VIDEO: JOHN HATTIE ANSWERS
“Tracking” or “ability grouping” is the widespread practice of grouping students by their academic ability. At the root of the practice is the question of how to educate large groups of students whose backgrounds and abilities differ widely. The assumption is that if students are grouped by their abilities, then they can get the instruction they need to learn the academic material. The real
question, of course, is “does it work?”
Professor John Hattie is a researcher in education. His research interests include performance indicators, models of measurement and evaluation of teaching and learning. John Hattie became known to a wider public with his two books Visible Learning and Visible Learning for teachers. Visible Learning is a synthesis of more than 800 meta-studies covering more than 80 million students. According to John Hattie Visible Learning is the result of 15 years of research about what works best for learning in schools. TES once called him “possibly the world’s most influential education academic”.
Hear what he has to say about tracking HERE.
All students can access rigorous coursework throughout middle school, and still access advanced coursework in high school (such as AP Calculus, AP Statistics or concurrent enrollment college credit bearing courses) without taking Algebra in 8th. We can simply move the decision point from middle school to high school.
Students are being asked to solve complex problems and communicate their thinking at an earlier age. They must exhibit deep conceptual understanding, fluency and be able to transfer their learning to new contexts. Meanwhile, they are also being asked to learn to work collaboratively to solve unstructured problems, construct viable arguments and critique the reasoning of others. The days of relying solely on procedural knowledge to get by are behind us. This deeper, more robust understanding of what it means to do mathematics takes more time than the traditional rote instruction of yesterday.
Students are introduced to the idea of solving for an unknown, and letting a symbol represent the unknown in the primary years of elementary.
The traditional algebraic sequence (solving for x) begins in grade 6 and culminates in grade 9. Topics that were in a first year Algebra course are now in 7th and 8th, with Algebra 2 topics now being introduced in Algebra 1. See more on this topic below.
Not only are the topics taught in grades 6-9 are critical for a strong foundation for high school mathematics, ACT.org surveyed college professors of first year credit bearing courses to determine which topics were pre-requisites for success in college mathematics. The vast majority of the top 20 topics listed are now taught in 6-9. Furthermore, the mathematics that we all use as consumers and citizens is also taught in 6-8. These critical topics must not be rushed, but taught to mastery to ensure the success for all our students, regardless of their life path.
Increased Rigor of Grade 8 and Algebra I standards
Success in Algebra I is crucial to students’ overall academic success and their continued interest and engagement in mathematics. Based on perceived redundancies in the former standards during the middle grades, districts have increasingly offered the former Algebra I course in Grade 8 to enhance rigor. The new Pre-K-8 standards, however, represent a tight progression of skills and knowledge that is inherently rigorous and designed to provide a strong foundation for success in the new, more advanced, Algebra I course.
The new Grade 8 standards are of significantly higher rigor than the former Grade 8 standards.
The new Grade 8 standards address the foundations of Algebra by including content that was previously part of the Algebra I course standards, such as more in-depth study of linear relationships and equations, a more formal treatment of functions, and the exploration of irrational numbers. The new Grade 8 standards also include geometry standards that relate graphing to algebra in a way that was not explored in the previous Grade 8 standards. In addition, the statistics presented in the new Grade 8 standards are more sophisticated than those previously included in middle school and connect linear relations with the representation of bi-variate data. The new grade 8 standards address more algebra topics than our previous grade 8 standards.
The new Algebra I course builds on the new Grade 8 standards and is correspondingly more advanced than the former Algebra I course.
Because many of the topics previously included in the former Algebra I course are in the new Grade 8 standards, the new Algebra I course starts with more advanced topics and includes more in depth work with linear functions, exponential functions and relationships, introduces quadratic relationships, and goes beyond the previous high school standards in statistics.
Adapted from: Making Decisions, Mass DOE 2011
SFUSD adopted the pathway to the right in 2014. See their success story at http://www.sfusdmath.org/
Southampton Union Free School District is creating a pathway to Calculus open for all students that take Algebra in grade 9.
CHANGING EXPECTATIONS FOR MATHEMATICS ACHIEVEMENT
Today’s children are growing up in a world very different from the one even 15 years ago. Seismic changes in the labor market mean that we are living and working in a knowledge-based economy—one that demands advanced literacy and Science, Technology, Engineering and Mathematics (STEM) skills, whether for application in the private or public sector. Today, information moves through media at lightning speeds and is accessible in ways that are unprecedented; technology has eliminated many jobs while changing and creating others, especially those involving mathematical and conceptual reasoning skills. One characteristic of these fast-growing segment of jobs is that the employee needs to be able to solve unstructured problems while working with others in teams. At the same time, migration and immigration rates around the world bring diversity to schools and neighborhoods. The exponential growth in interactions and information sharing from around the world means there is much to process, communicate, analyze and respond to in the everyday, across all settings. For a great majority of jobs, conceptual reasoning and technical writing skills are integral parts to the daily routine.
To prepare students for the changes in the way we live and work, and to be sure that our education system keeps pace with what it means to be mathematically literate and what it means to collaboratively problem solve, we need a different approach to daily teaching and learning. We need content-rich standards that will serve as a platform for advancing children’s 21st-century mathematical skills —their abstract reasoning, their collaboration skills, their ability to learn from peers and through technology, and their flexibility as a learner in a dynamic learning environment. Students need to be engaged in dialogue and learning experiences that allow complex topics and ideas to be explored from many angles and perspectives. They also need to learn how to think and solve problems for which there is no one solution—and learn mathematical skills along the way.
