Curriculum update
Curriculum update A series from the Head of School
MATH AT FRIENDS SCHOOL Dear Friends’ School parents, This is the second in an occasional series of updates on our curriculum at Friends’ School. These essays are intended to present parents with an overview of why and how we teach what we do, rather than an index of exactly what is taught at each grade. For those details, please ask your child’s classroom teacher for a complete curriculum guide for your child’s grade. This update addresses math at Friends’: our overarching beliefs about math, our philosophy of teaching math at each age, how we differentiate for individual thinkers, and the new math block schedule that we are introducing for grades 2-5 for this 2012-13 school year. Friends’ Beliefs About Math At Friends’ School, children are taught and learn to be confident and competent math thinkers. We begin by providing a variety of concrete, handson experiences to build real number sense that students can later apply to more abstract mathematics. Students work individually, as well as in cooperative groups, to discuss and reason mathematically while becoming flexible and creative in their approach to problem solving. The following principles are part of what we believe about math and how they guide our teaching practice day to day. • We present meaningful mathematical tasks, which engage and challenge children’s thinking and bring about better math understanding.
• We give attention and respect to the range of ways that students learn from auditory and visual to more kinesthetic (movement) modes, and we engage all of these in our math instruction. • We use mathematical language to help students understand math at a deeper level, starting from concrete and working toward abstract thinking. For example, we explore and play with manipulative materials, making piles of tens before we study the abstract procedure for adding groups of ten. • We connect to what the student already knows and build upon that prior knowledge. This supports effective, longer-term learning in what is known as constructivist learning. • We understand the skills that our children will need to succeed in the 21st century. It is essential that our students not only excel at knowing math facts, but also are capable of problem solving, reasoning and proving, communicating, connecting, and representing math. We work diligently to ensure that
students develop the ability to think mathematically, mentally manipulate numbers, learn math facts, and understand the abstract procedures of mathematics. • We value giving kids time to play at math. A 2007 study from Carnegie Mellon University showed that board games and card games impact numerical development. Results proved that young kids who regularly play board and card games make gains in number identification, counting, estimation on a number line, and comparing numbers. The study went further and looked at older students who played informal games regularly. Again, students who played more games performed better. During math play, wonderful dialogue can occur when children, teachers, and parents engage in conversations about numbers and math concepts. Teaching Math At Each Age In the preschool, block play and daily experience playing with manipulative materials give our students multiple opportunities to develop early math
2
CURRICULUM UPDATE – MATH
skills. Learning through play gives our preschoolers practice in learning the pre-math competencies they will need in Kindergarten and throughout their elementary school years. These skills include, but are not limited to, identifying shapes, understanding scale, classifying and sorting, counting sequentially, making predictions, problem solving, developing concepts of balance, measurement, and gravity, and improving pattern identification skills. As children enter Friends’ elementary school, math continues to be integrated throughout the curriculum and play continues to be emphasized along with math skills. Students are learning math in all its forms whether they are estimating numbers of pumpkin seeds in Kindergarten, laying out a garden in 1st grade, playing a dice game in 2nd grade, studying the pyramids of Ancient Egypt in 3rd grade, making a scale model of the solar system in 4th grade, or using exact measurement of a science experiment in 5th grade. Standards developed by both the National Council of Teachers of Mathematics (NCTM) and by the State of Colorado provide a structure for our elementary curriculum, as does Investigations Math that we introduced in the fall of 2011 in our K-5 program. The Investigations Math curriculum that we use in Friends’ elementary school represents the culmination of over 20 years of research and development aimed at improving the teaching and learning of elementary mathematics. The curriculum is designed to: • support students to make sense of math and learn that they can be mathematical thinkers
• focus on computational fluency with whole numbers as a major goal of the elementary grades • provide substantive work in important areas of mathematics rational numbers, geometry, measurement, data, and early algebra - and connections among them • emphasize reasoning about mathematical ideas
In addition, each of our skilled teachers uses a variety of other resources including Everyday Math, Marilyn Burns, Singapore Math, NCTM resources, and Math Olympiad materials to supplement and enrich the curriculum. Using these guidelines and resources, we teach children in a developmentally appropriate model – holding high expectations for all, yet differentiating to meet the needs of many – easier lessons for some, more challenging for others. In 2nd – 5th grade, each student receives an account for the math website ixl.com. This is primarily a practice program and augments our classroom instruction. Most grades use it once a week in the computer lab as well as periodically for homework. For math repetition, we do not think that our Kindergarten and 1st graders should be spending time on the computer. We therefore ask them to play the math back pack games that come home for practice.
