District High School Mathematics Curriculum Framework: Fill & Download for Free

Note regarding Advanced Placement (AP) founded in 1954, International Baccalaureate (IB) founded in 1968, and Advanced International Certificate of Education (AICE) by Cambridge first awarded in 1997.AP is open to high school students only, 9th to 12th grade. There are opportunities to earn “AP Diplomas” which are awards of merit and not a substitute for an accredited high school diploma from a U.S. public or private high school. AP is more common in the United States and Canada.IB consists of three programs: Primary Years Programme for ages 3–12, first offered in 1997; Middle Years Programme for ages 11–16, first offered in 1994; Diploma Programme for ages 16–19, first offered in 1968. Most high schools that offer IB programs offer a “Pre-IB” program, which is not part of the Middle Years Programme, for 9th and 10th graders in preparation for the Diploma Programme for 11th and 12th graders. An “IB Diploma” is an award of merit and not a substitute for an accredited high school diploma from a U.S. public or private high school. A few elementary and middle schools across the U.S. are beginning to offer Primary Years and Middle Years Programme, which are more common in other countries.Cambridge consists of four programs: Cambridge Primary for ages 5–11, Cambridge Secondary 1 for ages 11–14, Cambridge Secondary 2 for ages 14–16, and Cambridge Advanced for ages 16–19. Some high schools have begun to offer Cambridge Secondary 2 and Cambridge Advanced. Earning an “AICE Diploma” is also not a substitute for an accredited high school diploma from a U.S. public or private high school. Cambridge programs are relatively unknown in the U.S., but given that there are about a million Cambridge learners from 10,000 schools in 160 countries, people in higher education are indeed aware. I would expect some elementary and middle schools in the U.S. to begin piloting Cambridge programs soon, if they haven’t already.I would consider IB and AICE more world-renowned programs than AP, but no clear advantage or disadvantage in college admissions. The only potential advantage or disadvantage to the student is if he(she) is more adept to learning the IB way instead of the AICE way, for example.SOURCE: www.scoreatthetop.comNOTE: some of this is opinion so feel free to make your own conclusions and formulate your own opinions.AP, IB, and AICE Programs: A Brief ComparisonAP ― Advanced PlacementMost everyone in high school knows about College Board’s AP courses and exams. As the name implies, the curricula for these classes are more rigorous than non-AP classes in the same subject, and high scores on the year-end exams may garner college credit and advanced placement into college classes. More importantly, doing well in AP courses better prepares you for college and improves your chances for college admission. College Board recognizes five levels of distinction* among students who receive high scores on a designated number of AP exam.More recently, the College Board implemented their AP Capstone™ diploma program with three principal parts:SeminarResearchAP courses and examsStudents typically take AP Seminar in the 10th or 11th grade, followed by AP Research in their senior year. Students who earn scores of 3 or higher in AP Seminar and AP Research and on four additional AP exams will receive the AP Capstone Diploma™. Alternatively, students who earn scores of 3 or higher in AP Seminar and AP Research will receive the AP Seminar and Research Certificate™.* AP distinctions:AP ScholarGranted to students who receive scores of 3 or higher on three or more AP Exams.AP Scholar with HonorGranted to students who receive an average score of at least 3.25 on all AP Exams taken, and scores of 3 or higher on four or more of these exams.AP Scholar with DistinctionGranted to students who receive an average score of at least 3.5 on all AP Exams taken, and scores of 3 or higher on five or more of these exams.State AP ScholarGranted to the one male and one female student in each U.S. state and the District of Columbia with scores of 3 or higher on the greatest number of AP Exams, and then the highest average score (at least 3.5) on all AP Exams taken.National AP ScholarGranted to students in the United States who receive an average score of at least 4 on all AP Exams taken, and scores of 4 or higher on eight or more of these exams.IB: International BaccalaureateThe IB program, too, has become an established fixture in many schools across the US. Students can receive an IB diploma, and even add AP courses and exams to the IB curriculum. The IB Diploma framework requires the study of two languages and diverse cultures; it includes required courses within each of six subject groups:Studies in Language and LiteratureLanguage AcquisitionIndividuals and SocietiesExperimental SciencesMathematics and Computer ScienceArtsIB students also take a Theory of Knowledge course, write a 4,000-word Extended Essay, and complete 150 CAS (Creativity, Action, and Service) hours. They must take at least 3 higher level courses (a student takes either a standard level or higher level course and exam in a subject, but not both). Students must earn at least 24 points (based on exam scores of 1 to 7 and the Extended Essay) and complete