INCREASINGLY DIVERSE LEARNER POPULATIONS
The need for a deeper, more innovative approach to mathematics teaching comes at a time when the system is already charged with building up language skills among the increasingly diverse population. Students who are English Language Learners (ELLs)/Multilingual Learners (MLLs) now comprise over 20% of the school-age population, which reflects significant growth in the past several decades. Between 1980 and 2009, this population increased from 4.7 to 11.2 million young people, or from 10 to 21% of the school-age population. This growth will likely continue in U.S. schools; by 2030, it is anticipated that 40% of the school-age population in the U.S. will speak a language other than English at home. (1) Today, in schools and districts across the U.S., many students other than those classified as ELLs are learning English as an additional language, even if not in the initial stages of language development—these children are often described as “language minority learners.” Likewise, many students, large numbers of whom are growing up in poverty, speak a dialect of English that is different from the academic English found in school curriculum.
Each of these groups—ELLs/MLLs, language minority learners, and students acquiring academic English—often struggle to access the language, and therefore the knowledge that fills the pages of academic texts, despite their linguistic assets. Therefore, the context for this new set of Mathematics Standards is that there is a pressing need to provide instruction that not only meets, but exceeds standards, as part of system-wide initiative to promote equal access to math skills for all learners while capitalizing on linguistic and cultural diversity.
All academic work does, to some degree, involve the academic language needed for success in school. For many students, including ELLs/MLLs, underdeveloped academic language affects their ability to comprehend and analyze texts, limits their ability to write and express their mathematical reasoning effectively, and can hinder their acquisition of academic content in all academic areas in which learning is demonstrated and assessed through oral and written language. If there isn’t sufficient attention paid to building academic language across all content areas, students, including ELLs/MLLs, will not reach their potential and we will continue to perpetuate achievement gaps. The challenge is to design instruction that acknowledges the role of language; because language and knowledge are so inextricable
In summary, today’s children live in a society where many of their peers are from diverse backgrounds and speak different languages; one where technology is ubiquitous and central to daily life. They will enter a workforce and economy that demands critical thinking skills, and strong communication and social skills for full participation in society. This new society and economy has implications for today’s education system—especially our instruction to foster a deeper and different set of communication and critical thinking skills, with significant attention to STEM.
STUDENTS WITH DISABILITIES AND THE STANDARDS
One of the fundamental tenets guiding educational legislation (the No Child Left Behind Act, and Every Student Succeeds Act), and related policies over the past 15-years, is that all students, including students with disabilities, can achieve high standards of academic performance. A related trend is the increasing knowledge and skill expectations for Pre-K-Grade 12 students, especially in the area of reading and language arts, required for success in post-secondary education and 21st Century careers. Indeed, underdeveloped literacy skills have profound academic, social, emotional, and economic consequences for students, families, and society.
Overall, the number of students with disabilities is increasing nationwide, as is their access to the general education curriculum, and participation in the state ELA and mathematics assessments. Attaining proficiency and graduating with a regular high school diploma are areas where significant improvements are needed. Therefore, each student’s individualized education program (IEP) must be developed in consideration of the State learning standards and should include information for teachers to effectively provide supports and services to address the individual learning needs of the student as they impact the student’s ability to participate and progress in the general education curriculum. In addition to supports and services, special education must include specially designed instruction, which means adapting, as appropriate, the content, methodology or delivery of instruction to address the unique needs that result from the student’s disability. By so doing, the teacher ensures each student’s access to the general education curriculum so that he or she can meet the learning standards that apply to all students. The Blueprint for Improved Results for Students with Disabilities focuses on seven core evidence-based principles for students with disabilities to ensure they have the opportunity to benefit from high quality instruction and to reach the same academic standards as all students
The goal of a K-12 mathematics curriculum shouldn't be to get students through calculus but to give students a strong foundation in mathematics that will prepare them for a range of college majors.
The United States has fallen into a seriously dysfunctional system for preparing students for careers in science and engineering, guaranteeing that all but the very best rush through essential parts of the mathematics curriculum and then are forced to sit and spin their wheels while they try to compensate for what was missed. It will take time and work by all involved to repair the transition from high school to college. We cannot afford to wait.
“Many communities are finding that students who start Algebra early do not necessarily end up studying more mathematics.”
~Cathy L. Seeley, Past President NCTM
1. Public school students in grade eight shall have the opportunity to take high school courses in mathematics and in at least one of the following areas: English, social studies, languages other than English, art, music, career and technical education subjects or science courses.
3. Such opportunity shall be provided subject to the following conditions: The superintendent, or his or her designee, shall determine whether a student has demonstrated readiness in each subject in which he or she asks to begin high school courses in the eighth grade leading to a diploma.
The Regulation calls for the opportunity to be accelerated in Math and at least one other subject, however the determination of readiness for acceleration is made by the superintendent. If a student has mastered the intermediate (Gr 5-8) Math Standards, and a determination (using a consistently applied local policy) is made that a particular student would benefit from acceleration, AND the student asks to be accelerated, then the district must offer the opportunity. If the above does not happen, then it is conceivable that there may not be middle level students who demonstrate readiness for high school course work in a particular school or district. There is no mandate to provide acceleration if the district concludes that this is the case.