This relates to the threads on "Physics Education in the US", "Should Calculus be taught in high school" and similar threads. "What students learn about the science disciplines, technology, engineering, and mathematics during their K-12 schooling shapes their intellectual development, opportunities for future study and work, and choices of career, as well as their capacity to make informed decisions about political and civic issues and about their own lives. Most people share the vision that a highly capable STEM workforce and a population that understands and supports the scientific enterprise are key to the future place of the United States in global economics and politics and to the well-being of the nation. Indeed, the solutions to some of the most daunting problems facing the nation will require not only the expertise of top STEM professionals but also the wisdom and understanding of its citizens. Although much is known about why schools may not succeed, it is far less clear what makes STEM education effective. Successful STEM Education: A Workshop Summary discusses the importance of STEM education. The report describes the primary types of K-12 schools and programs that can support successful education in the STEM disciplines and examines data and research that demonstrate the effectiveness of these school types. It also summarizes research that helps to identify both the elements that make such programs effective and what is needed to implement these elements." Successful STEM Education: A Workshop Summary http://www.nap.edu/catalog.php?record_id=13230 (pdf is free to download) I would like to explore ideas for the best ways to teach arithmetic, mathematics and science, and particularly physics, in primary, or K-12, education. I'll probably develop a separate thread on mathematics pedagogy. ps - How can we instill a life-long love of learning?
http://www.stemedcoalition.org/ http://www.stemedcoalition.org/wp-content/uploads/2011/02/Coalition-One-Pager-2012.pdf Corporations (e.g., ExxonMobil) support STEM education U.S. Companies Investing in STEM Education http://www.exxonmobil.com/corporate/community_math_equation.aspx http://www.exxonmobil.com/Corporate/community_math.aspx?WT.srch=1 http://www.exxonmobil.com/Corporate/community_math_academy.aspx http://www.nationalmathandscience.org/blog/2012/03/27/exxon-ceo-champions-stem-education-and-rd National Math and Science Initiative (NMSI) http://www.nationalmathandscience.org/ Actually, I rather discuss the How of how we get from learning numbers and counting (K or 1st grade) to derivatives, differential equations and triple integrals, and linear and complex analysis (by grade 12). Similarly, I'd like to discuss How we get from simple science (or observation/descripton of nature) to modern physics (relativity, QM, . . . .) by grade 12. When and how should certain subjects be introduced? How should math and science be taught in parallel? What methods facilitate the learning of math and science at various levels? From the article U.S. Companies Investing in STEM Education Four years later, this statement is still true.
Count me in on this discussion! These are excellent questions with no simple answer(s). If I can paraphrase, you are defining startpoints (counting, listing observations) and endpoints (diff. eq.; modern physics) of a K-12 STEM curriculum and want to somehow make it all fit within a 12-year instructional plan (we can ignore differences in academic 'quality' for now, even though that will determine how any curriculum is actually implemented). Honestly, I think the math curriculum is easier to lay down (even though I think there's too much material- I took complex variables and diff eq sophomore year of college) and there seems to be a clear path to follow in terms of increasing abstraction. The science curriculum endpoints need work- kindergarteners are explicitly being introduced to hypothesis-driven research as a foundation of understanding our physical world, for example. Science curriculua should be allowed to be distinct from the mathematics curriculum. I would define the science start and endpoints differently- starting with constructing one or more hypotheses based on observations, leading to the design and execution of an experiment, resulting in analysis and discussion of how data is used to support or refute a hypothesis. The curriculum could progress by increasingly abstract hypothesis/models and technically difficult experiments. I could envision high school students learning relativity by using GPS, cell phones, etc- not to mention solid state physics.
I think the math for K-12 could be changed and made more efficient. I think learning diff eq in high school is too much a stretch, but certainly more kids could do AP Calculus BC. A lot of time is wasted because Algebra II repeats a lot of Algebra I, and then the Algebra/Trigonometry class repeats a lot of Algebra II. If there wasn't so much time reviewing and just learning new material, we could have some sort of sequence as follows Freshman: Algebra I Sophomore: Geometry Junior: Algebra II/Trig Senior: Calc AB for a B and lower in junior year, Calc BC for an A in junior year If any high school that isn't a magnet school could accomplish this, it'd be very impressive. On the other hand, there are many students who at that age just don't a hoot about school, so it's easier said than done. At my high school, chemistry was a prerequisite for AP Chemistry, and AP Physics had no prereq. Not sure why they felt that it be necessary for chem to have a prereq and physics not..but if you could do Biology in freshman year when the math knowledge is lower, and somehow incorporate some algebra do solve problems in biology to get kids thinking of applications of math.
