Math Curriculum Q&A

2019-2020 Math Q&A

[plsc_toggle title=”What is FXW’s philosophy of math education rooted in?” state=”closed” color=”green” radius=”square”]

Our philosophy of mathematics education is rooted in:

  • Everyone with the right teaching and messages, can be successful in math, and everyone can learn to high levels in schools. No one is born knowing math, and no one is born lacking the ability to learn math (Boaler, 2016).
  • Students who believe their talents can be developed (through hard work, good strategies, and input from others) have a growth mindset. They tend to achieve more than those with a more fixed mindset (those who believe their talents are innate gifts). Therefore, they put in extra time and effort, and that leads to higher achievement. The growth mindset can be fostered (Dweck, 2006).
  • Mistakes show your brain is hard at work. The brain sparks and shows that information is processing, even if we are not aware of it, because it is a time of struggle; the brain is challenged. Classroom culture and design is “mistakes friendly.” (Moser et al., 2011).
  • Active learning process – students learn best when they are active rather than passive learners. Students must be engaged in exploring, thinking, practicing, and using knowledge, rather than listening to verbal concepts. (Sun & Pyzdrowski, 2009; Curtain-Phillips, 2001; Schreiner, n.d.).
  • Mathematical discourse in cooperative groups provide students with opportunities to exchange ideas, ask questions freely, verbalize their thoughts, justify their answers, and debate processes. (Geist, 2010; Hellum-Alexander, 2010; Woodard, 2004; Haralson, 2002; Curtain-Phillips, 2001).
  • The aim of mathematics education is to create autonomous learners who persevere in problem-solving. The purpose of mathematics education is not to impart knowledge, but instead to facilitate a student’s thinking and problem-solving skills which can then be transferred to a range of situations (Bruner, 1961).
  • Math instruction should develop symbolic thinking in children, moving from concrete to pictorial to abstract. Concrete, conceptual understanding leads to procedural fluency (Bruner, 1961).
  • Instruction moves beyond instrumental understanding (the ability to execute mathematical rules and procedures) and focuses on relational understanding (knowing both what to do and why). Students are able to build schema and find new ways of “getting there” without outside help demonstrating great flexibility. (Skemp, 1976).
  • In addition to teaching mathematics for its own sake, we strive to teach mathematics so that students learn to value diversity, see mathematics in their lives, cultural backgrounds, through literature and in nature and analyze and critique social issues and injustices. These learn-see-analyze purposes require connecting mathematics to real-world contexts. (Felton et al., 2012).
[/plsc_toggle] [plsc_toggle title=”What does the data show and research say about the programmatic changes FXW has made?” state=”closed” color=”green” radius=”square”]

Throughout last year and over the summer, the instructional team has analyzed NWEA’s MAP assessment data, AIMSweb Plus data, and responses from teacher surveys. While research states that three to five years are required before data can be analyzed to show the effects of programmatic change, we are using the data now to inform instruction and work to continuously improve teaching and learning.

Overall, the standardized data from this year was comparable to previous years’ data. While it is just one snapshot of learning, we are analyzing it carefully to look for grade-level, school-wide, or cohort trends. The teacher survey showed embracing a growth mindset and an openness to learning from mistakes as areas of strengths in the classrooms. Areas we will continue to focus on are increasing the level of mathematical discourse, problem solving, and application of math in real world contexts.

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Amy Bilek (former fourth grade teacher and former Math Department Chair) has been hired as the K-8 Math Instructional Coach. She will travel between both campuses focusing on providing support to increase the quality and effectiveness of classroom instruction.

Additionally, in June, teachers had the option to join a 3-day workshop focused on math reflection and planning. Teachers worked to further articulate learning goals and develop assessments to help inform instruction. In addition to the work in June last year and the year before, all math teachers will have another workshop on math professional development in August. Mathodology, who lead all professional development for Think! Mathematics and Developing Roots (K program), will lead trainings focused on teacher reported “pain points” from this year, differentiation, and teaching through problems solving. These training have been uniquely designed for the FXW teachers to address the questions they have had during this first year of implementation.

