A spin off to Fulghum’s book (below) is that by high school, students have been presented with almost all of the math they need if they are not pursuing college.
High school math, aside from some exceptions, is largely designed to prepare students for college and subsequent careers.
If your student is entering high school and does not have a postsecondary goal of college (2 or 4 year) then you can turn the main focus of the math education to topics covered before high school.
Some of the topics in geometry and statistics are applicable to real life and most of those would have been covered in the Statistics or Geometry and Measurement domains from previous grades. There are topics unique to high school math that are prerequisites for some vocations, e.g., trigonometry for surveying. Some applications of the high school math address real life, but the focus is on the math and not the applications.
The image below shows a breakdown of a sample of topics for life skills math and for two vocations. Here is a link to a PDF of the document shown above. You can see the math topics. Here are the links to the pages for the plumbing topics and the welding topics.
Related to this value of college education for certain job sectors. The director of the Office of Higher Education in Connecticut, Tim Larson, stated that many companies have proprietary software, programs, or procedures that they will teach new hires. The take away from this is that much of the actionable knowledge needed would not be covered in college. Many of the skills they are looking for are not academic in nature. The Wall Street Journal published two articles that speak to the change in requirements for some jobs, in which a college degree is no longer a requirement (“Rethinking the Need for College Degrees“, “Is this the end of college as we know it?”)
A college education (or at least the degree) provides incredible opportunities, but it is not needed for many students.
In a recent Facebook group for high school math teachers, an interesting discussion arose about retests and how to respond to students who have a low score on a given test. A common perspective that I shared for a time is that we should eschew retests as we are preparing students for college. In this post I offer counter points to this argument, and attempt to unpack the college preparation issue. The focus is on math.
It appears that colleges universally have placement tests. Below are excerpts from universities in Florida, Texas, California, Washington, Nebraska, and Connecticut, along with a sprinkling of 2 year schools from some of these states. If a student makes an A in precalculus in high school, that does not qualify the student to take calculus or even to retake precalculus! A test score is required, whether it is the SAT or the college’s placement test. Indirectly, this appears to show that the colleges are not taking high school results at face value. Whether the student took a retest or not, or didn’t need one he or she still must prove content mastery to some degree.
Then consider what is happening at colleges. Dr. S.A. Miller of Hamilton College wrote an essay about grades in college (excerpt below left). In it, she cites Dr. Stuart Rojstaczer‘s article in the Christian Science Monitor about grade inflation in college. The focus here is not on how the grades are inflated, e.g., with a retest, but the evidence shows grades skewed towards the higher end and has increasingly become more pronounced over the past few decades. The rigor and accountability cited in the argument against retests is not what it appears.
Given the need to demonstrate content mastery through placement tests, and college academic expectations that are not quite what they seem, it makes sense to focus on mastery of content. This is illustrated by what is happening in Connecticut, a state that ranked 3rd in US News and World Report state K-12 education rankings and 2nd in Wallet Hub’s rankings of state school systems.
If this is happening in Connecticut, it may shed light on what is happening in other states. It certainly appears that there is something not working in terms of content mastery in math. I am not attempting to place blame and certainly do not suggest that the problem is a lack of retests. Another issue is self-help study skills and how well students are playing their part of the learning process. A report of a survey conducted by Manchester Community College in Connecticut included the most common reason people struggle in their classes. The 2nd most cited response, by 60% of faculty and 61% of students, was that the students do not know how to study effectively.
It appears the issue of retests is more an issue of why is there a need for retests to be considered and the implications of not filling in the content knowledge gaps. I will conclude with a bit of irony. UCONN is ranked as the 23rd best public university. Students are allowed 3 attempts on the math placement test.
Below is a photo of a hyper-doc that I use to map out a long range plan for math services and academics for students receiving special education services. Here is a link to a video explaining how the document is organized and how it “works.” (Note, the image of the document on the video is not crisp, so I suggest you look at the handout while watching the video.)