How We Differentiate For Individual Thinkers At Friends’ we recognize the wide range of learners, and their relative strengths and weaknesses, in every class. Our teachers work hard to plan a variety of math activities, to individualize learning programs, and to hold students accountable to make their best efforts. Based on extensive classroom testing, Investigations Math takes seriously into account the time students need to develop a strong conceptual foundation and skills based on that foundation. Therefore, each curriculum unit focuses in depth on an area of content, providing multiple weeks for students to develop and practice ideas across a variety of activities and contexts that build on each other.
In order to meet the needs of the range of math learners we have at each grade, this year Friends’ is excited to announce new enhancements to our math program in the elementary school. Our specialist math teacher, Erika Norman, will be devoting additional time to our Kindergarten and 1st grade classes, giving them the building blocks they need to develop the essential early concepts and skills, as well as assessing all the students to help guide instruction. Kindergarten and 1st grade math classes will continue, as we believe they should, to be taught by Erika, their lead teacher and Teacher Candidate in the comfort of their regular classroom. New Math Block Schedule For Grades 2-5 Beginning in the next couple of
3
CURRICULUM UPDATE – MATH
weeks, and continuing for the whole school year, the 2nd-5th grade classes will be having math class at the same time each day as part of our new Math Block. Through our own research, and after many conversations with parents and teachers last school year, we decided that this would be a positive move for our students and our school. We are serious about challenging our students to the best of their abilities and we are hopeful that this new structure will accomplish that and allow us to do an even better job of teaching math. For most students, math will be taught to them at their current grade level as it has been previously, with teachers dedicated to differentiating within their grade. Those who need additional challenge will receive it, and those who need a slower pace can also receive that. With two teachers in each room, there are multiple avenues to reach all our learners and keep high expectations for everyone. For a few students who have already mastered the skills that they will be taught at their current grade, they may have the opportunity to go to another class for math. No student will ever go down a grade, and for the most part students will continue to be in their current grade levels for math instruction.
At the 5th grade level, we have devised an advanced class that will meet during this Math Block time to help serve those students that have proven mastery of the current 5th grade curriculum. Erika Norman, our math specialist teacher, will teach this advanced level class, in cooperation with 5th grade teacher, Mandy Stepanovsky, and myself, and supported by the 5th grade Teacher Candidates. In the beginning weeks of school all students grades 2-5 will be assessed through a written test and observation and previous teacher input to determine if there is any reason to move them from their current grade level for math. Again, most children will remain in their classes receiving quality, differentiated instruction because we do not want students to have holes in their learning due to being moved out of their current grade. We want strong, capable math thinkers in all the math strands not just students who can do a little of this well but missed something along the way. Finally, another valuable aspect of our Math Block is the ability for grades to work together on projects and problem solving situations. For example, 3rd graders can work with the 4th or even 5th graders to learn about perimeter and area and design playgrounds, or the 2nd and 3rd graders can meet on a Thursday morning during Math Block and play a variety of differentiated probability games. These experiences build a math community, a place where math is celebrated and children can learn from each other with high expectations for all.
problem-solving abilities, and computational strength. We believe that when students are engaged and excited about what they are learning, the practice and hard work that is necessary is readily put forth. Our preschoolers are ready for Kindergarten and we have received excellent feedback from parents of our fifth-grade graduates that they are well-prepared for middle school, with many graduates placing in advanced level math classes at their respective middle schools. And we are continually seeking to improve. We believe that the newest changes to our math program will only strengthen it and give our students the tools they need to succeed. If you have any questions about our math program or your child’s progress, please do not hesitate to ask your child’s teacher, Erika, or me. We will be happy to answer your questions and respond to your concerns. In the meantime, enjoy the math that is around you every day, and keep playing those board games!
Steve de Beer Mandy Stepanovsky Head of School Associate Head of School
Summary In summary, we have a wellresearched, developmentally appropriate, and strong math program at Friends’. Our focus is on developing mathematical thinking,
Read curriculum updates for other subjects such as Literacy, Science, and Social Emotional on Friends’ website at www.friendsschoolboulder.org/programselementary.
