Mathematics

Math Vision

Every child is able to meet grade level expectations
Every child feels the joy of figuring out and applying rich mathematical concepts.
Every child feels that they are good at math / that they see themself as a mathematician

Mission

We build students’ abilities to understand and appreciate the richness of mathematics in their grade level.

What We Do

We carry out our mission by elevating every student’s independence and agency within a community of self-directed learners.

Watch the short video below highlighting our math program and the incredible learning underway.

Click on each of the sections below to see the elements we elevate with our classroom culture, our student practices, and our educator practices.

Classroom Culture and Routines

Students have choice. Classroom structures allow them to make choices in how they participate in the learning process.
Students are metacognitive. They reflect on what they are supposed to know, what they do know, and what they will do next. As often as possible, they assess their own work.
Students have a voice. Their ideas are heard by other students and the teacher. Students feel empowered. They have a sense of ownership in what happens in the classroom.
Students are active members of a community of learners. Students and teachers have a common purpose -- to learn as much and grow as much as possible, both as learners and as people. They feel a sense of belonging. They are consciously civic-minded; they pay attention to the good of the group.
Students are taught how to use freedom effectively. They are weaned off their habits of dependency on teacher direction. They are taught how to make good choices for themselves.
Tasks are rich. They have a low floor and a high ceiling. They are aligned with grade-level expectations. Scaffolds are temporary. Students explore tasks that are interesting and require critical thinking. Tasks require students to apply their knowledge to novel situations that require flexibility of thinking and the ability to apply what they know to new situations.

Student Practices

Students participate regularly in conversational learning. Classroom dialogue is rich. Students share the wealth. There is often more than one teacher in the room. Students’ voices are heard more than the teacher’s voice.
Multiple perspectives drive rich learning. Students consider alternative perspectives and multiple representations. They critique the reasoning of others, and use the perspectives of others to grow their own complete understanding of mathematical concepts. This is part of the collectivist practices in the classroom.
Students have a growth mindset. Effort is celebrated. Students are rewarded not for who they are, but what they do. Pre-existing fixed mindsets in students are actively challenged.
Students use rich vocabulary that is precise and descriptive.
Students are learning grade level math. All students, every day, are engaging with tasks that exemplify the rich and complex expectations of the grade level standards. Students with unfinished learning are given the support to finish that learning while accessing grade level tasks at the same time

Educator Practices

Mistakes are celebrated. Mistakes are the greatest opportunity to learn. Teachers and students explore incorrect thinking in order to unearth correct thinking. The process of learning from a mistake is honored and celebrated. Students treat mistakes and failures as feedback about what they still need to master.
Process is celebrated. Students’ thinking is celebrated and explored. Teachers rarely respond with “correct”, but rather with “how do you know?”
Effort is celebrated. Students are not praised for being something, but rather for what they’ve done. This is the difference between “you are smart” and “you worked hard”.
Student-directed work is prioritized. In the case of middle school, for example, Desmos lessons do not extend beyond 45-50 minutes, allowing daily time for self-directed learning in the math classroom.
Expectations are clear to all. Common assessments, complete with rubrics and exemplars, help define grade level expectations that are in line with common core standards. A student who is proficient is one who has met grade level expectations. Students, parents, and educators are all clear on the expectations.
Reporting Standards define course-level learning expectations. Teachers can accurately assess a student’s level of proficiency against any reporting standard of their grade. All assessments -- from daily formative assessments to summative assessments to district benchmark assessments -- are aligned with reporting standards. Students, parents, and educators are all clear on the expectations. The report card gives honest, accurate feedback to parents regarding where students are in their learning progression.
Collaborative Planning drives priorities of instruction. Teachers are engaged in PLCs to accomplish the goals described above, leveraging student work and evidence of learning to inform instructional choices. Interventionists and Instructional Coaches are aligned in this work with teachers.
Teachers have autonomy to use practices best for their students. Teachers are versed in the high leverage instructional moves that result in the student behavior above, as evidenced by high Danielson ratings. Instruction is not scripted, but a series of thoughtful teaching that is best described by the Danielson rubric.

The official Illinois standards for mathematics are the Common Core State Standards in Mathematics (CCSS-M). The CCSS-M is the foundation of District 65’s core curriculum in mathematics. The CCSS-M raises the bar for student performance as a way to enable college- and career-readiness in the 21st century. In other words, the CCSS-M guide the way to success for our students. They define what students should understand and be able to do at each grade level or course in mathematics.

View additional information about the Common Core State Standards.

Parents are also encouraged to access content and grade-specific parent roadmaps developed by the Council of the Great City Schools. These roadmaps include examples of grade-level focus in the content area, sample progressions of learning across three grade levels in the Common Core, and tips to parents on communicating with teachers about their child’s work and how to support student learning at home.

Monitoring Impact

Monitoring the Impact

District 65 continuously monitors the impact of its math program. We consider:

Student input - survey and interviews
Student proficiency as demonstrated by curricular-based assessments
Student Task Choices
MAP data trends
Educator observation and input

Since implementing our current structure, we have observed the following in our middle school program:

No racial predictability in terms of students making expected gains.
Little to no racial predictability in terms of students’ sense of challenge and sense of identity as mathematicians.
As a whole, students reported feeling challenged, prepared for high school, and generally feeling that this year was a better experience than the last.
About 95% of students say they are challenged or neutral on the subject of challenge (80% state that they have opportunities for challenge, 15% are neutral on the subject of challenge). Among students with the highest MAP scores, 90% state they are either challenged or neutral on the subject of challenge.
A strong majority of students feel prepared for high school, particularly students who are choosing Deeper Dive tasks during choice time.
The percent of middle school students making expected gains in MAP is up 6 points overall since 2019, but down 3 points since 2020.

Overall, the pandemic has shown clear impact on students' learning, yet the district has seen overall growth in student scores relative to other schools since 2019-2020, as well as advanced gains in the 2022-2023 school year for grades 4th through 7th, stronger than in 2019, prior to the pandemic.

Click "Learn More" to see presentations regarding our K-5 and 6-8 programs.

Learn More

Presentations/Learn More

K-5 Math. An hour-long presentation giving an overview of the K-5 Math program was recorded on May 24, 2022. The presentation provides:

Department Vision
Programmatic data showing impact in recent years
An overview of the process for selecting new instructional materials
Directions on how to access key resources to support families
An example lesson
Differentiation explanation
Ways teachers are supported
Math Pathways and options
Summer Support opportunities online
Q&A

The deck can be viewed via PDF in English and in Spanish. Please note that the deck posted here has been updated to include answers to questions asked during the presentation.

Middle School Math. A 55-min presentation giving an overview of the D65 Middle School Math program was recorded on February 10, 2022. The video provides:

Department Vision
Programmatic data showing impact in recent years
Example lessons
Curricular Overview
Curricular Options/Pathways
Q&A

This presentation can be viewed via youtube. To see videos referenced within the presentation itself, see the description details of the video.

The deck can be viewed via PDF in English and in Spanish.

Earlier Presentations

A report outlining the outcomes of the previous school year, along with recommendations for the fall were presented to the Board of Education on February 8, 2021. (This report can be found via the presentation that was presented at the board meeting or through the actual recorded meeting).

The STEM Department also hosted a Math Night onMay 24, 2021 providing an overview of the middle school program. The evening included the perspectives of students and educators, as well as an overview from administration. To learn more, families are encouraged to watch a recording of the event. The slide deck presentation for the evening is available in English and Spanish.

Looking for More?

For more information beyond what is provided on this website, please contact District 65 STEM Director David Wartowski (wartowskid@district65.net).

Acceleration

How District 65 Accelerates Learning

District 65 provides a rich array of learning opportunities within its math program. These opportunities come through the combination of a rigorous core curriculum and a library of resources that provide both enrichment and support, accelerating the learning of every student according to their individual learning needs.

The middle school program in particular, grade 6 through 8, combines daily lessons with daily Choice Time, during which students engage in topic-related tasks that are aligned with their level of readiness.

In addition, all middle school students in District 65 are automatically placed in an accelerated pathway that combines the three years of learning expectations from 7th grade, 8th grade and High School Algebra into the two years of learning in 7th and 8th grade.

For a very small number of students, additional advancement may be appropriate. We offer several methods for additional advancement, allowing for various opportunities depending on what is most appropriate for each individual student. To learn more, please read the tab "Further Advancement" on our Middle School Structures page.

Due to our accelerated pathway for all students, our robust differentiation approaches within the classrooms, and the variety of methods to access additional acceleration, there is no need for advanced placement tests or alternate placement in order to access advanced coursework (with the exception of grade skipping, which requires additional testing).

Please note that students wishing to follow an Honors-level math pathway to Calculus BC are not required to take or pass any high-stakes tests in District 65. Instead, they must simply perform well in their math classes.

All students in D65 are on a pathway to take Calculus BC in high school. Calculus BC is the highest level of mathematics accredited by the College Board.

If your child is interested in taking Mutivariable Calculus / Linear Algebra in high school, they should take Algebra 2 during their freshman year. To learn how to do this, please read the tab "Further Advancement" on our Middle School Structures page.

To learn more about high school pathways, and options available, follow the "Middle School (6-8) Structures" link at the top right of this page.

FAQs

Frequently Asked Questions

I am new to the district. How is my child placed?

Upon arrival to District 65, we will review your child's transcript and scores. Your child will be placed into the next sequential course based on the last math course that was successfully completed. If you have individual questions about your own child's placement, please contact the Director of Mathematics, David Wartowski (wartowskid@district65.net)

I feel like my child needs more support in math. What should I do?

Please speak directly with your child's teacher if you haven't already. There are many options for support in place in District 65, such as acceleration block, tutoring and choice time. Please work directly with your child's teacher to ensure that the right supports are in place.

District 65 generally does not encourage the use of for-profit math supports outside of school. Your child is likely involved in anywhere from 60-85 minutes of math instruction each day at school. We expect to be able to provide robust and complete learning during this time. If you do think that your child's learning needs are being met, contact your child's school directly in order to problem solve and put the right supports in place.

The middle school math program has been updated over the past years. How is it going?

While the pandemic has shown clear impact on students' learning, the district has seen overall growth in student scores relative to other schools since 2019-2020. Data from the NWEA Similar Schools Report indicates an overall rise of 17 points in 6th grade and 9 points in 7th grade. These increases are seen across all abilities, showing, for example, a ten point rise among students scoring in the top decile and a ten point rise among students scoring around the 50th percentile.

In addition to monitoring test scores, the Math Department also began surveying students annually, starting with the 2020-2021 school year. With now two years of data on student perspectives, we are able to notice several trends. Among them, we see that about 95% are challenged or neutral on the subject of challenge (80% state that they have opportunities for challenge, 15% are neutral on the subject of challenge). Among students with the highest MAP scores, 90% state they are either challenged or neutral on the subject of challenge. We also see that a strong majority of students feel prepared for high school, particularly students who are choosing Deeper Dive tasks during choice time.

To see a video presentation reviewing programmatic data evaluating impact, see the February 10, 2022 Math Night presentation.

Detailed reports on middle school math are reported annually to the Board; information is also posted on our website. The next report will be in April 2022.

What is Choice Time? How does it support learning?

