Monthly Archives: February 2007

Journal entry: “A more positive environment?”


February 15

I am trying to assign regular writing assignments to all classes. One paragraph, consisting of five sentences, including a topic sentence, three supporting sentences, and a conclusion. Complete sentences only. “Are fractions easy or difficult?” “Was yesterday’s lesson successful?”

I’m happy with the results. Most students required very little explanation to understand the assignment. Even more noteworthy, students had opinions about the assign itself; one girl insisted that these were not “essays” since they were only a paragraph, so I now refer to them as “mini-essays.” A few students cut corners, but most students really warmed to the opportunity to share their thoughts.

Ultimately, I hope to have the kids tell me what they get and don’t get about a lesson’s concepts, giving them access to higher-order learning modes.

February 16

A more positive environment? I work on this all week long. I have rewards cards (“operate the projector,” “one homework freebie,” “one minute tardy pass”) for good deeds or especially insightful questions. I give out gold stars and “Wow!” stickers. I give an EC point to anyone who points out (after silently raising his or her hand and waiting to be recognized) a typo or math error I’ve made on the whiteboard. I have a 15-minute period of music, videos, and origami at the end of each week – “Festive Friday” – set up as a reward for my classes which maintain a consistently high level of readiness and homework completion during the week.

So how can I create a more positive environment? I am working on “compassion-ifying” all my student interactions: corrections, suggestions, consequences and other behavior discussions need to be always motivated by concern for the student, even if I secretly would rather not deal with a given student ever.

February 19

For my 8th-grade Algebra classes, I’m developing a post-testing (probably May) project that will give the “non-math” kids an opportunity to succeed in math. I’m going to describe the optimal angle for solar cells at our latitude and then have the students survey the roofs in the school. (There are at least five different roof angles on our campus.) They will be measuring and computing slope. They will be required to present their results on a science-fair board, giving them all kinds of graphic-design opportunities. They will learn a bit of science and a bit of math. The rubric will include language-arts requirements.

Last year for the year-end project in my Geometry class, we made “creatures” out of rectangular prisms, cones, spheres and cylinders. They had to build the creatures, make up stories about them, measure all of their dimensions, and compute their surface areas and volumes. It was a huge success. They kids had fun, cooperated with each other, said they learned a lot and wished they could have done it earlier. It would be great to create something similar with this project.

February 20

This week I’m trying to come up with corrective actions for a student who makes inappropriate comments in the classroom. Danny has been doing this since we met in September. He has improved; he no longer chooses words such as “Jap” and “faggot,” words which got him a referral and us a meeting with his mother and sister (who had been told I was picking on him). However, I still hear “shut up” several times a week. Danny and his friends apparently say this to each other a lot. Danny apologizes to me now, sincerely I think, but continues to say “shut up.” Sometimes he says it to someone on the opposite side of the classroom.

I don’t really want to keep writing Danny up for these things. I’m trying to minimize the amount of paper I submit to administration. I’m looking for a small reminder, some kind of levy which Danny will have to fork over but which is outside of the usual escalating intervention matrix. We were collecting money for a cancer-charity campaign, and I was thinking of asking Danny for a quarter or two for each “shut up.” (This would not be “required” but would instead be a voluntary choice that Danny could choose in lieu of the regular escalating consequences.) The campaign is over, but I could still collect money toward a pizza party or something – after checking with the administration.

February 26

Today’s assignment was right out of the book, a review of the basics of the coordinate plane. I’m trying to help the kids get more involved with the material, especially in a verbal way. I required them to copy all instructions from the book and to underline several key terms, including ordered pair and coordinate. I good-naturedly chastised the room for verbal imprecision. I’m trying to deal with behaviors such as citing a single number or pointing at the board (when I tell someone to identify a point) instead of just naming an ordered pair, hedging verbal bets (“the y-intercept, or whatever…” and saying “and then” instead of “equals” or “over”), and hazy justifications for steps in solving equations.

February 27

I have a couple students with some issues. One boisterous girl who was belligerent and confrontational in September lately seems to be working hard to get my approval each day, at least when she’s with us. Her flakey attendance got worse lately – she recently disappeared for a week – and I found out today that she’s started having auditory hallucinations, voices that tell her to kill stray animals and classmates in ways that are detailed and bloody. The counselor is working hard to get her some mental health help. I’ve decided to give her a break on my usual lunch-”invitation” (detention) for a while: I’ll invite her in if she doesn’t bring in homework, but with no pressure, just as an opportunity to help her stay caught up with the rest of the class.

Another girl has some anger things going on, mixed in with complicated family dynamics. She also disappeared for a while. I found out yesterday that she was in the hospital for a week after slashing her forearm with a big piece of glass. She has been trying to strike up conversations with me, and I decided to let her visit once to talk during lunch. (I checked with the administrators this afternoon, who convinced me it’s probably not in my interest to do this again, even though I kept my classroom door open.)

I will find ways to make this girl more comfortable in the classroom, through errands and other responsibilities, regular greeting, and queries during the lesson. I’ll also be sure not to try to “rescue” her, as we’ve been trained to do in our CSUSB classes.

Why do group activities falter?

The assignment was, “Make a short list of what’s wrong with group activities.” My short list:

Reasons Why Group Cooperative Activities Falter

  1. A group’s threshold of distraction is at least as low as its most “distractable” member.
  2. Success is absolutely dependent on practicing the specific activity. If you haven’t practiced enough, groups and individuals will be confused about the process.
  3. Not all students are as motivated as all other students. This can create frustration and resentment between them in both directions.
  4. If roles are not clearly defined, students will be confused about their roles.
  5. Students must know how to turn off discussions instantly, or else time gets wasted during transitions.