MATH AT FRIENDS SCHOOL Dear Friends’ School parents, This is the second in an occasional series of updates on our curriculum at Friends’ School. These essays are intended to present parents with an overview of why and how we teach what we do, rather than an index of exactly what is taught at each grade. For those details, please ask your child’s classroom teacher for a complete curriculum guide for your child’s grade. This update addresses math at Friends’: our overarching beliefs about math, our philosophy of teaching math at each age, how we differentiate for individual thinkers, and the new math block schedule that we are introducing for grades 2-5 for this 2012-13 school year. Friends’ Beliefs About Math At Friends’ School, children are taught and learn to be confident and competent math thinkers. We begin by providing a variety of concrete, handson experiences to build real number sense that students can later apply to more abstract mathematics. Students work individually, as well as in cooperative groups, to discuss and reason mathematically while becoming flexible and creative in their approach to problem solving. The following principles are part of what we believe about math and how they guide our teaching practice day to day. • We present meaningful mathematical tasks, which engage and challenge children’s thinking and bring about better math understanding.
• We give attention and respect to the range of ways that students learn from auditory and visual to more kinesthetic (movement) modes, and we engage all of these in our math instruction. • We use mathematical language to help students understand math at a deeper level, starting from concrete and working toward abstract thinking. For example, we explore and play with manipulative materials, making piles of tens before we study the abstract procedure for adding groups of ten. • We connect to what the student already knows and build upon that prior knowledge. This supports effective, longer-term learning in what is known as constructivist learning. • We understand the skills that our children will need to succeed in the 21st century. It is essential that our students not only excel at knowing math facts, but also are capable of problem solving, reasoning and proving, communicating, connecting, and representing math. We work diligently to ensure that
students develop the ability to think mathematically, mentally manipulate numbers, learn math facts, and understand the abstract procedures of mathematics. • We value giving kids time to play at math. A 2007 study from Carnegie Mellon University showed that board games and card games impact numerical development. Results proved that young kids who regularly play board and card games make gains in number identification, counting, estimation on a number line, and comparing numbers. The study went further and looked at older students who played informal games regularly. Again, students who played more games performed better. During math play, wonderful dialogue can occur when children, teachers, and parents engage in conversations about numbers and math concepts. Teaching Math At Each Age In the preschool, block play and daily experience playing with manipulative materials give our students multiple opportunities to develop early math
2
CURRICULUM UPDATE – MATH
skills. Learning through play gives our preschoolers practice in learning the pre-math competencies they will need in Kindergarten and throughout their elementary school years. These skills include, but are not limited to, identifying shapes, understanding scale, classifying and sorting, counting sequentially, making predictions, problem solving, developing concepts of balance, measurement, and gravity, and improving pattern identification skills. As children enter Friends’ elementary school, math continues to be integrated throughout the curriculum and play continues to be emphasized along with math skills. Students are learning math in all its forms whether they are estimating numbers of pumpkin seeds in Kindergarten, laying out a garden in 1st grade, playing a dice game in 2nd grade, studying the pyramids of Ancient Egypt in 3rd grade, making a scale model of the solar system in 4th grade, or using exact measurement of a science experiment in 5th grade. Standards developed by both the National Council of Teachers of Mathematics (NCTM) and by the State of Colorado provide a structure for our elementary curriculum, as does Investigations Math that we introduced in the fall of 2011 in our K-5 program. The Investigations Math curriculum that we use in Friends’ elementary school represents the culmination of over 20 years of research and development aimed at improving the teaching and learning of elementary mathematics. The curriculum is designed to: • support students to make sense of math and learn that they can be mathematical thinkers
• focus on computational fluency with whole numbers as a major goal of the elementary grades • provide substantive work in important areas of mathematics rational numbers, geometry, measurement, data, and early algebra - and connections among them • emphasize reasoning about mathematical ideas
In addition, each of our skilled teachers uses a variety of other resources including Everyday Math, Marilyn Burns, Singapore Math, NCTM resources, and Math Olympiad materials to supplement and enrich the curriculum. Using these guidelines and resources, we teach children in a developmentally appropriate model – holding high expectations for all, yet differentiating to meet the needs of many – easier lessons for some, more challenging for others. In 2nd – 5th grade, each student receives an account for the math website ixl.com. This is primarily a practice program and augments our classroom instruction. Most grades use it once a week in the computer lab as well as periodically for homework. For math repetition, we do not think that our Kindergarten and 1st graders should be spending time on the computer. We therefore ask them to play the math back pack games that come home for practice.
