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.

The use of cash as a payment method is declining. This has implications for how we teach money, consumer math, and life skills math. This is especially true for students with special needs who need more concrete representations of math. This post presents an activity to practice with a running bank balance.

Cash vs Card Transactions

The Federal Reserve Bank of San Francisco conducted a study on payment choices. The study, using a sample of people, reports that the use of cash as the payment method was most frequent for purchases under $10 and then it was used in less than half of the purchases. Given the increase in online ordering, it seems that cash use will drop further. This has implications for the students we support.

Overview

Previously, I posted about using a gift card activity to as an entry point to the concept of budgeting. Students are asked to compute a running balance. This post provides details about a similar activity, but for a bank balance using a bank register (as opposed to a check register).

Bank Balance Activity

The student plays an online game for counting money (image below). In lieu of counting out money each time, the student uses a bank register (image below) to track balance as if the student is using a debit card for purchases. The game has 3 types of squares: spending, earning or receiving money, and a gift card that would not affect the balance.

This allows for engagement with budgeting and a limit on spending. It can also lead to a discussion about negatives.

Alternative Activity

An alternative activity is to weave the use of the register into daily activities with students, especially in a life skills program. A colleague of mine who ran the life skills program at a high school would have students check in each day on a time clock and they would have a job. They could be paid and maintain a balance (scaffolded as needed). This could be done in a resource setting in general, without an actual job or maybe a different type of job than is often used in transition settings.

I have found that most students have little understanding of the living expenses and take home pay. This post provides details of a monthly budget plan that is useful for all levels of students and can be customized accordingly.

Here is a link to a Google Document with all components: job, take home pay, list of categories of expenses, and directions for activities to estimate the pay and expenses, and a comparison of take home pay and expenses with a look at other possible expenses. This can be revised to meet the needs or ability level of the students, as well as the user’s location. I have used this in whole class instruction in a general ed settings and for individuals working on life skills math.

Budget Activity

The Assignment starts with finding a job. I work with one student who has a postsecondary goal of college. He searched for a salaried position. Other students may be working for an hourly wage.

There is a take home pay calculator used in this assignment (2nd photo below). It is based on annual pay. I scaffold the conversion of hourly pay, which is a good calendar activity in of itself.

The chart below is the master list of expenses. Some expenses are computed on subsequent pages and some have the link in the row. The amounts are estimates intended to allow the student to engage in a monthly budget.

At the end, the student compares pay and expenses. I find that this is an eye opener for many students. They are not simply asked to take the word of parents or teachers on what life has in store for them, they see it for themselves.

Individual Activities

The individual sections are useful in isolation. I use buying a car to as an introduction to 2-step linear equations with down payment + monthly cost times number of months = price of car. For students learning to count money, the shopping activities can be used. I task students to shop online at a store like Target as if they had a $50 gift card (see image below). Once completed, they count out money to pay for items in the cart and they compute the balance on the card. This is an entry point into budgeting as they compare money they have with money they spend. I will keep a running list of prompts on Google Slides as data for how well the student stays under budget.

The images above show a postsecondary planning documented to help a family prepare for a postsecondary transition planning meeting with the IEP team. This student was likely to be placed in a day program and live in group housing. Below are some images showing a focus on employment (no specialized education or college) and on education.

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.

In a Connecticut State Board of Education report, over 40% of students entering a state community college or state university (not including UCONN) needed to take a remedial course.

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.

Each year spent with a student with special needs is the first year of a chain of subsequent years, like a line of dominoes. EXCEPT, there are multiple lines of dominoes and a teacher may be tipping over the first domino in a line of several possible lines of dominoes. One line may topple towards community college and another towards a job, with no college.

Each year impacts the future, yet we often only see that one year in isolation. We see only the next domino.

In working with students with special needs on math programming and services, a common and important issue is that the student is behind and there is a tension between math intervention to fill gaps and addressing ongoing grade level content.

Unpacking the situation

There is no single grade level for math, as is the case for reading. Math progression is more like a web, not a line. For example, if a student can do 5th grade geometry but only 3rd grade level fractions, do we average out the grade level math to be 4th grade? (No.) Do we identify the student as working at a 3rd grade level? (No.) 5th grade level? (No.)

Like a suitcase, there is a capacity to the daily time a student has for school services. I often encounter situations in which the services recommended involve the student working on grade level content and catching up on the gaps during support time. If the student has only been learning 75% of the math content each year, he or she needs that support time to help learn the new content to get closer to 100%. There is too much being stuffed into the suitcase. Something has to give.

The focus of the services and programming often shifts away from post-secondary plans, with a focus on the short term. Like the situation facing the man in the image below, there are long term implications.

Recommendations

There are two recommendations I make in regards to addressing the gaps, without overstuffng the suitcase.

The IRIS Center is part of the Peabody College of Vanderbilt University.

Use triage to shift focus to the priority topics. For example, the parents of a student in 7th grade but working on math from lower grade levels wanted to pursue a math track that would allow the student to go to community college. I mapped out a long range plan (image below) that focuses on algebra as that is the type of math most likely encountered in a math requirement. Here is another plan which was to prepare a student to possibly work in a field related to cars.