Australia already has a national curriculum for primary & secondary. http://www.australiancurriculum.edu.au/SeniorSecondary/Science/Physics/Curriculum/SeniorSecondary Its mandatory of all government K-12 schools, and most private schools use it too. Its cost effective for students & teachers as - teachers & students can move schools with relative ease - only need one textbook for the entire country - no creationism or global warning anti-science rhetoric (we leave that to hillbillies) USA is decades behind the times in math/science teaching & does very poorly on OECD rankings for STEM.
This is the kind of topic that is often discussed using platitudes and false generalizations. Here are a few things for which I think there is at least some evidence. You often hear people say that there is a shortage of people with education in STEM. The trouble with this claim is that in a capitalist society like the US, you don't really have shortages, you have markets in which the buyers (i.e., employers) feel that they're paying too much. Often this kind of talk is code for wanting more H1-B visas so they can pay lower wages. What's a better description of reality is that over time, there has been a phenomenon of credential creep. For example nurses used to be able to get jobs with an AA, but now they're not very employable unless they have a bachelor's. Biology majors at the University of California used to be able to take algebra-based physics, but now they need calc-based physics. Physical therapists nowadays need a doctorate (DPT) -- which qualifies them for work in a "physical therapy factory" seeing one patient every 15-20 minutes, with pay that may top out at $60k. An op-ed piece on this topic: America’s Health Worker Mismatch, http://www.nytimes.com/2012/09/14/opinion/americas-health-worker-mismatch.html . So from this point of view, the problem, if any, may not be that STEM education is less successful than it should be but that we send people into STEM coursework who are not cut out for STEM. There's a recent book called Someone Has to Fail: The Zero-Sum Game of Public Schooling, (reviewed here http://www.theatlantic.com/magazine/archive/2012/09/cover-to-cover/309071/ ) that argues that you can't use the public education system to promote equality, because the families that consume education are motivated by the desire to get ahead of other families. I think this probably applies to STEM. In physics, there's a ton of pedagogical research by people like Halloun and Hake showing that traditional teaching techniques don't work, and that other techniques do work. Despite this, most people teach using traditional techniques. Another important recent book is Arum and Roksa, Academically Adrift: Limited Learning on College Campuses (summarized at http://www.newyorker.com/arts/critics/atlarge/2011/06/06/110606crat_atlarge_menand ) . Their results have been replicated by others: "How Robust Are the Findings of 'Academically Adrift?'" -- http://www2.education.uiowa.edu/cen...uments/AcadAdriftChangeArticleFINAL.sflb.ashx . This is about college in general, not specifically about the sciences. They have evidence that college students used to make bigger gains on a test of critical thinking but now make much smaller gains. The trend persists when they control for the different population currently attending college. The trend seems to be the result of lowered expectations by college professors. Higher improvement in critical thinking correlates with faculty's high expectations, high standards, and approachability. "Social engagement" and studying in groups are *negatively* correlated with improvement. Success rates vary widely between schools, but the reasons for this are not well understood. There used to be a theory (Vincent Tinto, ca. 1993) that "social integration" was important, but more recent evidence totally contradicts this. The factors leading to failure or success seem to be different at community colleges versus four-year schools. I suspect that a lot of the variation in success rates is simply that they aren't being reported accurately; these are statistics that administrators are highly motivated to fudge with. Many administrators at my school are highly focused on what they call the "achievement gap" between different racial groups. The trouble is that (a) they're idiots about statistics (e.g., they don't have any clue about the poor precision of small samples), and (b) even if we could really measure such a gap, nobody has any evidence that there's any way to do anything about it. Re male/female differences, research from ~10 years ago claiming low self-confidence among teenage girls seems to have been incorrect. Although Lawrence Summers seems to have been a loudmouthed jerk, the controversy that led to his downfall probably shows that our society isn't capable having a rational discussion about this. In physics, a lot of the research about racial and gender differences seems to be focused on how to produce more physicists, and why people drop out of the pipeline before becoming professional physicists. This seems silly to me, since physics is basically a service department. We teach mostly engineers and life science majors, not people who have any intention of becoming physicists.