How We Differentiate For Individual Thinkers At Friends’ we recognize the wide range of learners, and their relative strengths and weaknesses, in every class. Our teachers work hard to plan a variety of math activities, to individualize learning programs, and to hold students accountable to make their best efforts. Based on extensive classroom testing, Investigations Math takes seriously into account the time students need to develop a strong conceptual foundation and skills based on that foundation. Therefore, each curriculum unit focuses in depth on an area of content, providing multiple weeks for students to develop and practice ideas across a variety of activities and contexts that build on each other.
In order to meet the needs of the range of math learners we have at each grade, this year Friends’ is excited to announce new enhancements to our math program in the elementary school. Our specialist math teacher, Erika Norman, will be devoting additional time to our Kindergarten and 1st grade classes, giving them the building blocks they need to develop the essential early concepts and skills, as well as assessing all the students to help guide instruction. Kindergarten and 1st grade math classes will continue, as we believe they should, to be taught by Erika, their lead teacher and Teacher Candidate in the comfort of their regular classroom. New Math Block Schedule For Grades 2-5 Beginning in the next couple of
3
CURRICULUM UPDATE – MATH
weeks, and continuing for the whole school year, the 2nd-5th grade classes will be having math class at the same time each day as part of our new Math Block. Through our own research, and after many conversations with parents and teachers last school year, we decided that this would be a positive move for our students and our school. We are serious about challenging our students to the best of their abilities and we are hopeful that this new structure will accomplish that and allow us to do an even better job of teaching math. For most students, math will be taught to them at their current grade level as it has been previously, with teachers dedicated to differentiating within their grade. Those who need additional challenge will receive it, and those who need a slower pace can also receive that. With two teachers in each room, there are multiple avenues to reach all our learners and keep high expectations for everyone. For a few students who have already mastered the skills that they will be taught at their current grade, they may have the opportunity to go to another class for math. No student will ever go down a grade, and for the most part students will continue to be in their current grade levels for math instruction.
At the 5th grade level, we have devised an advanced class that will meet during this Math Block time to help serve those students that have proven mastery of the current 5th grade curriculum. Erika Norman, our math specialist teacher, will teach this advanced level class, in cooperation with 5th grade teacher, Mandy Stepanovsky, and myself, and supported by the 5th grade Teacher Candidates. In the beginning weeks of school all students grades 2-5 will be assessed through a written test and observation and previous teacher input to determine if there is any reason to move them from their current grade level for math. Again, most children will remain in their classes receiving quality, differentiated instruction because we do not want students to have holes in their learning due to being moved out of their current grade. We want strong, capable math thinkers in all the math strands not just students who can do a little of this well but missed something along the way. Finally, another valuable aspect of our Math Block is the ability for grades to work together on projects and problem solving situations. For example, 3rd graders can work with the 4th or even 5th graders to learn about perimeter and area and design playgrounds, or the 2nd and 3rd graders can meet on a Thursday morning during Math Block and play a variety of differentiated probability games. These experiences build a math community, a place where math is celebrated and children can learn from each other with high expectations for all.
problem-solving abilities, and computational strength. We believe that when students are engaged and excited about what they are learning, the practice and hard work that is necessary is readily put forth. Our preschoolers are ready for Kindergarten and we have received excellent feedback from parents of our fifth-grade graduates that they are well-prepared for middle school, with many graduates placing in advanced level math classes at their respective middle schools. And we are continually seeking to improve. We believe that the newest changes to our math program will only strengthen it and give our students the tools they need to succeed. If you have any questions about our math program or your child’s progress, please do not hesitate to ask your child’s teacher, Erika, or me. We will be happy to answer your questions and respond to your concerns. In the meantime, enjoy the math that is around you every day, and keep playing those board games!
Steve de Beer Mandy Stepanovsky Head of School Associate Head of School
Summary In summary, we have a wellresearched, developmentally appropriate, and strong math program at Friends’. Our focus is on developing mathematical thinking,
Read curriculum updates for other subjects such as Literacy, Science, and Social Emotional on Friends’ website at www.friendsschoolboulder.org/programselementary.
