During the Superintendent’s two Elementary Math Discussion Forums on January 23rd and February 26th, 2018, summarized on the previous page, a number of solutions were proposed. The solutions are grouped into similar pedagogical strategies or ideas, and discussed in greater detail below. Each idea is given a title, the source of the idea, the problem it proposes to solve, a summary of the idea, and the history of its use and/or links to research or precedent for the idea. Several ideas are variations on a return to homogeneous grouping. The broader issue of homogeneous grouping, as distinguished from heterogeneous grouping, is discussed in a special issues page here. And the broader issue of acceleration is discussed here.
A. Same-Grade Homogeneous Grouping
Source: LCUSD Staff
Problem to be Solved: Lack of differentiation for advanced math learners; Improved teacher attention and resources for struggling learners
Summary: For grades 4, 5 and 6, students within a grade would be grouped by math ability and during math instruction time would go to the class best aligned with the individual student’s ability. Students would receive differentiated instruction particular to their group by a teacher, and then return to their regular heterogeneous classroom for non-math instruction.
History/Links: This used to be the normal practice in the upper elementary grades in LCUSD about seven years ago. The practice was abandoned in LCUSD because of parent complaints about their children being placed in the “wrong” group, because of uneven implementation of the policy across the three elementary schools (i.e. at one elementary school the students were kept in their math groupings for the entire school day), and lower self-esteem from negative labeling of students in lower groups. It should also be noted that homogenous grouping of students in math classes is the norm in the LCHS middle and high schools. LCHS and LCHS 7/8 currently offer two nominal tracks for mathematics — a “college preparatory” pathway, and an “advanced college prep” pathway.
B. In-Class Homogeneous Grouping
Source: LCUSD Staff
Problem to be Solved: Lack of differentiation for different levels of math learners
Summary: Also called the “math workshop model”, in-class homogeneous grouping does not require students to leave their homeroom class when it is math instruction time. Students are divided into groups by ability during math time based on a pre-test, which is administered before each unit or topic is taught. The grouping is re-done at each unit, which allows students to move up or down in group, thus addressing the concern that homogeneous grouping is too much like tracking. During math instruction, the teacher rotates between the groups, leading instruction or activities tailored for each group’s level of understanding, while the other groups either do independent work or are led by a parent volunteer or teaching assistant. The practice allows students to benefit from math instruction more closely aligned to their level of understanding, but requires more work from the teacher since he/she has to prepare different instructional plans for each group.
History/Links: Recommended by LCE Principal Blaney as a practice she utilized when she was an elementary teacher, in-class homogeneous grouping is less like tracking because every student has a chance to move up or down a group at each math topic, which occurs every few weeks. Blaney used to implement this practice with three groups during math instruction time. She usually benefitted from parent volunteers who helped lead one of the two groups she was not facilitating. During the second Elementary Math Discussion Forum, a teacher pointed out that this practice is already done by the Everyday Mathematics curriculum, which provide three differentiated group activities for each lesson plan. Parents respond that the level of differentiation is insufficient since acceleration is prohibited.
C. Cross-Grade Homogeneous Grouping
Source: LCUSD Staff
Problem to be Solved: Lack of differentiation for all levels of math learners
Summary: A variation on the first solution, cross-grade homogeneous grouping would expand on the idea and add the following elements:
- Synchronize the math instruction period in targeted grades (4th, 5th & 6th) to allow cross-grade grouping by ability. Students could take math classes in higher grades (i.e. single subject acceleration) if they meet the upper class prerequisites.
- Further, if the math period were synchronized during the 1st period, middle school math teachers could come to the elementary schools to teach advanced math topics (e.g. pre-Algebra or Algebra) to the most-advanced elementary students.
History/Links: The same research for A) is cited by supporters of this plan. In addition, longitudinal studies of mathematically gifted students in subject acceleration show no long-term emotional side effects and significant benefits in high-school, college, graduate school, early career and mid career. This practice is selectively used in private and select public school districts nationwide.