The basics for this are fairly simple, but the actual answers are pretty hard: Education is 50% motivation and 50% general aptitude on the side of the student and on the teachers side something like 50% teaching skills and 50% knowledge/understanding of the subject. (ore something like that) The more advanced you are in the subject the more important become aptitude and knowledge and vice versa. The last factor is time spend on the subject. You cannot change much in the general aptitude of the students. Teachers who don't understand their subject might possibly get a better education, and teaching skills are an art or a craft, that academia is not being able to teach all that well. (You don't need ipads, and multimedia presentations and all that junk to do a good job at teaching) So I think on the teachers side it is mostly talent that counts. You can change the curriculum to include more STEM time that would be the most easy part, but I believe the most effective screw is the motivation. If people held math and science in higher regard and doing science and engineering would be seen as the cool jobs that people want to have, then students would have motivation to learn more/faster. You could see that in Soviet Russia, where the scientists had more freedom then the average person. For the average woman in Russia some twenty five years ago it was desirable to marry a scientist or engineer, because a communist state didn't allow for that much proliferation and scientists were highly regarded. Hell, science was sexy! And STEM skills of students were through the roof. On the teachers side it is very similar. If you have a talented person who is good at math or physics, these days this person will be drawn to finance or industry. Being a teacher is not cool at all. Therefore many talentless STEM teachers are out there, neither getting the students motivated nor the facts right. How to get there I have no idea. Maybe pay the Scientists better. These are my principles. If you don't like them... I have others. --Groucho Marx
My high school, which at the time (early 1970s) was not a magnate school, did that. Actually, I attended two high schools, one in 10th grade, the other for 11th and 12th grades. The 9th grade was at a junior high school. My math program went: Freshman (9th grade): Algebra I Sophomore: Geometry (1st semester), Trigonometry (2nd semester) Junior: Algebra II (more trig and hyperbolic functions, some analytical geometry) Senior: Analytical Geometry, Calculus BC The second high school did the trimester system, so rather than take the normal 4 courses/trimester, I took 5. I have 2 years of chemistry, and during the second year, we started learning first order differential equations. Unfortunately, I only had one semester of physics. During the summers, I took 6 week courses (math, physics, programming - but also German language, history, and other humanities) at a local university. Between 11th and 12th grade, I did an 8 week NSF science training program at Colorado School of Mines in nuclear and electrical engineering, which included a week of introductory calculus, which I had actually started studying during one of the earlier summer programs as well as on my own. Somewhere along the way, probably one of the earlier summer programs, one of the math courses included matrices and matrix algebra, but as far as I can remember, it wasn't tied to systems of equations, linear algebra, or linear analysis. It would have been great if the math courses had been tied together and better coordinated. I had to wait until university to get the connection and tie up loose ends. I never considered any of that extraordinary, but rather, I took advantage of available opportunities. I started university at the sophomore level. Yet I felt I had wasted a lot of time not learning what I need to learn earlier - e.g., linear algebra/analysis, etc. I felt I could have done so much more in junior high and high school if the system had better organized. Until I got into upper level courses and graduate school, I found myself rather frustrated with the educational system - and I still am because of what it doesn't do in terms of preparing students. I want to address the previous two posts after I give them some thought. I should point out that one student a year ahead of me went to university (U of Tx) and majored in EE. He then went to frad school at Stanford, and subsequently founded a company. He later sold the company to Qualcomm and made a few hundred million dollars. Now that's exceptional.
I was thinking of a more radical approach, starting with Kindergarten. Realizing I'm not a professional mathematician, I started with a list of broad topics- arithmetic, algebra, geometry, statistics, and functional analysis; each of which can be taught over multiple years with increasing complexity, and each topic can be taught in a way that is integrated with the other topics. Again, my goal is to provide the high-school graduate with minimal numeracy skills as well as provide sufficient preparation for the student continuing into a technical field. For example, early childhood is still spent on basic numeracy, while middle and high school are then used to both deepen connections between topics (for example geometry and algebra) and introduce applications (here, it could be CNC machining, architecture, and soap bubbles). At the end of high school, the student would be exposed to (approximately) the same amount of material currently covered. Given the importance of statistics in daily life, I would greatly increase the amount of time students spend on this particular topic. Early exposure would simply cover mean, median and histograms. Later topics include standard deviations, error analysis, and Bayesian inference. Students graduating high school should understand how to parse something like (from Wiki): "In the United States, 10 to 20 percent of patients with breast cancer and patients with ovarian cancer have a first- or second-degree relative with one of these diseases. [...] the BRCA mutations, confer a lifetime risk of breast cancer of between 60 and 85 percent and a lifetime risk of ovarian cancer of between 15 and 40 percent. [...] However, mutations in BRCA genes account for only 2 to 3 percent of all breast cancers."