Choice Time - sometimes called "What I Need Time" or "WIN Time" - is offered as part of the middle school math curriculum on a nearly daily basis. This is typically a 25-minute part of the lesson where students are working on a task that is created to accelerate their learning within the topic of instruction. Tasks are taken from a task library that has been built by district 65 educators over two years. Students are asked to reflect on their current level of learning and then make a choice as to which task will most effectively advance their learning -- choosing between "Pause and Build", "More Practice" and "Deeper Dive". Teachers consistently monitor students' choices, ensuring that their choices are appropriate and effective.

Building students' agency and decision making when it comes to learning pathways is a research-based approach the builds more effective and longer-lasting learning traits that increase learning outcomes. Middle school is a critical time for students to build the agency to make strong decision, with the guidance and support of their teachers.

Choice time also offers individual differentiation so that all learning needs are met on a daily basis, according to each student's needs that day, based on the topic at hand.

To learn more about Choice Time, see the the February 10, 2022 Math Night presentation.

How are MAP Scores used by teachers?

MAP acts as a universal screener and as a method to show general growth in a subject area. It is an adaptive test that gives questions at, above, or below a student's grade level in order to determine the student's overall amount of knowledge relative to other students nationwide who have taken the same test. Individual questions cannot be viewed by teachers - only overall scores and categorical scores.

Teachers use MAP to screen for students who may need additional support. Teachers may also use the categorical scores of MAP to determine students' relative strengths and weaknesses. This can help inform instruction, giving more weight to areas of relative weakness as appropriate.

MAP scores are not a measure of whether students have met grade level expectations. Educators rely on criterion-based, standards aligned assessments to determine whether students are meeting the expectations of the grade. These include benchmark assessments, unit assessments, and standards-based formative assessments. The Illinois Assessment of Readiness (IAR) also acts as an external measure of our students' proficiency against grade-level standards.

Is differentiation in middle school limited to Choice Time?

No. Daily lessons also differentiate by the nature of their design. The Desmos materials, based on Illustrative Math, present tasks that are considered "low floor, high ceiling". These tasks are accessible to all students, yet provide nearly endless solutions and depth, allowing students to go as far as they would like in exploring particular problems. Students are encouraged to offer unique and various approaches, as well as to build off the thinking of others. Differentiation comes not only from the use of these rich tasks, but also through the emphasis on student voice and dialogue. Students are encouraged to offer their robust thinking through voice, writing and pictures, while also building off the thinking of others to further advance their own thinking. On occasion, students are also invited to create their own tasks, offering limitless creativity along with even more opportunity for extended thinking within the lesson.

Differentiation ultimately takes many forms, through both homogeneous and heterogeneous settings, and is integral to the design of our middle school math curriculum.

Do the two districts (D65 and D202) work together?

District 65 works directly with District 202 any time updates or changes are made regarding mathematics programming. Our shared commitment is to strengthen our middle school curriculum, to increase its alignment with the high school, and to retain a pathway for students seeking additional acceleration. As a result, we expect to increase high school readiness, while also extending opportunities for enrichment and challenge for all of our students. We believe that our partnership with District 202 only strengthens our ability to provide equity and excellence to all our students.

Any changes in practice seek to expand opportunities for our students. District 65 and District 202 are jointly committed to making honors coursework accessible to all students who wish to follow this level of rigor, as well as preserving a pathway to Multivariable Calculus/Linear Algebra for students who wish, and are qualified, to follow this high school pathway.

What if I want to take Advanced Algebra 2 Honors freshman year?