The middle school math teachers have met extensively throughout the summer to further articulate their curriculum and work to gather resources that align to FXW’s philosophy of math education. They are putting together resources focused on problem solving, collaboration, and applying math in the context of the real world.

Finally, FXW will be growing their partnership with Lesson Study Alliance out of DePaul University. Lesson Study is a Japanese model of teacher-led research in which a group of teachers work together to target an identified area for development in their students’ learning. Using existing evidence, participants collaboratively research, plan, teach, and observe a series of lessons, using ongoing discussion, reflection, and expert input to track and refine their interventions. We are excited to share that all math teachers in the school will be part of a Lesson Study team this year that will meet during the late start Wednesdays.

[/plsc_toggle] [plsc_toggle title=”What action items will FXW engage in during the 19-20 school year?” state=”closed” color=”green” radius=”square”]

Along with Lesson Study, there are three other action items we’d like to share. First, the gap analysis that was done last summer to aid in the transition from Everyday Math to Think! Mathematics has been adjusted to reflect what is needed in year two of the roll-out. A priority has been placed on pacing to support teachers in their efforts to deeply cover all the content intended for their grade-level and make meaningful connections between concepts. Secondly, classrooms will be engaging in open-ended “number talks” multiple times per week. Number talks are short discussions among a teacher and students about how to solve a particular mental math problem. Both external research and our internal data shows that this practice has a significant positive effect on students’ computational fluency and number flexibility. Finally, grade-level teams will work together to carefully analyze data. Teachers will look at both classroom-level, authentic data and standardized data to inform their instruction and maximize student learning.

[/plsc_toggle] [plsc_toggle title=”What is new with the school-home connection?” state=”closed” color=”green” radius=”square”]

We really value the school-home partnership when supporting children in their math journey. To facilitate communication home about what is happening in the math classroom, grades K-4th will be sending home a “Math Family Letter” with each unit. This letter includes sections entitled: “What We’re Learning,” “Mathematical Language,” and “Do-Anytime Activates.” In 5th-8th grade, teachers will be posting this information on their Canvas page for both students and parents to see.


2018-2019 Math Q&A

[plsc_toggle title=”What is FXW’s Philosophy of Math Education?” state=”closed” color=”green” radius=”square”]

A philosophy statement was written by the Math Curriculum Review Committee at the onset of the review process to create the pathway for future work together. Rooted in research of best practice for math education, we spent time articulating what we want math to look like at FXW.

FXW’s Philosophy of Math Education: The mathematics curriculum and instruction at FXW manifests our belief in and commitment to all students needing and deserving the opportunity to develop comprehension, competence, and confidence to master the mathematics challenges in grade school and develop the skills, love, and appreciation of mathematics to succeed in higher levels of education and in life. Through fostering a perpetual growth mindset, students grow confident that they can improve as mathematicians and that mistakes are valuable to develop the brainpower that will lead to higher achievement. Instruction, demanding high-level student engagement and mathematical discourse, challenges students to reason with flexibility and imagination to explore multiple approaches to problem solving. By openly and consistently supporting perseverance and resilience at FXW, students internalize the confidence that they can succeed if they keep trying. Mathematics is inclusive of and essential to all students, so teachers challenge each student at his or her appropriate level. Students engage in an active learning processes from the concrete to pictorial to abstract. Finally, FXW works to teach math in an authentic manner, using an interdisciplinary approach when possible, so that students can apply what they have learned to enrich their experiences in the world around them.[/plsc_toggle]

[plsc_toggle title=”Why is the School reviewing the math program?” state=”closed” color=”green” radius=”square”]A common practice in independent schools is to review the curriculum, at every level, on an ongoing basis. Schools often choose to review one or two subjects in a given year. The review, revision, and implementation period can be anywhere from a year to three years. At FXW, our efforts will always be to operate in a spirit of continuous improvement and this review meets that objective.


