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 the photo above you see a contrast between how children learn and how educators often teach necessary skills. Children learn to ride a bike by actually performing the target skills. This is a performance point – the setting in which the child actually performs. In school students are often taught necessary skills in isolation, away from the performance points. Imagine teaching a child to ride a bike by having him sit at a desk while the parent points out all the steps for riding a bike.
Often accommodations and supports are provided in isolation or out of context. Students with autism have lunch buddies in a contrived setting with an educator leading conversation. Students with ADHD have a weekly time to organize their notebooks. Students who have trouble functioning in a general ed classroom may be pulled out as a result.
Below are a couple of examples of how support can be provided at the points of performance. The photo below shows a checklist I used for a students with autism in my algebra class. They would follow the checklist and self-evaluate by checking off each step as it was completed. They were learning how to perform necessary skills at the point of performance.
Another overlooked point of performance is in organizing a notebook. Students should organize a notebook while IN CLASS and on a DAILY basis. I use the rubric below to help support students with this task.
Dr. Russell Barkley, an expert on ADHD, talks about performance points for students with ADHD in his book and in his ADHD Report. This focus at the “points of performance” can and should apply to any student with a disability (and students in general).
A major challenge for students is not content but how to “do math” which includes perseverance. The photo above shows a table that can be used to monitor progress on perseverance. It addresses two situations involving perseverance (see below).
The focus of perseverance in math is making an informed attempt when a path or next step is unclear (and does not necessarily result in a solution). Paths can be categorized as using a strategy, e.g. drawing a picture, or following an algorithm, e.g. steps to solve an equation. (See excerpt of CCSS Standards of Mathematical Practices below).
Perseverance in math involves two situations:
The initial entry point (strategy or algorithm) is not apparent but one is selected and implemented
An ongoing strategy or algorithm is determined to be insufficient and an alternative strategy or algorithm is selected and implemented
From the CCSS Standards of Mathematical Practice (bold font is my emphasis on the perseverance component)
1. Make sense of problems and persevere in solving them.
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
This is the figure from Mrs. Olsen’s Sidewalk Problem from the CT CAPT test 2010 (released to public). The problem has four major steps: divide the figure into common shapes, use Pythagorean Theorem to find height of the resulting triangles, find area of these shapes and compute total cost for pouring the asphalt for the sidewalk. Simply finding an entry point into this problem is a major challenge as is keeping track of the multiple steps.
Below are photos of the handouts I use to break the problem down into parts – scaffolding. Eventually the students have to learn to find an entry point and navigate the steps on their own. They learn to do this incrementally with the teacher shaping the problem-solving skills.
In my MATH class I use Picasso’s Guernica to get students to think – shaping critical thinking. This is a tribute to my art and architecture class which was the coolest class I had as an undergrad – the act of art speaking to life blew me away. I show them a photo with the following directions:
What do you notice in this painting? Write any ideas at all on your own paper.
I find that after prompting, prodding and not accepting “I don’t know” almost all will share something, e.g. “people look sad.” That singular effort alone is a big step for many. Here is information about the painting that I share afterwards (credit to Wikipedia):
Guernica is a painting by Pablo Picasso, in response to the bombing of Guernica, Basque Country, by German and Italian warplanes at the behest of the Spanish Nationalist forces, on 26 April 1937, during the Spanish Civil War.
Guernica shows suffering people, animals, and buildings wrenched by violence and chaos.
The overall scene is within a room where, at an open end on the left, a wide-eyed bull stands over a woman grieving over a dead child in her arms.
The centre is occupied by a horse falling in agony as it had just been run through by a spear or javelin. It is important to note that the large gaping wound in the horse’s side is a major focus of the painting.
The bull’s tail forms the image of a flame with smoke rising from it, seemingly appearing in a window created by the lighter shade of gray surrounding it.
Under the horse is a dead, apparently dismembered soldier; his hand on a severed arm still grasps a shattered sword from which a flower grows.
A light bulb blazes in the shape of an evil eye over the suffering horse’s head (the bare bulb of the torturer’s cell.) Picasso’s intended symbolism in regards to this object is related to the Spanish word for lightbulb; “bombilla”, which makes an allusion to “bomb” and therefore signifies the destructive effect which technology can have on society.
To the upper right of the horse, a frightened female figure, who seems to be witnessing the scenes before her, appears to have floated into the room through a window. Her arm, also floating in, carries a flame-lit lamp. The lamp is positioned very close to the bulb, and is a symbol of hope, clashing with the lightbulb.
From the right, an awe-struck woman staggers towards the center below the floating female figure. She looks up blankly into the blazing light bulb.
Daggers that suggest screaming replace the tongues of the bull, grieving woman, and horse.
A bird, possibly a dove, stands on a shelf behind the bull in panic.
In leadership class I studied the Lone Ranger approach to problem-solving. When a problem arose in an organization the boss would ride in and solve the problem. Afterwards he or she would ride off and the employees would be no better prepared for the next crisis or problem. The point of the analogy is empowerment – get the individuals to take responsibility for problem-solving.
The same holds true for the relationship between educators and students. All too often educators jump in to solve problems for the students without training students on responsibility. The students are not empowered or held responsible. This problem is magnified for students with special needs.
The most common example occurs during meetings with parents. When a student struggles the first suggestion is often asking teachers if there is additional time available to tutor or help the student individually (parents are not the only ones asking this). The original problem of poor self-help skills is not addressed and the adults shoulder more of the responsibility. As a consequence, the students’ belief that external forces will or are necessary to fix their problems is reinforced.
My suggestion is to look at how the student can be supported as he or she is trained to be more effective in employing self-help skills. Is he taking notes? Is she doing all of her homework? Do the students follow examples in the book or use other resources?
The following are anecdotes of how learned helplessness is developed.
A student was having problems with a math problem. The para asked if he needed a calculator and walked over to get one for the student.
A student had notebook organization as the focus of an IEP objective. Each week his PARA was organizing his notebooks for him.
A special ed teacher started to copy a homework assignment for a student because he didn’t have a pencil.
Many math teachers, when asked for help, will show students how to do a problem instead of pressing the student to find and follow an example.
The evidence is clear. Students learn to say “I don’t know” and the adults show them what to do as the students passively observe.
I use what I call a table of contents notebook strategy. Each item (notes, handout etc.) that is to be placed into the notebook is dated and labeled with a “page” number. Each page is recorded in the table of contents. This helps students maintain work in chronological order. For example, on a single day a student may have a warm-up/do now, notes and classwork solving a 1 step equation (e.g. x + 3 = 9).
This helps the student because he or she can find the notes and classwork when he attempts homework. This helps the parent monitor the student’s work and organization efforts. Also, if a parent needs to help a student he or she can see the notes to assist with homework.