the equivalent of six 2-year courses to receive an IB diploma.Many former IB students say the extended essay was the most satisfying and challenging thing they did in high school, because it prepared them well for college research. In today’s average high school curriculum, it’s rare to find such an emphasis on writing!Due to its rigorous nature, preparation for the IB program is offered through the IB Middle Years curricula in the 9th and 10th grades or through other accelerated curricula.So how do colleges view the applicant who has followed an IB curriculum? It depends. While institutions like Johns Hopkins and Bucknell University view IB and AP as equal in academic rigor, schools like Stanford and University of Chicago judge IB coursework to be more rigorous than AP. You can always call a college admissions office to ask for their perspective on curricula.By scoring well on IB exams, students can receive college credit or advanced standing, just as they can for top AP exam scores. For instance, Florida State University (FSU) will award up to 30 semester hours of credit for the IB diploma. At the University of Florida, for incoming freshmen who receive credit for scores of 4 or higher on both higher level and standard level IB examinations, a maximum 45 credit hours can be applied toward college-level courses. Florida’s northern neighbor school, Oxford College at Emory University, will grant up to twelve hours of credit for IB scores of five, six, or seven on the higher-level examinations. An IB curriculum, combined with the right scores on the Higher Level exams, provides excellent chances for placement beyond introductory courses – with college credit to boot.AICE: Advanced International Certificate of EducationThe University of Cambridge’s AICE Diploma program is the newest advanced curriculum in the United States; it has long been implemented in Europe and around the globe. Currently, AICE is more akin to the International Baccalaureate in that both diploma programs offer a wide range of courses, and stress a global perspective. Between 1997 and 2000, AICE curricula were successfully piloted in Florida, where today the inclusion of AICE classes continues to grow and receive state legislative support.Students who complete an AICE course then take A- or AS-level exams that can lead to an AICE Diploma. Students must pass six credits worth of examinations. At least one examination must come from each of these three subject groups:Mathematics & SciencesLanguagesArts & HumanitiesAdvanced Subsidiary (AS) Level exams count for one credit and covers the first year of the two-year A Level curriculum. Advanced (A) Level exams count for two credits and cover approximately two years of college-level curriculum in a subject.The University of Cambridge International Examinations maintain a list on their website of US universities that have provided written statements of their AICE (which includes AS and A Levels) recognition policy. Do the schools you’re applying to recognize AICE credits? And like AP and IB, students with high exam scores can receive college credit and advanced standing; a challenging AICE curriculum is excellent preparation for college and can improve chances for college admission. In fact, all public universities and community colleges in Florida award up to 30 hours of college credit for AICE exams passed. As with virtually any questions regarding school policies, an office of admissions is the best source of answers regarding credits.ComparisonsSo how does AICE compare with IB and AP? All three programs are well established in high schools and recognized by universities around the country. Both AICE (AS and A Level) and IB are accepted at universities around the world, too. The main difference between AICE and IB is the flexibility of the AICE Diploma. Students have the freedom to create their own educational experience within the three AICE curriculum areas. We feel that AICE combines the best of both AP and IB in that students can pick and choose what courses they want but still earn an internationally-recognized diploma.Here’s an important fact to account for in the college application process. On the Common Application (accepted by 550+ colleges), AICE is not recognized like AP, IB, and even Dual Enrollment; there’s no pull-down menu from which to select AICE. But that doesn’t mean colleges don’t recognize AICE! As the newest of the advanced academic program in the US, AICE is described in a high school’s profile that is sent to colleges along with a student’s official high school transcript. There will be no problem with college admission.Our students tell us that IB Higher Level courses are harder than their AP counterparts, while IB Standard Level classes are not quite as hard…and that AICE courses don’t seem quite as hard as AP or IB courses.In any case, here’s one crucial difference between AP and IB exams: IB has significantly more emphasis on writing than AP. The IB exams, unlike AP, rarely contain multiple choice questions. Students answer in essay form.Finally, keep this all-important point in mind as you plan which high school courses you’re going to take: colleges value rigor of curriculum above all else, so taking AP, IB, or AICE serves you better than enrollment in Honors and most Dual Enrollment classes.

