Social promotion often results in wildly disparate proficiency levels within a middle school math classroom. I am not making any judgment concerning social promotion. I am just stating the obvious. This results in a set of extreme challenges for middle school math teachers. Educational theory explains the individual student’s needs quite well: a teacher should identify the student’s zone of proximal development. This is the set of math concepts the student can master with assistance. The teacher then supports the student in learning these concepts with the necessary support also known as scaffolding. The extreme challenge comes when students in one classroom have zones of proximal development that range from kindergarten through and beyond their middle school grade level. Students with Individual Education Plans (IEP’s) and English Language Learners (ELL’s) add to this challenge.
Differentiation is often used to describe how teachers are to make the grade level curriculum accessible to all students. However, this assumes that the grade level curriculum lies within the zone of proximal development for all students in a classroom and this is often not the case. Common Core aligned curriculum has been misused by forcing all students to be taught the grade level curriculum regardless of their mastery of prior levels. When a consortium of math teachers developed “Principles and Standards for School Mathematics” (PSSM) in 2000 (the foundation of Common Core Mathematics), they laid out a sequence for how mathematical concepts could be mastered, K-12. Mastery of each level within Common Core is dependent on mastering the prior levels. So, rather than having all students in a classroom learn the same material, Common Core Math is better understood as a sequence of concepts that must be mastered level-by-level in order for a student to continue to grow in their mathematical thinking and proficiency.
State-mandated end of grade math tests are generally based upon the Common Core Math grade level only and not on growth through the Common Core Math levels. This causes many administrators to require math teachers to focus on teaching their grade level skills while providing little time for students to work within their zone of proximal development. This is a perfect recipe for widening achievement gaps. Students at or above grade level continue to make progress while students who are even a little behind grade level often fall further behind.
Fortunately, with technology and a focus on growth rather than grade level mastery, it is possible for math teachers to meet this extreme challenge and serve every student within their zone of proximal development. As a first career software engineer I followed with great interest the development of Khan Academy and had the chance to fully implement it for three years in a 100% minority middle school with 90% free and reduced lunch. When students were given the support and encouragement to work and grow at their own level they progressed an average of 2.25 years each school year. Growth was consistent when measured by race and gender. English Language Learners (ELL's) and students with Individual Education Plans (IEP's) made similar progress. I was able to continue to implement this program for three years because students were increasingly reaching grade level mastery from 13% to 33% the first year to 52% to 78% in three years.
Students were supported by ELL teachers, IEP teachers, after school tutors, and their math teacher to work within their zone of proximal development on courses in Khan Academy. They were also encouraged to master their math facts in Xtramath.org, both free tools with no advertising distractions. Students who were less than 2 years behind grade level were assigned specific prerequisite skills in Khan Academy along with the associated grade level skill. Students who were further behind and working above the 2nd grade level were assigned the "Arithmetic" course of study. This is a fast path through Common Core Arithmetic (addition, subtraction, multiplication, division, fractions, decimals, and negative numbers). Students below the third grade level were assigned the "Early Math" course, a complete Common Core aligned K-2nd curriculum.
Language learners were fully supported in learning mathematics regardless of their English proficiency level. All the Khan videos can be subtitled and translated into any language just like Youtube videos. There are 17 languages fully supported in Khan Academy. Language learners greatly benefit by completing one subject in their first language because it helps them to maintain their first language proficiency while mastering English. Students had clear and comprehensive math goals in their Individual Education Plans (IEPs) and progress was easily tracked in Khan Academy.
Due to administrator constraints grade level instruction was not eliminated. Instead, mini-lessons that aligned with Khan Academy middle school courses were developed. This allowed grade level instruction time to be economized and student work within their zone of proximal development to be maximized. Students practiced math facts in Xtramath.org until proficient and worked on individualized Khan Academy courses. Students were tutored individually and in pairs only after they attempted a skill, watched the associated Khan Academy video, and sought help from their partner. Students took responsibility for their own learning and were attentive when tutored.
Students were graded based on a "growth mindset" model. A large portion of their grade was based upon the amount of daily effort given to practicing skills in Khan Academy. Students were awarded laminated certificates when they completed a course or mastered their math facts. Students learned to appreciate the efforts of their peers and gave the same enthusiastic applause if a student completed the Khan Academy course for 8th Grade Math or for 2nd Grade Math. Each quarter students were given a color chart showing their growth using the Scholastic Math Inventory (SMI) adaptive test tool.
I am now retired and support math teachers who are interested in implementing Khan Academy in their classrooms. It is a great tool for online or partially online classrooms due to Covid-19. More importantly, it allows math teachers to fully respect and support the individual learning needs of each student and close achievement gaps. All my Khan aligned teaching materials are available free at https://www.teacherspayteachers.com/Store/Khan-Academy-Support-For-Middle-School-Math