The document contains several links to resources such as videos, websites and blog posts that provide additional information. Feel free to reach out to me using the Contact Form on this page if you have questions or would like input. I am happy to help.
Ask employers what skills are desired in graduates and you will not see academic competence at the top of the list. In schools we talk about creating life long learners and similar qualities but the major focus in the 7+ K-12 schools in which I have served is academics, or more appropriately grades as a proxy for academic mastery. Add to this the focus on exit exams for graduation and you see major disconnect between the desired outcomes and the focus.
I have taught math at 5 colleges or universities and have seen first hand students struggle with content but also with independent study skills. Manchester Community College in Connecticut conducted a survey of students and asked students to cite reasons why students struggle in their classes. The second most commonly cited responses by students themselves is that students don’t know how to study (see below). In high school we talk about study skills. Teachers will share they expect students to be independent but often the focus is on academic mastery and not the study skills.
At Manchester Community College I serve as an instructor at a highly successful (based on objective outcomes) bridge program for first generation students. A major emphasis is a focus on student academic discipline with a mantra that discipline is the bridge between goals and accomplishment (see below). Learning how to BE a good math student, especially academic discipline, is as important as developing the prerequisite skills to be successful. This could be a major focus in the IEP for students who have a goal of college or post-secondary training..
In special education and in K-12 education in general graduation is viewed as a culmination or the end game. In fact it is just the opposite. Graduation is a STEP towards the future. If the plans for your student is post-secondary education, including vocational training, it is important to understand a couple false assumptions.
A diploma indicates the student has the academic mastery for post-secondary education. Below is a link to some documents. One is a study of how well prepared high school graduates in Connecticut are for college. In 2009 more than 2 out of 3 students entering a community college or a Connecticut State University needed to take a remedial (developmental) course in English or Math despite earning a high school diploma (and passing a state graduation exam).
A diploma indicates the student has the ability to perform as an independent student. In a survey from Manchester Community College (Connecticut) students were asked why students struggle academically. 60% of MCC students reported that students don’t know how to study.
Here is some information about the placement tests, with Manchester Community College used as an example. The placement test results are what determine if a student will have to take a remedial course.
The SAT has a different scale. To get a rough prediction of the SAT score add around 80 to the total PSAT score (or add 40 to math and add 40 to Verbal)
Here are related documents including those referenced above. The placement test is the Accuplacer and the documents linked include a handout with example problems for math and English from the Accuplacer.
I’ve had discussions with multiple caregivers and parents recently about IEP objectives and evaluation/assessment. I think this is not only an important issue but is an issue that is a foundation for special education.
The purpose of special education, as established in IDEA, is outcome based. The focus is on the future life of the student. Decision making and services are made in this context. With this in mind I believe evaluation/assessment and the development of the IEP, especially objectives, fall under this context. There should be an alignment to the long range future of the student.
Often the focus of special education is on deficits. Evaluations identify deficits and the programming is developed to address the deficits. Certainly many or most educators are conscientious of long range outcomes but the deficits are the priority. Contrasting this is a standards based approach. I do not mean every student working towards grade level work as this would be entirely inappropriate for severely impacted students (like my son). I mean more of an outcome based focus with long range goals as the priority. If the purpose of special education is to prepare students for life after K-12 education then the standards or outcome based approach is necessary. A deficits based approach can result in progress but progress that does not translate into necessary preparation for the future.
Here’s an analogy. A person gets up in the morning and has to go to work. She has a range of tasks from the essential, e.g. getting dressed, to the desired but not essential, e.g. send an email to a friend or make a cup of coffee to go. As is often the case with me, she runs out of time. Maybe she can try to send the email but then has no time for the coffee. Maybe she needed to print a report for work but overlooked it because she was preoccupied with all the other tasks. At some point she has no choice and has to leave regardless if the coffee is ready or the report is printed.
Our kids have a limited amount of time in special education. Like the person going to work, at some point our kids are exited from IDEA regardless if they are prepared. We know a great many of our kids are not prepared. A deficits approach prioritizes urgency at the expense of important. The email is sent but the report was overlooked. A standards/outcome based approach focuses on importance not urgency. This doesn’t mean deficits are overlooked but they are prioritized.
