Summer School

I am teaching Algebra 1 for summer school this year, finally.  I’ve been teaching Geometry during summer school for a number of years, but prefer to teach Algebra 1.

…but … I’m taking a big risk in summer school this year.  Yup.  And there will be consequences if I fail.

But before I explain those consequences and the risk, let me set the stage.  The first idea is this:  In high school, even good high schools like where I work, there is an enormous amount of pressure on teachers to pass students.  The unintended result is that standards are lowered.  In math, and this is well articulated in nearly every TED Talk about the state of mathematics in education today, but students are taught these disparate procedures.  Students don’t learn concepts and thus cannot connect ideas or build upon past learning.  The end result of trying to make it easier by just showing kids how to arrive at an answer is that math becomes this enormous weight with seemingly thousands of things to memorize and recall.

That is tragic because the beauty of math, to me, is that you only need to understand a few things and those seemingly thousands of things just present themselves to you!

The second idea to consider is the population of students taking Algebra 1 in summer school.  The upperclassmen will have failed many times and will be jaded.  The freshmen will likely be behavior problems.  There will those that failed due to truancy and others still that failed because they’re simply lazy.  Then there will be the truly fearful students and the self-defeating students, those who never give themselves a chance.  (It’s easier to not really try and fail then really try and have to face failure without the out, Well, I never really tried.)   All of these kids have the aptitude to be successful in math, but getting them to realize it is where the art of teaching really comes into play.  The easier group is the very few who truly lack the aptitude in math, though it’s likely all students in summer school would identify themselves as belonging in this group!

The last thing to consider is that learning takes time and the time cannot be compressed.  Yet, summer school will be 11 days per semester, 7 hours of instruction time per day.  One day will be state testing and final exams.  So 10 days of class time.

I have set a goal within those 70 hours, in an environment where it is acceptable to lower standards a little bit, and with a group that would greatly resist pushing themselves.  I want all of the students to be truly proficient in Algebra 1, first semester.  I am going to try and teach them to be aggressive learners who challenge themselves and their understanding.  I want them to be introspective and reflect upon mistakes, beliefs and thinking.

In short, I am going to try and mold their thinking about math and education like I do with my honors students who take the Cambridge IGCSE test.  I will hold the standards high, I will not be dumbing down anything we cover, though I will be selective about the specific things we learn.

At first, students are going to struggle mightly with the idea that I will not be explaining everything to them, I will not be writing out steps.  They will struggle with the idea that their notes should be things they’ve realized, not just things I’ve written. I will be writing as little as possible and guiding them, with vigilant reminders to be actively engaged and so on.

If I am successful then the students will not only learn Algebra 1, but they’ll also recast the light in which they see themselves.  They will learn how to learn.

If I fail, they’ll fail and their bad mindsets will be reinforced by yet another bad experience in math class.  I take a lot of pride in the service I provide to students and this outcome would be completely unacceptable to me!

But, I think the reward is worth the risk.

A few specifics about how I’ll execute my plan … without a plan, remember, a goal is just a dream.

  1. The expectation of active engagement will be made explicit on day one.  (I’ll share the essence of this post with them.)
  2. I will provide accessible and engaging (I hope) support materials for them that focus on concept and show procedure as a consequence of properties of the concept.
  3. Organization:  Students will know the plan for the 11 days, and I will break each day’s activities down for them so they know exactly what to expect.
  4. Remediation plan:  Quizzes will be taken daily, short and sweet.  Students will grade these check-point type quizzes themselves and will be given a small amount of participation points for correct grading.  Homework will be fixing the errors made and completing a remediation assignment.

Here’s a map of what’s going to be covered, generally speaking:

Day 1:  Sets of numbers, prime numbers, LCM/GCF, and Percent problems

Day 2: Time Problems and the calculator, Algebraic Fractions (rational expressions), Order of Operations and function notation introduction.

Day 3:  Square Roots, Cube Roots and Exponents

Day 4: Test 1, Reading and Writing in Algebra, solving simple equations

Day 5: Inequalities, solving rational equations, variation

Day 6: Functions, graphs of various functions, function arithmetic and inverse functions

Day 7: Test 2, Linear Equations introduction, t-charts

Day 8:  Slope, intercepts, graphs of vertical and horizontal lines, slope-intercept form

Day 9: writing equations of lines, parallel and perpendicular lines, linear inequalities

Day 10: Systems of equations by graphing, substitution, elimination

Day 11: Review, Final Exam, AZ Merit

Once summer school begins I’ll be posting a daily vlog on my YouTube channel about how it is going, what I’ve tried and how the students have responded.  So, stayed tuned!