Taking Advanced Algebra 2 Honors freshman year is an appropriate placement for any student who will take Multivariable Calculus/Linear Algebra (MV/LA) their senior year. Historically, about 4% of students in Evanston take MV/LA. There are a number of ways that a student may end up following this route. Options include:

Taking High School Geometry over the summer. The summer between 8th grade and 9th grade would be the recommended time to take this course. Students would not have to make the decision until late in their 8th grade year. Currently there is no summer school Geometry course offered at ETHS for rising freshmen. We are developing plans to offer Geometry by ETHS or D65 starting in the summer of 2023. Options may be available this summer for Geometry outside of the district. Contact ETHS if you are interested in this option.
Grade skipping. In unique cases, a student may benefit from skipping a grade. Students who skip a grade in math alone will be on a pathway to take HS Geometry during their 8th grade year. This model is two years advanced past the standards for College/Career Readiness. For more information on testing procedures, please review information regarding Alternate Placement.
Independent Study. Students with strong independent learning skills may opt out of a Geometry course by learning Geometry via other means, including self-study. Upon demonstration of having learned the topics established by ETHS for its Geometry course, a student would be allowed to take Advanced Algebra 2 Honors their freshman year without having had to sit in a Geometry course. Prior approval from the ETHS Math Department is required before selecting this option. This option is extremely rare.

Families of 8th Grade Algebra students who are contemplating taking Advanced Algebra 2 Honors during their freshman year are encouraged to reach out to the ETHS Mathematics Department Chair during the time of Incoming Freshman course requests or sooner to determine the best option for their child.

Can I take Advanced Algebra 2 Honors freshman year even if I don’t plan on taking Multivariable Calculus/Linear Algebra?

It would not be advised to work toward taking Advanced Algebra 2 Honors freshman year if MV/LA is not your goal. Algebra 2 is defined by Common Core as a junior year course. Taking it freshman year is something that is suitable for the highest level math learners in the country. A student at this level would be advised to continue their high school math learning through Multivariable Calculus/Linear Algebra.

Can I take Honors/AP Math in high school without taking Advanced Algebra 2 Honors freshman year? How about ChemPhys?

Absolutely. Taking Geometry freshman year places a student one year ahead of the standard progression outlined by the Common Core and College Readiness standards. By taking Geometry freshman year, and Algebra 2 sophomore year, a student is on track to take Calculus their senior year. Strong performance in Geometry and Algebra 2 would lead to AP Calculus BC, the highest level Math course offered by Advanced Placement (AP). ChemPhys is open to all students sophomore year who are enrolled in or have already taken Advanced Algebra 2 Honors. To take ChemPhys, a student must earn honors during Geometry their freshman year and then place into Advanced Algebra 2 Honors their sophomore year.

Does District 65 offer High School Geometry?

Yes, although very few students take it during the school year. Taking Geometry during the school year would require taking Algebra prior to the 8th grade, which would require grade skipping.

About 99% of District 65 students take Algebra in their 8th grade year. The majority of District 65 students will then take Geometry as a freshman; some students, based on ETHS placement procedures, will then take Geometry as a sophomore. See the ETHS Math Course Sequences and Course Placement for more information. Taking Geometry as a freshman is considered by the Common Core Standards as an accelerated pathway.

Students who take Geometry during their 8th grade year are taking a class two years earlier than suggested by the Common Core. This requires skipping a grade of math. Skipping a grade of mathematics is rare, yet appropriate for a small number of students. For more information, see the grade skipping section of this site.

Summery Geometry is a course that is available to all students, without the need for additional testing. District 65 coordinates with ETHS to ensure that this course is offered. District 65 and ETHS share the same curriculum for High School Geometry, no matter where it is taught or who teaches it. Currently there is no summer school Geometry course offered at ETHS for rising freshmen. We are developing plans to offer Geometry by ETHS or D65 starting in the summer of 2023.

Do I have to pay for Geometry if my student is interested in learning Geometry independently?

No. There are several free online resources available to support independent learning of Geometry, including OpenUp, Illustrative Math, FishTank and CK-12. Please coordinate with ETHS if you are interested in this option. ETHS has the final determination as to whether a student has mastered the competencies expected of High School Geometry. Learning Geometry through independent study is best for students who are highly self-motivated. The decision to follow this option should optimally be made no later than 7th grade in order to provide time to learn the content.

Can my child skip a grade in math?