In my experience in school and in working with many different parents I have found a focus on deficits.
A sophomore in high school spent an entire year on arithmetic (doing this by hand) and basic pre-algebra skills because these were deficits. The goal is for him to go to a community college where he would qualify under ADA for use of a calculator.
A junior moderately impacted by autism was taking a basis algebra class. His postsecondary plans focused on some level of independence and maybe a supported work placement. He couldn’t count money but he was being taught how to simplify 3x + 2x.
Often, accommodations, e.g. teacher prompts, are included in assessment of IEP objectives “because the student needs this to be successful.” I’ve heard this in multiple situations.
Contrast this with another situation. I helped a family with a middle school student with autism. His mother explained to me that they had a goal of him having some type of job and some level of independence. He was very much interested in cars and working with cars in some capacity for his job. The math needed for auto repair is mostly measurement. We mapped out a muti-year plan for his math to focus on measurement and consumer math. He was not going to learn to simplify 3x + 2x but would focus on what a 5/16 inch wrench is and what is meant by 5/16 of an inch.
The first student I ever helped when I began my work in special education was a sophomore with aspergers. He received ineffective special education support and entered community college with the same challenges and gaps in math as he had his sophomore year. I served as a kind of case manager for him as he worked through community college. He needed help with study skills, math content, stress, completing work etc. This semester he is likely to graduate from community college and plans on transferring to a university.
Again, I am not proposing that deficits be marginalized. The deficits can be prioritized based on long range goals and addressed accordingly. The photo of the table above shows 3 categories of post-secondary outcomes and the level of focus on standards and curriculum.
Some level of independence – no formal vocational training or college course work
Some vocational training or college course work or a community college certificate or degree.
4 year college
My position is that the current student work and support should be aligned with the appropriate outcome.
This is a photo of a table I created for a former 7th grade student of mine. It laid out his academic future leading up to college. The arrows were a visual part of my explanation of how college applications are largely based on the 9th, 10th and 11th grade high school years.
This is significant because many students struggle their freshman year of high school. If they have a bad year academically one third of their courses used to compute their gpa for the application is a drag on the gpa. There are other negative consequences for a bad start to high school such as a diminished confidence, poor study skills, shifting into a lower level academic track and self-fulfilling prophecy.
Preparing for college (or post-secondary education in general) really does start in middle school. This is magnified for students with special needs. Training them to be self-sufficient and to self-advocate can take a long time. The longer it takes to start this training the longer it takes for them to become fluent at these self-help skills.
As a long time adjunct instructor at various colleges and universities I have repeatedly been witness to the same poor study skills in college as I see in high school and middle school.
Unprepared College Freshmen Could Be The Cost Of High Schools
Huffington Post Education has a story about states considering action to hold school districts accountable for their graduates having to take remedial courses upon entering college.
Of course there are many factors that affect a student’s performance in college but high schools can do more to prepare students for post-secondary education or training. The current set of evaluation and accountability measures are actually counterproductive for preparing students for subsequent education and training. SAT scores, graduation rates, standardized testing and grades in general do not measure independent learner skills. Such skills are essential in a post-secondary setting that offers far less support provided in high schools.
This could have a major and very positive impact on students with disabilities. In lieu of the current approach of helping a student with special needs pass his or her courses to get a diploma the focus would be on training a student to be a more independent learner with competence in study skills such as maintaining and using a notebook.
Manchester Community College (CT) surveyed their students and asked for reasons why students struggle in their classes. The number two most common response was that students didn’t know how to study effectively.
If the students in the general population struggle with this imagine students with special needs. As I’ve posted elsewhere on this blog, students with autism or asperger’s are very likely to have executive functioning deficits which directly and significantly impacts the aforementioned self-help skills.
Note: commentor asked for link to this study. Here it is. Find “Survey Results at the bottom of the list of handouts – page 11 on the Word document.