CURRICULUM AS A CHANNEL OF INFLUENCE: WHAT SHAPES WHAT IS TAUGHT TO WHOM?Policies, practices, and resources of the federal government, states, districts, schools, and teachers all play roles in influencing the development of curriculum and instructional programs, their implementation, and thus, what is actually taught to particular students. Exploring curriculum as a channel of influence means addressing:Policy decisions about curriculum and resources to support the curriculum,Development of instructional materials and programs, andProcesses and criteria for selecting instructional materials.CURRICULUM IN THE EDUCATION SYSTEMImplications of Policy DecisionsMany states play prominent roles in determining public school curricula—the content outlines and sequences of topics that, as a whole, specify what mathematics, science, and technology content students are to learn. This state role has expanded considerably as state standards, curriculum frameworks, and accountability measures have emerged as key strategies in the search for educational improvements (National Science Foundation [NSF] U.S. Department of Education [USDoE]. State education agencies may establish high-school completion requirements or exit exams, which, in effect, often define the core content students are expected to learn.Some state policies directly address the intended curriculum and the resources needed to enact it, as well as other facets of the education system that affect curriculum, such as regulations governing remedial or special education programs. State policies addressing student access to classroom laboratories and information technologies also can influence what is taught. Accreditation protocols, including compliance reviews of federally funded programs, place increasing demands on schools to clearly define and support mathematics, science, and technology content congruent with state learning standards and frameworks.The federal government influences the school curriculum mainly through policy decisions that affect resource allocations. For example, NSF provides funds for science, mathematics, and technology materials-development projects. USDoE also supports programs that may implicitly or explicitly encourage particular visions of mathematics, science, and technology education, as well as particular strategies for attaining these visions, for example, through enactment of the Eisenhower Professional Development Program (Dwight D.Eisenhower Mathematics and Science Education Act, PL 103–382). On occasion, federal government officials make use of the “bully pulpit” to issue direct statements about curriculum. For example, fueled by concerns about U.S. student achievement results in the Third International Mathematics and Science Study (National Center for Education Statistics [NCES], 1996), the Secretary of Education emphasized the importance of algebra and geometry instruction at earlier ages for all students.School district policies and practices such as graduation requirements and course offerings also affect the range and depth of science, mathematics, and technology content in schools. These policies, in turn, are influenced by community values and culture, including traditions and expectations regarding what schools should teach and what resources should be allocated to mathematics, science, and technology education. In addition,school-based decisions about class scheduling and the time allotted for science, technology, or mathematics instruction can influence the quality of the programs offered to students (Council of Chief State School Officers [CCSSO]. For example, programmatic “tracks”—combined with expectations about what particular students can or should learn, and what should be taught to whom— often reflect school or district level policy.The curriculum channel is linked to the other components of the education system in multiple ways. Teacher development programs, the use of assessment and accountability to spur educational reform, and public influence on policy decisions may directly affect the school curriculum. These factors will be addressed in later chapters.