In unique cases, a student may benefit from skipping a grade. To learn more about grade skipping, see the grade skipping section of this site. For more information on testing procedures and important deadlines, please review the district's guidance regarding Alternate Placement.

My child is taking Math classes on their own, outside of District 65. Can I use this to skip a course?

No. District 65's curriculum is designed to create a learning path that supports a strong foundation for success. Summer camp courses, such as CTE, are not seen as viable replacements for a year-long curriculum offered by District 65. In order to build a strong foundation for long term success, District 65 requires that students complete the full math program offered by the District.

Geometry is one subject that may be honored from summer or independent learning. Students interested in taking Advanced Algeba 2 Honors during their freshmen year may often do so by taking a summer Geometry course prior to 9th grade. Please, however, contact the ETHS Math Department Chair prior to enrolling in a summer Geometry course/camp. It is critical that you coordinate all placement decisions with the ETHS Math Department Chair prior to enrollment in any summer courses.

If you have further questions regarding a particular situation you are facing, please email the D65 Director of Mathematics, David Wartowski (wartowskid@district65.net)

How much math homework should my child be getting?

It varies depending on several factors, including the grade level, the type of learning taking place, and the individual needs of the student. In general, no more than 20 minutes of homework is necessary for additional independent practice. Often, there may be no homework at all for math. Students are already spending 60-80 minutes a day learning math at school; it is often important to also rest and take on other activities. If you have more questions about homework and the specific needs of your child, please reach out to your child's teacher.

What are ways that I can support math learning at home?

Here are some basic tips:

View your child’s learning directly
- Have your child show you a Desmos lesson on the ipad and explain to you: What was the point of the lesson? What did it make you think?
- Ask your child about the Choice Boards. Are they choosing the most challenging tasks they can do? Have them show you an actual task.
Be curious!
- Solve things more than one way.
- Listen for other perspectives for a single problem.
Be connected!
- Become familiar with the learning expectations of your math class (Shared by your teacher): What is my child expected to know right now for this unit?
- Talk to your teacher! If you have questions or concerns – discuss them with your child’s teacher!
Refrain from explaining math to your kids. Insead - ask questions
- “How did you do this?”
- “Why were you thinking that?”
- “How do you know you are right?” (or “How do you know that you are wrong?”)
- “Is there another way to do this?” (or “Is there another way to explain it?”)
Refrain from messages with unintended consequences. Example: “You are so smart” (vs. “You clearly worked hard.”)

Research Base

Research Base, Professional Positions and Articles

Dr. Jo Boaler, Stanford University

Dr. Rochelle Gutierrez, University of Chicago: Context Matters: How Should We Conceptualize Equity in Mathematics Education?

National Council of Teachers of Mathematics (NCTM) Statement from the President: Initiating Critical Conversation on the Discontinuation of Tracking

National Council of Supervisors of Mathematics (NCSM) Position Paper: Tracking Policies and Practices Widening the Opportunity Gap

ASCD: How Tracking Creates a Poverty of Learning

Ed Week: A Bold Effort to End Algebra Tracking Shows Promise

Megan Staples, University of Connecticut: Promoting Student Collaboration in a Detracked, Heterogeneous Secondary Mathematics Classroom

George Lucas Educational Foundation: Is It Time to Detrack Math?

Washington Post: Can honors and regular students learn math together? A new approach argues yes.

Curriculum Associates: Why Districts Should Re-evaluate Their Middle School Math Acceleration Programs

Brewer, D., & Rees, D. (1995): Detracking America's Schools: The Reform without Cost? Phi Delta Kappan, 77.

Huss, J.A. (2006): Gifted Education and Cooperative Learning: A Miss or a Match? Gifted Child Today, 29(4): 19-23. A key finding is that in mixed (detracked) environments where the pedagogical core is substantively focused on problem-based learning, cooperative learning, cultivation of critical thinking and where teacher mindsets are supportive, learning and achievement improve at all ability levels. (Huss, 2006)

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