How to Save Time Grading


How to Grade Efficiently

and Promote Assignment Completion


Grading papers is one of the most time-consuming responsibilities of teaching.  Hours upon hours can be, I argue, wasted, pouring over daily homework assignments.  This article will discuss how to integrate awarding credit for daily assignments in a way that saves hours of time while increasing your awareness of student progress, increases student completion rates and better informs students regarding their progress in the subject.

This routine described here is a daily variety, not how I grade quizzes, tests or projects.  However, there are some tips that apply to recording those grades later in this article.

Let’s begin with a question: What is the purpose of homework?  For me, it’s practice needed for students to gain proficiency.  Homework is about trying things, working out how to struggle through difficult problems and making, and learning from, mistakes.  Without effective homework, students will not integrate their learning into a body of knowledge that they can draw upon for application or just recall.

The breadth of the purpose of homework and how that purpose is best served is beyond the scope of this article, but I would like to suggest that homework is something done in their notes, whenever possible.  The reason being is that notes are a receipt of their learning, to be reviewed in the future to help remember observations and important facts.

Overview of How It Works:

At the beginning of class, often before the bell rings, I begin walking around the classroom stamping homework that deserves full credit.  (What merits full credit is up to your discretion, but it should be a clear and consistent expectation, known to students.)  As I circle the room, I look for common mistakes, ask kids if they have questions or difficulties and make small talk.

Students that didn’t do, or complete, the homework have to answer for it on the spot!

Then, I simply mark those that did not receive credit for the homework on a student roster I keep on a clip board.  (For a video of how this works, visit the link here: )

Quick Notes:  This method has students ready for class because they have their notes.  They’ve also asked me questions if they had any, so I can begin with meaningful review.  I also have forced students that are remiss to account for their actions and done so in a way that applies positive peer pressure.  The scores are recorded by leaving blanks for completion and only marking those that do not get credit (which will be very few).

Credit:  I award full credit or zero credit when checking homework.  If a student attempted all problems, with evidence of attempt demonstrated by work shown and questions written, they get full credit.  Those that fail to receive full credit have the opportunity to reclaim 80% (the percentage is arbitrary but again needs to be consistent, clear and known by all), the students must see me during tutoring time by the Friday of the week of the assignment to show that they’ve fulfilled the expectation.  Students that did not attempt the homework can also see me during tutoring time (before or after school, not between class times or lunch), and receive partial credit.

But the rule of being due the Friday of the week assigned is big.  The purpose of homework is practice.  Without proper practice skills and knowledge are not developed.  Homework is not about compliance and fulfilling an expectation with a grade as a reward.  Students that are hustling to complete homework from two months prior are likely not promoting their understanding of current materials.  Plus, by having the time requirement applied to the homework policy, students are not enabled to fall too far behind.

The added bonus is that you will not be buried with make-up work the last week before grades are due to be reported!

Work to be Turned In:  If the nature of the work is not something that can be kept and must be turned in, have the students pass their work forward by row.  As you collect each row’s stack, count them.  If a row’s stack is incomplete, ask who in the row didn’t turn in the work.

If students can NOT fulfill the expectation and only receive a bad grade from it, and that reprimand comes well after the unwanted behavior, they will quite happily go along thinking nothing bad is going to happen.  Having to answer, publically, for their lack of work, especially when the vast majority will work, is a powerful deterrent!  Just as when checking the work of students and asking those who failed to complete for an explanation, this keeps them accountable and will increase the amount of students completing their work.

When collecting the papers, alternate the direction of the stacks and do not mix them up when grading.  This will allow you to quick return the papers after you’ve been done.  If it is a daily practice type of work turned in, I’d suggest awarding full or no credit and only recording, again on the printed class roster, those that were awarded no credit.

Recording Grades:  Whether you’ve collected daily practice or are carefully grading quizzes and tests, how you record those grades can either waste your time, or greatly reduce the amount of time spent.

By recording each grade as it is calculated by hand on the student roster it is quick and easy to transfer them to the computer.  This is a huge time-saving practice.  You don’t need to hunt on the computer screen for each student, and do so for each assignment.  When they’re recorded by hand, you can simply enter the column of numbers in the computer.  When the last name lines up with the last number that you entered, you know they’re all entered correctly.

By following this method, the data entry side of grading is done in a few moments of time instead of over hours, working through those stacks of papers, again!

Final Thoughts:  By looking at, and discussing, homework with students on an individual basis, very briefly, you gain insight into their progress.  They get a chance to ask questions.  Students that need a little bit of motivation receive it as an immediate consequence for poor behavior, rather than waiting until the end of the quarter, when a lot of pressure will be placed on you to help them bring up their grades.

This routine has proven to be a cornerstone of my classroom management.  It gives me a way to set the expectation that we are here to learn and that learning is done through work and reflection.  Students that need discipline receive it immediately and in a way they find uncomfortable, but it is done so with an invitation that guides them to the desired behavior (of completing their work).