Integrated Math - Frequently Asked Questions

Common Core State Standards for Mathematics (CCSSM) is a set of goals and expectations of skills and knowledge that students need. The standards are robust, rigorous and relevant to the real world. These standards are used to determine the content being taught within the curriculum at Lemont High School. CCSSM identifies critical components necessary for students to be successful in college or within their careers.

More than 40 states initially adopted the “Common Core” standards. Learn more about these standards.

The Standards for Mathematical Practice build on the National of Council of Teachers of Mathematics (NCTM) process standards. The eight practice standards are universal for all students from kindergarten through 12th grade. 

1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.

The Mathematical Practices are the processes, or methods, used to master the concepts.

One math skill that all high school students must demonstrate is “to write an equation of a linear function based on information.”

In the past, students were asked a question in this format: Given the point (2,5) and (7,25), write the equation of the line.

This is an example of a question using the Standards for Mathematical Practice: Jeff is trying to save to buy a new phone. After three weeks he had $14, and he continues to save the same amount every week. Four weeks later he has $32. Using Jeff’s information, create a function that can be used to calculate when Jeff will have the required $200 to purchase the new phone.

Various studies compare American students to those in other countries. For many years, two studies in particular – the Trends in International Mathematics and Science Study (TIMSS) and the Programme for International Student Assessment (PISA) have collected data that have shown American students are not among the world’s leaders in academic achievement in mathematics. For a specific example, the 2007 PISA detailed 15-year-old United States students to be 25th of 30 developed nations in math literacy and problem solving.

The curriculum often used in the United States can be described as “a mile wide and an inch deep.” The United States attempts to teach students a large quantity of concepts. However, a resulting consequence often is that students do not have the deep understanding of any one concept, but rather have a more shallow understanding of many concepts. Curricula in other developed countries result in students developing proficiency in a smaller number of important mathematical topics. Most high-achieving nations do not use a single-subject sequence (i.e., Algebra, Geometry, Trigonometry, etc.).

The combination of the Common Core State Standards for Mathematics and the Mathematical Practice Standards creates a set of content that is to be taught with an emphasis on the skills to be developed and practiced through problem solving and other techniques to deepen understanding. There are three shifts in mathematics as a result of implementation of the Common Core State Standards for Mathematics. 

• FOCUS: Focus deeply on what is emphasized in the standards so that students have a strong foundation. The quantity of standards is narrowed to increase the level of understanding of mathematics.
• COHERENCE: Think across grades to link major topics. This requires students to build new understandings on foundations built in previous years. The standards have a progression plan of how students learn from Kindergarten to 11th grade.
• RIGOR: In major topics, students pursue conceptual understanding, procedural skill and fluency, and application of concepts. Conceptual understanding means that students know how to get an answer rather than through a step-by-step procedure, and also understand the meaning of the answer. Procedural skill and fluency is needed, and teachers must structure time for students to practice core skills. Application of the mathematics to real-life situations is part of the curriculum.

The curriculum at Lemont High School is designed by Lemont High School’s faculty. The courses, sequence of topics within those courses, and methods of instruction and assessment all are designed by Lemont High School faculty. This has been true in the past, and it will continue to be true, as Lemont High School teachers incorporate the Common Core State Standards for Mathematics and Mathematical Practice Standards.

The names of courses and sequence of courses changed beginning with the 2014-15 school year.

In past years, Lemont High School taught the “traditional” approach to mathematics, with students completing a subject course – for example, Algebra I, Algebra II, Geometry and Trigonometry. Each subject is independent of others.

The “integrated” approach to mathematics creates a curriculum where students learn significant components of each subject each school year. Students will complete a course of Integrated Math I, Integrated Math II and Integrated Math III prior to taking a fourth-year math course.

In the real world, problems do not come in isolation. There are not “Algebra” problems and “Geometry” problems. The integration of mathematics allows students to decide what skill to use for a given problem. Algebraic, geometric or statistical skills can allow students to approach a problem with a variety of strategies. 

Integrated Math I will contain concepts of Algebra, Geometry, Statistics, Number and Quantity, and Functions. Both Integrated Math II and Integrated Math III will contain different concepts from those same categories. Each course will have different concepts. The curriculum is a coherent plan of those categories over a three-year period. Students are expected to build skills throughout the curriculum in all areas of study.

Lemont High School teachers have always been up-to-date with the best practices of teaching. Utilizing the best practices of instruction, the faculty uses researched methods of instruction to teach a curriculum that is designed from research-based models.

Technology will continue to be used to support and enhance the mathematics curriculum.

Lemont High School will continue to have high expectations for student mastery of mathematical concepts, with teachers helping students to learn how and why concepts are true, in addition to learning the process of solving the problems.

Yes. The curriculum found in the Integrated Math I, II and III courses will teach the same concepts as a ‘traditional’ curriculum. At the conclusion of Integrated Math III, students will be prepared for fourth-year math courses.

Additionally, the standards require students to think differently from past practices. They will be expected to think critically and to be able to justify their solutions to problems. Again, these practices work towards fulfilling Lemont High School’s mission.

