Introduction/Explanation Paper

Overview of unit, weekly, and class structure and timing

Unit Structure overview

Mondays - Thursdays were 80 min class periods; Fridays were typically 55 min. periods.

Weekly Structure Example

Although days off sometimes caused me to adjust this model, here is how I would typically structure a week.  The text I use, CME Project Algebra I (EDC/Pearson, 2009), structures its chapters into "Investigations".  For instance, Chapter 6 is organized into Investigation 6A (Sections 6.1 - 6.5), Investigation 6B (Sections 6.6 - 6.11), Investigation 6C (Section 6.12 - 6.15).  I aim to do an investigation in 1-2 weeks.  For example:

Monday: "Getting Started" section.  A Getting Started section is always the first section of an Investigation.  This section would not have a homework preceding it like the one below.  This section is designed to be an introduction into the Investigation ahead.  There is a problem set, but the questions are more inquiry-based and open-ended.  The initial Brain Warm-up of the week was also typically given on Mondays.  Monday night's homework (due Tuesday), would be an introduction into Tuesday's topic.

Tuesday - Thursday: Would cover the next consecutive sections after the Getting Started.

Friday:  Given that Fridays were a shortened class period, I typically would wrap up the week by having students do a review activity.  This activity could be a Collins-type writing assignment, group work, or targeted individual review and Gateway retakes.

Class structure

This is the class structure of a typical Tuesday, Wednesday, or Thursday class.  Class periods were 80 minutes in length.

Example of Homework Preview sheet (given the night before)

In this example, the class itself took place on March 19, so students would receive this packet at the end of class on March 18.  It would be due before class on the morning of March 19.

Brain Warm-up

The purpose of the Brain Warm-up is twofold:  first, it serves as a Do Now (sometimes called a "Bell Ringer") to get students working and focused at the beginning of class.  Second, it serves as daily spiraled work so that students are constantly reviewing previously learned skills.

I would use a test software to print out four versions of the Brain Warm-up at the start of the week, for Mondays - Thursday.  Friday typically served as targeted review on any skills students still hadn't mastered by then.

The Brain Warm-up typically consisted of 10-20 questions, based on length (the example below doesn't contain word problems, though I added word problems to each Brain Warm-up later in the semester).  These questions were completely skill-based, and intended to be higher order thinking type questions.  On Monday, each student would complete each question to the best of their ability.   We would trade and grade, and review answers in depth on Monday.  On Tuesday, students would use their Brain Warm-up from Monday to assist them with the current version.  Also, they would only be required to complete the questions that they didn't get correct from the day before.  The general idea is that students will get weekly review of almost every topic, but will only have to focus on the topics they aren't sure about as the week moves on.

Let's use the example attached below to illustrate:

A student completes all 10 questions on ID:1 on Monday.  That student gets #1,3,5,7,9 correct.  On Tuesday, they will get ID:2, but only complete #2,4,6,8, and 10.  They will not attempt #1,3,5,7,9.  Let's say on Tuesday the same student gets #4,8 and 10 correct.  That means on Wednesday, for ID:3, the student will only complete #2 and #6 correct and leave the rest blank.  This continues until students get all the questions correct, or until Friday, when they would have targeted reteaching and review practice on the topic for any question they still hadn't gotten correct after 4 attempts.  If students have all questions correct earlier on in the week, they simply start on the question set for the day.

Example of daily Brain Warm-up

Note: All four Brain Warm ups, for Monday - Thursday are included in the same .pdf

Examples of and structure of class group work and questions

For copyright reasons, I can not include reproductions of the actual problem set.  Typically, students would begin group work by peer reviewing each other's Homework Preview Sheets, we would pause for any questions, then students would start some broader, inquiry-type questions as a group.  After justifying their responses, they would separate into rows and continue to work on the individual portion of the problem set by themselves.

Example of Daily Quiz

This would be given at the end of class on March 19.  Note that there are 12 questions; I will often put 2 extra questions on a 10pt. quiz so students have the opportunity to earn 2 extra credit points if they are really understanding the concept.

Link to Khan Academy lesson and video

This is the Khan lesson that students would be asked to master (10 in a row correct) if they did not score at least 8 correct on the above quiz.  This would happen after class that day, in this case on the evening of March 19.  Hence, students would have to master this Khan Academy lesson and do the Homework Preview Sheet for March 20 as well.

Khan Academy Lesson: Negative Exponents

Statistics, before and after, and success

I keep a variety of statistics to aid in tracking my students' learning, but these were perhaps the most telling:

Here is a breakdown of my grades before I started this model, and after.  These grades are based on a standard 4-point scale, where an F is below a 60%.

Note the drastic upturn in grades, as the majority of the students with B,C,D's in December finished with A's in June.  Failures did stay the same, but I can attribute several of those to attendance issues.

I would typically worry that such numbers would simply indicate a lack of rigor, or a teacher simply lowering expectations for students.  In my case, the opposite was true.  My course was like many other math courses, in that the rigor increased as the year progressed.  Despite this, my average test scores were higher after I began using this model.  

The most telling were my averages on my end of semester exams.  The average score on my end of 1st semester exam in mid-January was 63%.  The average on my exam in June was an 80%!  This tells me that in 2nd semester, students were not only catching up on information they should have learned 1st semester, but also learning new information faster than they had before.  If only I had started this model from the beginning of the year!

Examples of student work

Since I give work back to students very quickly, I was unable to save any student work from this particular section, Section 6.4. 

Gateway Quizzes

One last component of my teaching this year was a series of 17 "Gateway" quizzes.  These quizzes were intended to measure the baseline level of skills a student should have to promote to the next year, as decided upon by the math dept.  Students needed to score at least a 9/10 to master a given quiz, and students needed to master all 17 quizzes by the end of the year.  Quizzes were administered in class regularly, in addition to weekly after school retake opportunities.  Some of the topics for the quizzes would not be considered Algebra I topics, but my 9th graders entered my class with varying levels of mastery of pre-Algebra skills.  Hence, we felt the need to include some topics from earlier grades.

Here is the list of topics, with original administration date.  Note that students were allowed to work ahead, and many were finished with all 17 by end of first semester: