Tag Archives: self-help skills

Perseverance in Math

perseverance checklist

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.

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Self-Help Skills Video Presentation

See the video (link below) to find out about this photo.Slide28I believe one of the greatest problems in education is the challenge students have in taking an active role in the learning process.

This is a video of a presentation on issues related to academic self-help skills and how to develop them. This is especially important for students with special needs.

The sound quality is not what I want it to be but the slides may help make up for this. I intend to re-record this presentation.

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Scaffolding Multi-step Math Problems

sidewalk problem

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.

sidewalk problem scaffolded

 

side walk problem PT

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Conceptual Understanding

discount tax problem

I gave a student a pop quiz on percent change – find discount and tax – after she completed  independent practice on this objective. The student followed the steps very well, as you can see in the photo (I added the ink later) up to the very end. At that point she added the tax to 6 for a total cost of $9.36 – good deal for an $80 coat!

This is hardly uncommon if not typical in education both at the secondary and post-secondary level. The focus is largely on steps and not concept building. I asked her follow up questions (as opposed to telling her what to do to fix it) to flesh out the concept. “What did you do first and why?” “What does discount mean?” “What did you do here (pointing to the 6/100 part)?” “What do you pay the cashier?” She was confused because she wasn’t thinking real life situation but got caught in the weeds of the math steps.

What often happens is that students give up when pressed to think. I often have students tell me “can’t you just tell me the answer?” and “you’re the teacher, you’re supposed to teach me.” I respond “Yes, I can show you and I already taught you; now it’s your turn.”

 

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Middle school to college

college long range planning (2)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.

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Lone Ranger vs Self-Help

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. lone_ranger

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.

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Post-Secondary Outcomes as Accountability Measure

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.

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Addressing Homework Completion Problems

Addressing Homework Completion Problems

Nice article Dr. Gary Brannigan (@GaryBrannigan) with 9 suggestions for helping a student with homework completion problems. #3 is especially pertinent to math:

Initially assign homework with which the struggling learner is unlikely to have difficulty. Mark the homework for punctual submission and content. Gradually increase difficulty but never beyond the struggling learner’s ability to succeed with moderate effort.

This is called shaping behavior. By starting slowly and moving a student towards the desired outcome. Simply getting the homework turned in on a regular basis is often a major task.

I also posted about notebooks. My approach is to have students use a simple folder for storing homework and to leave their notebook in class. The initial focus is on completing homework and submitting it on a regular basis. As the homework becomes more challenging the student will begin to take the notebook home.

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Manchester CC Survey about Student Struggles

Manchester CC Survey about Student Struggles

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.

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