While all students will take a similar pathway – Integrated Math I, Integrated Math II and Integrated Math II – there is a level of Integrated Math for honors-level students. Students may be placed into Integrated Math I Honors as freshmen using the placement criteria. Students who excel in Integrated Math I potentially can move up to the Integrated Math II Honors curriculum the following year.

While success in learning involves more characteristics than course curriculum, the integrated approach often is found in other countries that outperform the United States. The adoption of the integrated approach is newer in the United States. In the Journal for Research in Mathematics Education, a study through the University of Missouri revealed students in an integrated curriculum demonstrated higher student achievement when compared to students enrolled in traditional math classes. The study involved more than 3,000 students in 326 classrooms. Despite controlling for a multitude of variables, the organization of the curriculum was found to be a significant factor of predicting student outcomes.

Lemont High School knows that it will require more than a curriculum for students to be successful in mathematics. Longitudinal results from other countries and recent studies in the United States have led Lemont High School teachers to believe the integrated curriculum meets the school’s mission.

Lemont High School’s expectation is for teachers to stay current with the best instructional techniques within their given disciplines. Math teachers attend workshops and conferences and read articles about curriculum, assessment and instruction. In January 2013, math teachers formally began studying the Standards for Mathematical Practice. Many of the practices found in these standards already existed at Lemont High School. To strengthen the implementation of those standards, teachers adjusted instruction techniques during the 2013-14 school year.

In Summer 2013, the Mathematics Department studied various options of course sequencing when creating a curriculum based on the Common Core State Standards for Mathematics. The most effective instruction and most challenging curriculum were at core of the decision to transition to the Integrated Math curriculum beginning with the 2014-15 school year.

The Common Core State Standards for Mathematics identify specific standards students must learn in order to take advanced math courses. These standards are commonly referred to as STEM (Science, Technology, Engineering, Mathematics). Lemont High School’s faculty studied the STEM standards and determined the need for a semester course to focus on the STEM standards prior to a student’s enrollment in Calculus-level courses. Students at the honors level will be expected to enroll in a one-semester STEM Math Honors course concurrently with Integrated Math III Honors. Students at the academic level of Integrated Math III have the option to take STEM Math concurrently with Integrated Math III or to enroll in STEM Math after completing Integrated Math III. Each student can determine how the curriculum best fits into his/her goals for high school, college or the workforce.

No. There is a significant amount of mastery of content required in the areas of algebra, functions, statistics and geometry in Integrated Math I. Mastery of this content is necessary for success in Integrated Math II.

Yes. Successful completion of Integrated Math I Honors, Integrated Math II Honors, Integrated Math III Honors and STEM Math Honors will prepare students for AP Calculus BC or AP Statistics. Students completing levels of Integrated Math I, Integrated Math II and Integrated Math III will be qualified to enroll in AP Statistics.

The NCAA has approved the Integrated Math curriculum.

Additionally, performance on standardized tests (ACT, SAT, etc.) will serve as clear evidence of a student’s success.

If the family disagrees with the placement based on a student’s mathematical mastery as demonstrated on the EXPLORE test (and other data when provided), the student’s parent/guardian should contact the Mathematics Department Chair to discuss the placement.

While the offering of an 8th grade course at Lemont High School is a decision made annually, Lemont High School and Old Quarry Middle School currently offer 8th grade students the opportunity to enroll in Integrated Math I Honors if they have met the criteria based on past course completion and placement test results.

The courses of “Pre-Essentials for Integrated Mathematics” and “Essentials for Integrated Mathematics” will prepare students for the rigor and detail required to master Integrated Math I, Integrated Math II and Integrated Math III. The Essentials for Integrated Mathematics course is intended to prepare students to enter the Integrated Math curriculum the following year. Both the skills and processes needed for success will be the focus of the 'Essentials' course.

Additionally, the courses of Integrated Math I and Integrated Math II provide students the option to enroll in a double-blocked section (i.e., the course meets daily). The additional time in the classroom will provide support for students.

The current pathway at Lemont High School has students taking Algebra I, Algebra II, Geometry (with Trigonometry) and Pre-Calculus. This is not an option of course sequence with the adoption of the Common Core State Standards for Mathematics in the state of Illinois. Schools must select either the traditional (Algebra, Geometry, Advanced Algebra) or integrated (Integrated Math I, Integrated Math II, Integrated Math III) pathway.

For several years, data has shown that the percentage of Lemont High School students meeting or exceeding state standards has grown on a limited basis. While this is an accomplishment for the majority of the students, the school’s faculty and administration aim to have the percentage of students demonstrating mastery to increase from the current level, and also desire for students to master mathematics at a deeper level with a stronger understanding. 

There are multiple approaches to reach the same endpoint. It is Lemont High School’s belief that the Integrated Math pathway will provide a better opportunity for students to reach their potential.

Lemont High School continues to analyze the success of its students. In the classroom, students have common assessments for local verification of their ability to demonstrate proficiency. Additionally, the school continues to study the success of students on standardized tests.

Lemont High School welcomes your questions. The Mathematics Department Chair is Kathy Young, who can be reached at (630) 243-3263, or via e-mail by clicking on her name. Our intent is to educate students and parents/guardians alike about the research-based decisions made in relation to the adoption of the Common Core State Standards for Mathematics.