As a 20+ year veteran teacher, what I observe is that many bright but disadvantaged students end up underperforming. That underperformance is directly a result of what is happening in America’s classrooms.Here are the two main culprits:I. Adherence to failed teaching philosophyConsider the fact that wealthy parents are more likely to take their children to museums……or national parks…… or book stores.Kids from economically advantaged backgrounds are more likely to be read to, to spend free time reading, to watch educational television. They are more likely to have cultural experiences that imprint knowledge into long term memory.Kids from less advantaged backgrounds tend to spend more time watching TV……and generally have fewer of the experiences that build up knowledge in long term memory. So they enter school at a deficit. That’s where current teaching models come into play.This requires a bit of context.The Traditional Model strongly emphasizes having an ordered learning environment where the teacher can transmit knowledge to the students. This model recognizes that learning is dependent of individual students focusing on specific tasks to learn specific material. When teachers demonstrate a skill and have students practice what the teacher demonstrates, they are using the traditional model of instruction.The Progressive Model places emphasis on inquiry learning. Instead of the teacher explaining or showing, the teacher’s job is to set up conditions where the student can explore an idea, usually in groups, and construct their own understanding. Experts who advocated the Progressive Model often touted “productive chaos” where students were moving about the classroom and sharing ideas. The key feature of this model is that knowledge is de-emphasized. As far back as the early 1900s, progressive educators were saying that it doesn’t matter if students know X because they can go to a library and look X up.22 years ago, when I was earned my first credential, my state of California had fully embraced the progressive model. My first experiences observing classrooms were a shock as almost every assignment was group work, called Cooperative Learning, with almost no individual assignments. Math instruction revolved around group learning projects. I never once saw students practicing times tables or what appeared to be math problems. My district had adopted the Mathland program that failed to teach even the most basic of mathematical skills.How did we get here?According to Chris Wolski, American schools have abandoned knowledge in favor of emotionalism. It’s certainly true that schools have abandoned the idea that transmitting knowledge is an important component of education.In the 1970s, sociologists Pierre Bourdieu, Basil Bernstein and Michael FD Young published Knowledge and Control, a work that argued that the traditional way of transmitting knowledge was actually an artificial construct by ruling elites designed to keep the working class down.The book raised questions rarely asked before about the basics of formal education: the curriculum, examinations, subjects, definitions of intelligence, the teacher’s authority. School knowledge, Young suggested, could be seen as a ruling-class construction designed to ensure working-class children failed and meekly took their places on factory assembly lines.The ideas expressed in Knowledge and Control appealed to a new generation of teachers who had gone to college during the height of the Counterculture movement. Young “hippie” teachers in K-12 and higher education were eager to implement something the opposite of what had been done traditionally.While every kid didn’t end up in a non-school, the de-emphasis on knowledge would end up harming the education of all students.As I was entering the profession, the general public came to understand that our educational system was generally failing our students. Teaching practices that de-emphasized knowledge and rote practice, shockingly, produced students with little knowledge and dismal skills. Parents, and most teachers, sought a more balanced approach to education. But even while parents and effective teachers wanted to step back from the progressive model, education professors and activists wanted to move even further from traditional teaching.One of the better ideas to come from the traditionalist camp was the idea of a Common Core of knowledge as proposed by English professor E. D. Hirsch, Jr.Hirsch is the author of numerous books such as Cultural Literacy: What Every American Needs to Know, The Knowledge Deficit: Closing the Shocking Education Gap for American Children, and Why Knowledge Matters: Rescuing Our Children from Failed Educational Theories. Through his writing Professor Hirsch popularized the idea of a Common Core of knowledge that all students should learn, and there was a push to implement such a Common Core of knowledge.Hirsche has used the tem Mathew Effect to describe what’s happening in education.In education, this refers to the accumulation of advantages those with knowledge have over those with less knowledge.As schools emphasize things like group work, critical thinking and technology, those who come to school with less knowledge fail to make the