[plsc_toggle title=”What did the math curriculum review process look like?” state=”closed” color=”green” radius=”square”]

During the 2016-2017 school year, the process began with a three-tiered approach. The first tier focused on the overall professional development of the faculty. Chicago Lesson Study Alliance partnered with the School to promote teaching through problem-solving. This model has continued into this school year.

The second tier, focused on exploring our present program, Everyday Math, by digging deeper into select units of study in kindergarten through fifth grade and examining the expectations of the grade levels above and below. Research from other programs was brought into these units of study to begin to test different methodology. Feedback was gathered from faculty and from student output.

The third tier focused on the junior high. A first step was to gather information from many of the high schools the FXW graduates attend. We collected course options/tracks, 9th grade curriculum maps, placement tests, and knowledge gleaned from site visits. From there, we created a list of topics for a 9th grade-level Algebra I course, and were then able to create a 7th-grade Pre-Algebra course that contains 8th grade-level Algebra, and a 6th grade course that contains 7th grade Pre-Algebra. Our junior high curriculum was articulated by back mapping topics starting at the 9th grade level and working our way down to the 6th grade.

During the 2017-2018 school year, the process continued with focus on these three tiers. The professional development model continued. The junior high worked through the newly designed curriculum gathering feedback from faculty and from student output. Class placement for the Class of 2018 and continued graduates will be taken into consideration as well. A Math Curriculum Review Committee, teachers from grades K-8, was established to review present programs and worked to articulate FXW’s Philosophy of Math Education. The committee analyzed different programs based on how well they fit with the philosophy using standardized tools. To analyze if Everyday Math was the best fit for FXW, a comparison to other programs was necessary. Information was gathered on other programs from other Independent Schools, as well as the National Council of Teachers of Mathematics (NCTM).  We reviewed NCTM’s threads where math teachers, coaches, professors, mathematicians, and researchers responded, as well as various math education publications and leading professionals in the field.

[/plsc_toggle] [plsc_toggle title=”Are there programs that fit with FXW’s philosophy?” state=”closed” color=”green” radius=”square”]

After reviewing all the data collected from the Math Curriculum Review Committee which included data from standardized tools, conversations, and student output based on trying some of the programs and materials in classrooms, we found philosophical fits and are ready to make some changes. As a committee, it became clear that we wanted to focus on the philosophy and approach to our curriculum first and then find resources that best fit. Keeping that in mind, our priority will be providing professional development and support around the philosophy that we created. Secondarily, we do need a program that will allow us flexibility to use a variety of resources to create maximum impact and fit our philosophical needs. A program that can serve as a framework or springboard. We have decided to move forward with Think! Mathematics for kindergarten through fifth grade. Think! Mathematics is adapted from approaches used in Singapore, which emphasize the use of problem solving, hands-on learning, and group work. This program has a clear and cohesive scope and sequence and will still allow teachers the flexibility to use desired and effective components of Everyday Math, as well as other programs, to meet students’ needs.

[/plsc_toggle] [plsc_toggle title=”What is being done to ensure a smooth transition?” state=”closed” color=”green” radius=”square”]

Throughout this school year and continuing into next, we have participated in extensive professional development focusing on philosophical approaches to math instruction. In the coming year, Wednesday mornings will provide opportunities to collaborate by engaging in math instruction and analyzing student output.

We feel that moving all grade levels at once is more beneficial than a six-year rollout. All training and collaborative conversations can happen together across grade levels. An extensive gap analysis is taking place to avoid the six-year rollout and proactively put a systematic solution in place. This means that there will be adjustments needed each year as we learn and grow together.