D. In-Class Subject Acceleration
Source: Parents
Problem to be Solved: Lack of differentiation for advanced math learners
Summary: This an alternative practice to same-grade or cross-grade homogeneous grouping. The practice involves allowing qualified students to work independently or in small groups using either accelerated printed or online mathematics curriculum such as IXL, EPGY, Khan Academy, Art of Problem Solving, Russian School of Mathematics, or Reasoning Mind. Students remain in their homeroom classrooms during mathematics instruction time and are excused from in-class lessons or work. Students need to show that they have already mastered the material that will be taught to the rest of the class. This is typically accomplished by having the teacher administer pre-assessments before the beginning of a math unit or topic.
History/Links: In-class subject acceleration is one of the most common and well-researched educational practices for providing advanced instruction in specific subjects to gifted learners. For a summary of research on gifted acceleration in mathematics, see the Davidson Institute’s summary of research articles on gifted mathematics instruction and summary of research on acceleration for gifted students. In-class subject acceleration in mathematics where students work independently at their own pace is the norm for some private schools like The Learning Castle in La Canada. In-class subject acceleration has also been allowed in a few, select cases by individual students in LCUSD in the upper elementary grades.
E. Math Intervention Resources
Source: Parents
Problem to be Solved: Lack of intervention resources for struggling math learners in elementary grades; Teachers giving passing grades to students who have not mastered grade-level standards
Summary: Create a comprehensive program of math intervention support in the elementary grades similar to what is in place in the middle and high schools. Math Intervention Program elements can include: peer tutoring from middle-school, high-school or even upper elementary school students; hiring math intervention specialists to work with individual students or groups of students; and providing reimbursement credits to families of struggling math students to obtain tutoring assistance from outside tutors or companies.
History/Links: Currently, the middle and high schools offer a plethora of math intervention resources: mandatory counseling sessions with student and parent if a student’s grade in math class falls below a threshold grade; after-school teacher-facilitated math labs are offered twice a week for any student needing help with homework or who is struggling in class; peer tutoring by high school students for middle school students in math is offered for part of the school year in the IRC after school; identified students are pulled out of their regular math class and placed in a remediation class with intervention specialists to attempt to bring the student back up to speed so they can re-integrate in their regular math class. In a similar fashion, the elementary school PTAs pay for reading intervention specialists to help students who are struggling in reading. Identified students receive one-on-one intervention from trained reading specialists at least once a week. Though the district insists that it provides math intervention resources for struggling math students in the elementary grades, this intervention is provided through the student’s regular classroom teacher and surveys of elementary parents show the level of intervention is often inadequate. Teachers and principals have been known to tell parents of struggling students off the record to seek tutoring support from private tutors or after-school math companies such as Mathnasium.
F. Math Labs (‘Pull Outs’)
Source: LCUSD Staff
Problem to be Solved: Lack of differentiation for advanced math learners; Lack of intervention for struggling math learners
Summary: If homogeneous grouping, or subject acceleration is not feasible, a compromise solution is to pull identified students or groups of students needing intervention and/or acceleration/advanced differentiation support out of their regular math instruction time, have the students meet in a designated “math lab”, and work in supervised groups or independently using accelerated, differentiated, or intervention curriculum. This is how GATE instruction is accomplished during the school day in the elementary grades. In the math lab, advanced students could use computer-based resources or curricula such as IXL, EPGY, Reasoning Mind, Art of Problem Solving, or Khan Academy, or printed curricula.
History/Links: There is precedent for using this solution both within and outside LCUSD.
G. Dual Math Track
Source: Parents
Problem to be Solved: Deficiencies with current K-5 curriculum; Parent disagreement with the type of math instruction used by Everyday Mathematics.
Summary: District should offer a dual track for elementary mathematics. Parents who prefer the constructivist approach of Everyday Mathematics may keep using it through 5th grade, while parents who prefer a traditional math curriculum like Math In Focus could switch. This would require purchase of additional textbooks or reversion to using old pre-Everyday Mathematics textbooks, and grouping students during math instruction to their chosen track, as well as re-assigning teachers to meet parent demand.