same progress as the students who come to school knowing lots of stuff.Eventually Michael FD Young, The counterculture class warrior who opposed traditional education would join ED Hirsch in pushing for a a re-emphasis on knowledge.Today, its author has changed sides in the knowledge wars. Like the American ED Hirsch, Young has become a guru for the growing number of teachers who argue that children need knowledge and lots of it. He broadly supports the former Education Secretary Michael Gove’s curriculum reforms restoring academic subjects to pre-eminence. Some quote his book Bringing Knowledge Back In (2008) as a sacred text, just as Knowledge and Control was to their parents’ generation. Schools should teach things that children can’t learn elsewhere, Young now argues. There’s no point in them otherwise.Since these groups roughly correspond to socioeconomic status, we can see that the Progressive Educational model with it’s deemphasis on knowledge and its overemphasis on soft skills advantages the economically advantaged over the economically disadvantaged.II. Chaotic classrooms harm learning of disadvantaged.I have a friend I’ll call Karen. Karen is an English teacher turned stay-at-home mom. Karen is the kind of liberal who gives money to the ACLU and Planned Parenthood and uses the word “Nazi” as an adjective when describing Republicans. She and her husband lived in the upscale Cherry Hill neighborhood of Denver, and sent their only child to the best public middle-school in the city. This school also receives students from a less affluent neighborhood.During his 6th and 7th grade school years, Karen would call me and tell be about the bullying and disruption going on at the school, about students screaming profanity in the hall, about students who weren’t even in the class entering the room simply to cause disruption.This year Karen and her husband, Anders, put their son in an elite (non-religious of course) private school. I was recently told how nice it was not to have students wandering the classroom all period either trying to copy answers or mess up your work, and to not have class interrupted with profanity fueled outbursts. That is a fine solution for a couple like Karen and Anders with one child and a high income.But what about the kids left behind? What about the kids who’s parents cannot possibly afford an elite private school?And I know this won’t be popular with some readers but… what about that kid in the picture above about to throw a desk across the room?Isn’t he being cheated as well? Doesn’t he deserve not just a better future, but a better present?As I’ve described the chaotic conditions that exist in classrooms in my previous answers, some readers have exhibited an antipathy towards kids who scream at teachers and disrupt class. But the fact is, they’re not just disrupting the learning of their fellow students. Their behavior is disrupting their own learning. This child preparing to throw the desk didn’t create the system that allows him to avoid schoolwork by engaging in disruptive behavior. That system was created by experts with doctorates in Education, Sociology and Law, experts rewarded with both generous paychecks and the power to impose their philosophical whims on children who can’t possibly know better. This disrupting, that the student above is enjoying in the moment, isn’t just cheating his schoolmates out of an education. It’s cheating him as well.The fact that he’s about to throw a desk at a fellow student doesn’t mean he’s dumb. He likely did the 6th grade version of a Cost–benefit analysis of throwing a desk and realized that it’s not going to cost him anything and it will enhance his social standing among peers. Maybe he has the cognitive ability to go to college. Maybe if he were in a calm, structured classroom, where he had no choice but to be civil and productive, he could grow up to be a Materials Science Engineer or an Oncologist. But the time he’s losing to his own classroom disruption is time that isn’t improving his academic skills or knowledge base.Someday in the not-too-distant future, that boy is going to be a man. The opportunities he has as an adult will result from how productively his educational time is used during the about 2,200 days he spends in his 1st -12th grade education.If he is allowed to waste this time, he is going to be educationally disadvantaged for the rest of his life. If my own experience as a young man with a learning disability and my 22 year career have taught me one thing, educational progress cannot take place until the student has a calm orderly place to learn.How did we get here?When I started earning my first credential 23 years ago, the philosophical trend was the “progressive model” of education which dated back to the early days of the 20th Century. Intellectuals and educational theorists like John Dewey proposed that education should be about doing, not learning.The idea was that if a teacher or a book imparted something to a student, that bit of learning lacked meaning and authenticity. But if the student discovered or “constructed” his own knowledge that would be more meaningful. One can see the reasonableness in the argument. A scientist who makes a discovery during