[/plsc_toggle] [plsc_toggle title=”How are teachers being supported through this transition?” state=”closed” color=”green” radius=”square”]

This school year, the Math Department meetings focused on fostering a mathematical mindset by using Jo Boaler’s Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching. These resources allowed our Department to engage in activities together. They focused on the curriculum they teach through connecting related ideas and prioritizing topics of emphasis at each grade level by using the National Council of Teachers of Mathematics (NCTM) Teaching with Curriculum Focal Points.

Many math conferences were attended and online courses were completed by teachers across kindergarten through eighth grade including NCTM’s Regional, National and Innov8 Conferences, Math Leadership Summit at Stanford University, Bureau of Education and Research math conferences, and Stanford University and University of Phoenix online courses.

All Math teachers in K-8 will spend an entire week of the summer in intensive math professional development, focusing first on instruction.  Bill Jackson, a leader in professional training of math educators, will be providing ongoing support, as well as our continued partnership with Chicago Lesson Study Alliance. The Math Curriculum Review Committee will continue their work this summer to further develop curriculum to share with grade-level teams. Additionally, monthly math curriculum meetings will take place to complement regularly scheduled monthly Math Department meetings.

[/plsc_toggle] [plsc_toggle title=”What will math instruction not look like?” state=”closed” color=”green” radius=”square”]

As we all remember math from our days in school, another way to explain what our program will look like is to share what our math will not look like. Math will not be “answer-getting” oriented. Teachers will not be leading students toward the right answer; rather, they will be asking questions to push students’ thinking and will allow students to make mistakes. Students will not just memorize procedures. They won’t go through the steps without developing conceptual understanding first. There will not be a focus on speed. Students will be encouraged to think deeply about problems and work to develop their number flexibility. You will see a shift in approach to math facts. Rather than focusing on the use of flashcards and timed tests that promote memorization, there will be emphasis on strategies and reasoning with numbers. Teachers will work towards allowing students to learn through problem-solving, discovering the learning target through engaging problems and collaboration. Students will learn from pushing themselves and from each other while the teacher acts as a guide.

[/plsc_toggle] [plsc_toggle title=”What can you look forward to in terms of the math instructional approach in the classroom?” state=”closed” color=”green” radius=”square”]

FXW classrooms will have policies and classroom cultures that foster a growth mindset. Students will know that their talents can be developed through hard work, good strategies, and input from others. Students with a growth mindset tend to achieve more than those with a more fixed mindset, those who believe their talents are innate gifts. Classroom culture and design will be “mistake friendly.” Students will engage in high-levels of collaborative conversation which will provide students opportunities to exchange ideas, ask questions freely, verbalize their thoughts, justify their answers, and debate processes. Students will grow their ability to persevere in problem-solving. The focus will not be so much about imparting knowledge, but instead to facilitate a student’s thinking and problem-solving skills, which can then be transferred to a range of situations.

[/plsc_toggle] [plsc_toggle title=”How can you support your child in math?” state=”closed” color=”green” radius=”square”]

Math instruction should develop symbolic thinking in children, moving from the concrete to more abstract. You can support your child’s need to develop an understanding through hands-on manipulatives and visuals before they learn the procedure or algorithm. At times, teaching students procedural algorithms or “math tricks” (e.g. subtracting two large numbers with crossing out and borrowing) prevents students from developing a deeper conceptual understanding. Thus, students may struggle to develop the “how” and “why” behind these math skills.
Please encourage your child to solve a problem in various ways. Math is about connections, and the more connections students can make, the deeper and longer-lasting the learning. Instruction moves beyond instrumental understanding (the ability to execute mathematical rules and procedures) and focuses on relational understanding —knowing both what to do and why. Students will be able to build schema and find new ways of “getting there” without outside help demonstrating great flexibility.
Help your child see math in your daily lives. Engage them in the math that is embedded in cooking, baking, nature, playing sports, telling time, etc. In addition to teaching mathematics for its own sake, strive to teach mathematics so that students learn to value diversity, see mathematics in their lives, cultural backgrounds, through literature and in nature.