History/Links: Everyday Mathematics has been problematic in dozens of school districts that have adopted it over the years since it was first released in 1998 as summarized elsewhere on this site. Parent dissatisfaction with EM has resulted in parent battles with school districts and school boards all over the country. Multiple outcomes have resulted, from wholesale replacement of EM before its planned life expectancy (Pottsgrove, PA 2017, Radnor Township, PA 2015, Manchester, NH 2014, Seattle, WA 2014, Hookset, NH 2013, Haverford, ND 2013, Ithaca, NY 2012, Menlo Park, CA 2009, Reading, MA 2000) to parent flight from districts that chose to keep it (Conejo Valley, CA 2008.) A compromise solution — offering dual mathematics tracks — was reached in a number of districts in California during the height of the Math Wars in the late 1990s, among them Chico, Davis, Escondido, Mountain View, Orange, San Diego, and Torrance.
H. Math Academy
Source: Pasadena Unified School District (PUSD)
Problem to be Solved: Lack of differentiation or acceleration opportunities for advanced math students
Summary: Begun in PUSD four years ago, Math Academy is a program “aimed at radically accelerating the learning curve of mathematically gifted students by providing a curriculum that matches their abilities. The goal of Math Academy is to prepare these students to excel in the honors math and science programs at the most elite universities in the world.” In PUSD, the top 5% of math students are targeted, though the cutoff could be lowered by LCUSD if adopted. The curriculum begins in the 6th grade and proceeds through high school. Student take Math Academy courses instead of their regular math classes. Adoption of Math Academy in LCUSD would require aligning and approving PUSD’s Math Academy curriculum for use in our district, and dedicating resources to share or hire Math Academy instructors to teach the classes at district schools.
History/Links: More information about Math Academy can be found on the program’s website: http://www.mathacademy.us/ .
I. Homeschool Cooperative
Source: Parents
Problem to be Solved: Lack of differentiation or acceleration opportunities for advanced math students; Lack of intervention opportunities for struggling math students
Summary: First proposed at the first Elementary Math Discussion Forum on January 23, 2018, this idea would create a homeschool cooperative for students whose needs in some subjects like mathematics cannot be met in a traditional public school environment.
J. JPL/Caltech Mentoring Program
Source: Parents
Problem to be Solved: Lack of differentiation or acceleration opportunities for advanced math students
Summary: Volunteer JPL, Caltech and other educational or STEM institutional professionals would pair up with identified LCUSD students to mentor them in advanced mathematics. Students would enter the program by request of the parents or teacher, after taking an assessment to demonstrates that s/he has already attained grade-level proficiency in math. If the child passes this test, s/he is paired up with a volunteer mentor from JPL or Caltech (for math). The mentor would evaluate the student, evaluate possible online courses that the student can take during his/her regular math class, be available to answer student questions online, and be able to meet with the student at regular intervals to monitor progress, discuss the material, and guide the student. The district could pair up a small number of students with a single mentor, e.g., say up to 4 or 5 kids maximum. Since this is a proposal for acceleration, the number of mentors is very small because the number of kids that can be in these groups is small.
K. Improved Parent/Teacher Communication
Source: Parents and Teachers
Problem to be Solved: Poor communication between home and school
Summary: Improved parent/teacher communication is a catch-all category for the various solutions recommended to solve the problems of:
- Poor understanding of new math concepts by parents
- Low level of parent confidence/trust with math instruction
- Parents are attempting to solve the lack of student differentiation with their own solutions and are not understood or supported by the school
- Parents do not understand what standards, expectations and specific math topics are expected of students or what lies ahead
- Teachers believe they are already providing adequate and high quality differentiation but parents are simply not aware of it
Solutions suggested to improve communication include:
- More frequent parent/teacher conferences than once a year
- Provide more parent classroom observation opportunities
- Provide other means of communication from teachers to parents
- Teachers should identify supplemental resources available to parents
- School should provide a map or syllabus of standards / topics to be taught during the year, the sequence of topics, and expectations for mastery