an experiment would likely communicate that discovery better than he could communicate something he learned doing background research before the experiment.The progressive model of education favored the idea of students constructing their own knowledge, rather than having knowledge dispensed to them by an expert or a “sage on the stage” as progressives like to say dismissing teachers who lecture. And as I said, to a certain extent this is true.Hélio Gracie was able to construct the some of the most profound knowledge on the subject of ground grappling of any martial artist in history, and did so through the intense experimentation of Jujitsu competition and life-or-death street challenge matches.Likewise Chinese grappling master Tung-Sheng Ch'ang became one of the world’s leading experts in throws by constructing his own knowledge over decades of competition during which he was never defeated by an opponent.But before either of those masters could construct their profound knowledge in their respected specialties, they first had to learn through direct instruction and repetition. And that is something that the progressive model I was originally trained in leaves out. The progressive model wasn’t particularly strong on discipline either.By the time I started earning my MA in Education, the progressive model was being bullied out to the way by the Critical pedagogy model of teacher training. Many ed-schools were claiming to teach the Progressive Model, but what they were teaching was actually Critical pedagogy. This was definitely the case for many of my graduate Education classes.So what is Critical pedagogy. Basically it comes from a political philosophy called Critical Theory, which is basically a version of Marxism where economics have been replaced with relationships of “power” and “oppression.”Douglas Kellner, a proponent of the neo-Marxist Critical Theory, describes the evolution of thought from Karl Marx to what I had to learn to get my credential in California 20 years ago in From Classical Marxism to Critical Pedagogy by Douglas Kellner.“Alongside of the proliferation of neo-Marxian theories of culture and society and globalization of cultural studies, forms of an oppositional critical pedagogy emerged that explicitly criticized schooling in capitalist societies while calling for more emancipatory modes of education. In his now classic The Pedagogy of the Oppressed (1972), Brazilian educator and activist Paulo Freire criticized the "banking concept of education" while calling for more interactive, dialogical, and participatory forms of pedagogy that are parallel in interesting ways to those of John Dewey. While Dewey wanted education to produce citizens for democracy, however, Freire sought, in the spirit of Marxist revolutionary praxis, to develop a pedagogy of the oppressed that would produce revolutionary subjects, empowered to overthrow oppression and to create a more democratic and just social order.”Within the framework of Critical pedagogy, the emphasis is on equity and redress of past injustices. If a student is acting up, it’s because our racist capitalist system has so victimized this student that he is merely reacting to his oppression. A system of discipline that would coerce this student into what the white, hetero-normative patriarchy considers “good behavior” is actually further oppression. It’s kind of the educational equivalent of the 1970s cliche where the criminal is the “victim of society.”Now don’t get me wrong. Most teachers are not coming out of Ed-school as raving Marxists. At this point many of the people teaching these courses don’t know about the origins of what their teaching. They actually think their teaching old fashioned 20th century Progressive Education, the Critical pedagogy is so intertwined with the teacher-training curriculum that it would be hard to separate it. What I’m saying is that when you go through such a program, teaching you to get “control” of an unruly student isn’t just a low priority, it might be seen as “further oppression.”ConclusionThe only feasible path towards reducing educational inequality is to transition our curricular model away from the constructivist model of theorists like John Dewey to a modernized version of the knowledge centered classroom as advocated by the Core Knowledge Foundation. We also need to guarantee a calm, structured and disruption free learning environment for all students. This is most important for the students prone to causing the disruption and they tend to become the adults with the most profound educational deficiencies.This won’t be an easy transition. Advocated of the Progressive and Critical pedagogy approaches to education are firmly in charge of teacher training programs at the university level, as well as the federal Department of Education. Many of these are as attached to their respective educational philosophies as a members of the Westboro Baptist Church or the Black Hebrew Israelites are to their religious philosophies. For these professors and bureaucrats, turning to an educational model that contradicts their philosophy is Heresy. Better educational outcomes for all students will only happen when parents override their commitment to a philosophy.