More efficient, that is a central issue here. My opinion says that if US students have to repeat and recover material year in and year out, they ARE NOT SPENDING ENOUGH TIME LEARNING THE MATERIAL, i.e. the standard 180 days of school isn't enough. As for STEM education, the Boy Scouts of America has a huge thrust in this area and has offered a program this past year. I am on the local STEM committee, but given my recent travel and work requirements I have been unable to attend any meetings or give any input.
Do you mean, like the K-12 systems had done many, many years ago, like this: ? That worked well in the 1960's and 1970's, so that should work just as well today. The course sequence in Math like that is for college preparation. The first part should still be done today as it was so many years ago. The second part is typical. That's how students in general are at that age. It has not changed.
I've been meaning to read these- I'm intrigued by the idea that group projects are negatively correlated with improvement. One word of caution regarding "lowered expectations by college professors". While grade inflation is a real problem, it's also true that students and parents apply pressure to the system- one recent example I know of is a student (not in my department but in my college) who wrote our college president complaining about her grade in BIO 200 (this is a 200+ enrollment intro class). Actually, she didn't complain about her grade, exactly- she couched her complaint in terms of 'bad teachers who didn't teach me anything'. In any case, for whatever reason the president- the person who oversees the entire university- initiated a series of meetings and is requiring written explanations from multiple faculty members (including the chair) regarding this student's grade. This is inexplicable to me. Another pressure (at least in Ohio) comes from the State government. There is currently a push to increase retention and graduation rates. While I agree that this is a good idea, one potential result will be pressure to pass more students- even students who have not come close to mastering the course material.
I generally agree with this. On the student side, the 'motivation' to study must compete with all the other distractions in life: home life, work life, love life, sports, social media, entertainment, etc. etc. Students, like everyone else, often have difficulty setting priorities. As for 'aptitude', the underlying tension is between providing opportunity and demanding excellence. Open-access institutions (real or online) either have *huge* dropout rates or gain a reputation of being worthless. On the teaching side, it's also true that 'teaching' and 'content', especially in STEM programs, are completely distinct- someone wishing to become a K-12 teacher gets a degree in education, not science. Conversely, someone wishing to become a STEM academic gets *no* instruction in education. Fortunately, I think this is changing through cooperation between STEM and Education programs.
At my high school, the only math requirement is finishing algebra I. That is all you need to graduate high school. There are kids that struggled to meet even this requirement, they hate math so much they go out of their way to be bad at it I think.
At least from my experience in high school, the general problem is that the students who want to be college-bound are held back and the students whose skillsets and interests lie somewhere else i.e. vocational training, job after high school, etc. are pushed into subjects they don't necessarily want. Last year, my high school principal proudly stated the performance level of all students show less of a gap (lower standard deviation) than before. Never mind the overall performance of the school still decreased... Another thing is that so many of the opportunities available are based on time and age instead of ability... When I came back from India for 9th grade, I possessed thorough knowledge of Math through Algebra II yet they made me repeat three years... Three years I felt so cheated out of and wished I would've spent on Physics instead of playing catch-up. No placement test, no hearing of my begging. Math can certainly be streamlined IMO. Cut out repetition (Various Pre-Algebra Courses --> Algebra I --> Geometry --> Algebra II --> Trigonometry/Pre-Calculus is highly inefficient...). Maybe include a build-up of mathematical foundations/logic. Ending with Calc II should be doable; those who don't want to continue with math are done with it faster and can focus on its applications in a subject area they wish to pursue; and hopefully options for continuing further aren't barred because of age...
That is a big problem. Culture or upbringing is the reason; what I mean by culture is mostly, "environment". Those students are bad at so much as Algebra 1 because they do not like it, and try to avoid the effort to study because they are not good at it and do not like it; the way to succeed is to put in enough effort on a regular schedule, which is exactly opposite of those students way. No wonder such students do poorly at Algebra 1.
This dodges the point, I think. AFAIK (at least for the high school graduations requirements I know), 'algebra I' is not the requirement, the requirement is '3 credits', or '1 year', or something like that. The State of Ohio has a 'common core' which is a list of specific skills (e.g. 'add and subtract fractions and mixed numbers with like denominators'), but that only covers primary school (K-4). That leaves at least 5 years worth of opportunity to improve STEM instruction without having to involve state-level politics. The reality that a student can graduate high school without being exposed to appropriate math and science is not a failure of the student; it is a failure of the curriculum.
A certain fact in many k-12 school districts IS the requirement of 1 year of Algebra for high school graduation.