Math Curriculum FAQ for Grades K-5
- What is the educational philosophy of the District regarding mathematics instruction?
- What is flexible ability grouping?
- What are the Eight Mathematical Practices?
- How can parents encourage the mathematical practice of “perseverance” in their children?
- How can I learn more about the Singapore Math methods and strategies that are essential to the Math in Focus math series used in Grades K-5?
- Why is bar modeling a key strategy in the Math in Focus series?
- How are 5th graders being prepared for the transition to middle school math?
- What was the process used to select the Math in Focus and Big Ideas resources for math instruction in D181?
In District 181, we believe a high-quality mathematics curriculum engages students with a balanced approach to developing conceptual understandings, procedural knowledge, building fluency, and applying knowledge to real-world problems.
- Number sense is the foundation for mathematical proficiency. Students must develop a strong understanding of how numbers are formed and related.
- Learners build new knowledge by making connections to their previous experiences.
- Learning occurs when students explore ideas, discover patterns, and find logical order using a variety of tools.
- A community of learners must discuss, explain, and justify solutions to develop conceptual understandings.
- All learners must engage in meaningful tasks and persevere in finding solutions.
- All students can learn mathematics when engaged in a responsive, supported curriculum.
Ability grouping is the practice of grouping or sorting students based on their academic or instructional level with others whose learning needs are similar to theirs. In District 181, placement is flexible; teachers regularly, minimally three times a year, examine student data to ensure appropriate placement within ability groups.
For 2016-17, District 181 has developed the following parameters for a flexible ability group model at the elementary level:
- Elementary schools should group across grade levels. Administration recommends that this be done for grades 3-5, but K-2 teachers can also do this if they feel it is best for students.
- Each school will divide their students by ability based on the number of teachers at that grade level plus other teachers who are available to assist with instruction (e.g., Differentiation Specialist).
- There will be some level of inconsistency at each school depending on the number of sections/teachers who are available to teach math and the number of students in the grade level (e.g., two vs. three section schools).
- Teachers and principals will make the final decisions on how to best group the students but they should use the flexible ability grouping model.
The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important ‘processes and proficiencies’ with longstanding importance in mathematics education.” - http://www.corestandards.org/Math/Practice/
- Make sense of problems and persevere in solving them
- Reason abstractly and quantitatively
- Construct viable arguments and critique the reasoning of others
- Model with mathematics
- Use appropriate tools strategically
- Attend to precision
- Look for and make use of structure
- Look for and express regularity in repeated reasoning
Learning occurs through the process of solving a problem and trying multiple approaches to solve it. With that understanding, parents can support the development of perseverance by praising the child’s effort, not only praising the child for arriving at the correct answer. For example, instead of telling a child, “You must be really smart because you got the right answer,” the parent can say, “I can tell you worked hard on that problem. Tell me your thinking. How did you arrive at that answer?” Parents are also encouraged to consider providing less direct assistance, letting the child work through his/her challenges, perhaps encouraging him/her to try a different approach, or take a break and come back to the problem. If the student is struggling with math homework, it is okay if the student does not necessarily get the right answer. The purpose of homework is to allow students to independently apply the knowledge and skills learned in the classroom. Parents are encouraged to write a note to the teacher sharing that the student worked hard but found difficulty with aspects of the assignment to help facilitate a positive home-school relationship.
Each D181 student in Grades K-5 has an account on ThinkCentral, the online component of the Math in Focus program. This account allows families access to a library of short videos highlighting the instructional methods used in Math in Focus, as well as information on how parents can support their child’s learning at home. ThinkCentral also includes an overview video for each chapter of the Math in Focus book, so parents can follow along to understand the concepts their child is learning. Parents and students can further use to the site to access a digital version of the hardcover textbook, and virtual manipulatives similar to those used in the classroom. Student login information was provided on the individual student password sheet sent home early in the school year; parents should contact their child’s teacher for assistance.
Students should be able to use a variety of approaches for solving mathematical equations. As educators, we also want to help students understand the concept that numbers represent something. Bar modeling is a visual way for students to connect numbers to real values. This strategy requires a student to demonstrate that he/she understands the problem and knows what is being asked. Bar modeling becomes a key foundational skill in later grades as problems become more complex. For further detailed information on bar modeling, please click here.
Mathematics instruction prepares elementary and middle school students to master the applicable Common Core State Standards, regardless of grade level or resources used. Mastery of content in the standards helps to ensure a successful transition from fifth grade to sixth grade. Further, multiple data points are used to determine a student’s placement in an appropriate middle school math course. District 181 staff work collaboratively to continually review student data to ensure that instruction is meeting student needs.
The District’s Math Committee created a rubric based on the District’s math philosophy and identified aligned materials. The committee analyzed quantitative and qualitative information about the materials and reviewed research, then used that data to make a collaborative decision regarding which materials to pilot. During the pilot, teachers reflected on the materials to provide feedback on how well they aligned with the requirements of the CCSS, supported best practices in mathematics instruction, and assisted teachers in meeting the standards. At the end of the pilot, participating teachers completed a rubric, and both parents and middle school students completed a survey asking for their input. Following that effort, Math in Focus and Big Ideas were selected for District-wide implementation which began in the 2015-16 school year.