that students are able to manipulate and compare numbers in various real world situations.
Students learn the hows and whys of math – and apply it to the world around them. We give our students opportunities to discover both how to solve problems and why those
procedures work and reinforce these deeper understandings with lots of practice so that important skills, understanding place value and the relationship between tens and ones,
become second nature. We show our students the power of the math they have learned by giving them challenging, real-world problems that require them to apply their
understandings in a meaningful way.
Students do the thinking. We already know how to think and communicate like a mathematician, and we also know that our students won’t gain these skills if we do the work for
them. We check the ratio of teacher work to student work in each and every lesson and ensure that our students get many more opportunities than we do to grow as mathematicians.
Our students do computations, persevere through challenging questions, and reason quantitatively. We set students up to communicate their ideas, critique others’ reasoning, and
reflect on their approach to problems. We give students ownership for identifying patterns, structures, and repetition in order to find efficient pathways to solutions and make
connections between ideas, and we help students see themselves as problem-finders and problem-solvers capable of posing meaningful questions, making productive inquiries, using
the tools that their disposal and modeling real-world situations with math.
Student Actions
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Spend more time learning the most important content (number sense, counting,
addition and subtraction, place value, measuring length).
Develop a conceptual understanding of key mathematical concepts, including how
topics are connected.
Approach problems from multiple angles to discover how to solve problems and
why those procedures work.
See math as a useful and relevant tool for solving real world problems, not just a set
of mnemonics or memorized procedures.
Do fewer, more challenging problems that require deeper thought and analysis
Persevere in the face of challenging work.
Build confidence and fluency by practicing procedures and computations so that
they are fast and accurate, and apply those skills to real-world problems.
Communicate their thinking and reflect on their approach to problems.
Articulate their mathematical reasoning through explanation and in images (K)
and/or writing (1-2).
Take ownership for identifying patterns, structures, and repetition in order to find
efficient pathways to solutions.
Communicate clearly and precisely about math.
Reflect on their own approach, critique others’ reasoning, and pose mathematical
questions.
Articulate relationships between numbers and explain how this knowledge will help
them in the real world.
Teacher Actions
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Spend more time grappling with numbers and number sense, rather than explicitly teaching
operations, so that students are able to make numerical connections and understand our
number system intuitively.
Spend the vast majority of class time going deep on the most important topics for the grade
level.
Build the foundation for what students will need to know by 3rd grade.
Allow students to discover how to solve problems using multiple approaches and why
mathematical procedures work.
Expose students to mathematical situations before naming them or explicitly teaching them
so that students can self-discover methods to solve.
Assign fewer, more challenging problems worth doing and discussing, with scaffolds that
promote independence.
Reinforce effort and give students strategies to tolerate and overcome frustration.
Provide opportunities to practice carrying out procedures and applying understandings to
real-world problems.
Listen and respond for the right answer and to the thinking that led to students’ responses.
Sequence problems and experiences to set students up to discover patterns, structure, and
repetition in order to help them identify efficient pathways to solutions.
Push students to speak and write precisely about math.
Prompt for reflection, critiques, self-correction and mathematical questions.
Scaffold mathematical development appropriately and in a way that matches the child’s
cognitive development.
Our Vision of Excellent Instruction
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Develop fluency in number sense, math facts, and numerical operations, so that they
are able to meet and exceed expectations for mathematics in late elementary.
What this Looks Like
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Daily Math Meetings that develop students’ fluency in basic skills. These skills can include (includes a mix of K-2 skills):
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Calendar
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Counting
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Identifying numbers
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Basic addition/subtraction
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Place value
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Identifying and comparing shapes
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Measurement
Daily Story Problems that provide real world situations for math computations. These Story Problems should vary in problem type and no procedure or operation should be taught before
students get a chance to grapple with the context of the story first.
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In discourse, students are providing numerically logical arguments for why an answer is correct or incorrect upon first glance. For example, if a student knows that they are trying to
find the difference between two numbers, but the answer is the sum of the given numbers, students should argue that it is incorrect without even computing the answer.
Use of math manipulatives as an option, always.
Meaningful math experiences that relate to students’ everyday lives and allow for a variety of ways to solve problem and arrive at answers and conclusions Integration of math with other
content areas and activities throughout the day
Number sense is a concept that should be cycled through each unit by using performance based assessments like Counting Jar. Counting Jar is an assessment that measures early counting
skills like ordinality, cardinality, organization, 1:1 matching, and grouping.
Each Independent Practice and/or Exit Ticket should have questions for students to explain, in writing, why they believe their answer to be true (1st grade and up). In kindergarten, this can
look like a picture to explain mathematical reasoning, or using other strategies to show the process of their thinking (i.e. labeling a pattern or being metacognitive about the steps taken to
get to a result).
Habits of Discussion used in mathematics to agree with, disagree with, or build on other students’ strategies, and the appropriate vocabulary resources to enforce proper mathematical
vocabulary.
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Students should be able to argue for or against another student’s mathematical reasoning to foster academic discussions around mathematics.
Enduring Understandings posted and discussed in the classroom as “aha” moments arise in the classroom.
Mathematical “conjectures” posed to challenge students’ understanding of what is always “true” in math.
Planning for a debrief portion of a lesson, whether it’s after guided practice and before independent practice, or after independent practice and before the exit ticket, to strategically show
student strategies, and address student misconceptions in the lesson, rather than retroactively addressing misconceptions the next day.
Charting all mathematical debriefs in a neat and student friendly way, and posting them as resources for future lessons.
Teaching mathematical understanding, not methods and procedures. This means that students are able to demonstrate understanding of a mathematical concept in a different context. This
could mean applying it to a real world situation, or presenting the content in a different manner to assess true understanding.
Spiraling the most important content throughout the year to ensure long-term understanding rather than temporary understanding of mathematical concepts.
Use of data and periodic assessments to drive instruction. Assessments should take place every 6-8 weeks and should include multiple questions for each standard taught.
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Anchor instructional units with high-quality performance assessments.
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Our Vision of Excellent Instruction