Lesson: Whole-Group Interactive Lecture Mathematics Lesson


At the conclusion of this lesson, the student will be able to:

  • Choose between point-slope and slope-intercept forms of linear equations as a starting point, given resources such as slope, one or more points, and intercepts.
  • Substitute and simplify chosen form and then convert to standard form.

Subject and ELL Standards

  • CA State Algebra Standard 7.0: Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.
  • Strategy 5b: Use multiple media to support concepts.


  • LCD projector, with remote
  • OpenOffice presentation software
  • OpenOffice presentation files
  • Overhead projector
  • Transparencies
  • Whiteboard
  • Pull-down eraseable coordinate plane

Introduction (Anticipatory Set)

  • Post three homework problems on the board (from PDFs supplied by textbook publisher) and ask students to write down, in complete sentences, what the given info is for each problem and what information the problem is asking for. Provide examples of “given info,” recalling earlier lessons’ examples such as y-intercept, slope, a point (or two points).
  • Randomly call students (using deck of cards or dice) to read answers. List answers on board, without commentary, under headings of “given info” and “type of answer.”

Teacher Activities (Instruction)

  • Quickly review prior lesson’s activity: building a table used to choose between two linear-equation forms and converting to slope-intercept (if in point-slope) and then graphing the result.
  • Announce that today’s activity will be very similar, but instead of trying to get all information into slope-intercept, we’ll be converting to standard form. Announce that there will be a short quiz at the end of the activity, and students will be turning in their work.
  • Display sample homemade student worksheet on LCD projector. (See illustration.)
  • Demonstrate populating first row, using first set of given information: m=-2, b=3. Complete row will look like this:


given info. m point b S-I/P-S? sub/simp. –> standard
m=-2, b=3 -2 —- 3 S-I y = mx + b
y = -2x +3
y = -2x + 3
+2x +2x
2x + y = 3


  • Demonstrate second row, using given info: m = -2, (1,3). This time, point-slope will be the initial form of linear equation, but the process of conversion to standard form (after the distribution step) will be reminiscent of row 1.
  • Give students two more rows to work on, supplying a slope and intercept for one and a slope and non-intercept point for the other. Guide them through this practice.
  • Survey students to recall ideas from previous lessons: What if there is no explicit m (students are given two points)? What if there is no explicit b, but the point contains an x-coordinate of zero? Conversely, what if there is an x-intercept given? How do they choose between initial forms? (Students should say that S-I is preferred, for its ease of graphing.) During these questions, call on students randomly (using dice or deck of cards), giving the class time to consider and discuss answers before rolling, and allowing no “I don’t know” answers. (Students who say “I don’t know” should be given time to discuss the question with neighbors.)
  • Give students two more rows to work on independently, supplying a slope and the point (0,1) for the first (students should recognize the number 1 as the y-intercept) and two points for the second (students should realize that they will need to compute m using the slope formula, which they have previously studied).
  • Administer quiz: three more questions, on new paper. Students should work alone.

Accommodations for ELL/SDAIE/Exceptional Learners

  • Use of LCD projector.
  • Use of white board.
  • Use of multiple colors of text on LCD presentation; use of multiple colors of marker on white board.
  • Speak slowly, clearly.
  • Use of gestures/expressions.

Student Performance

  • Students build semantic concepts table which leads them through the steps of choosing an initial form of linear equation, substituting the given info, simplifying, and converting to standard form.
  • Students use new paper and build table which they use for quiz. After the quiz, students hand in work for grading by teacher.


  • Students hand in quizzes for grading by teacher.

Teacher Reflection

The work itself represents a lot of steps for some students, manageable by few. (This is a “foundations” class; I believe many of these students do poorly in algebra because they cannot focus on a problem longer than two steps. This was demonstrated in this exercise, and it’s demonstrated dramatically when solving linear equations: they can do a two-step equation, but when it comes to equations requiring distribution or collecting terms on one side, they seem to run out of steam almost before they even begin.)

Students occasionally needed reminders of tracking negatives and distributing. I also ran into the classic questions about how to handle more than two factors at once. (When point-slope equation has a fractional m, students have been taught to “clear the fraction” by multiplying both sides of the equation by the denominator. This confuses students who are drawn to next-door factors in a construction like this: ½ (x-3) (2). The students don’t see the cancellation of the 2 and the ½ but instead want to distribute one or the other – or both! – of these. Teacher should take care to write the denominator-canceling integer next to the fraction.)

A student who is conscientious failed to plan and ended up squeezing a lot of work into a single line on her lined paper. The teacher should anticipate this and tell students to allow five rows for each problem.

I have trained the class to recognize b (given either as “b=2” or as the point “(0,2)”) and to use this as their criterion for deciding whether to begin with point-slope or slope-intercept. However, some of the students in this exercise failed to recognize the “hidden” b and chose point-slope when they could have worked with slope-intercept instead.

The formatting of these papers represents the typical poor quality I see each day. I’ve spent a lot of time explaining how the papers should look. I may devote a whole day to this in the future. It’s hard to resist telling the students that this work is insulting to me. Since the students can’t all be counted on to actually draw the table, next time I would stop at this point and have students hold up working showing table before proceeding.

Illustration: Projector Slide demonstrating table students are expected to draw and populate.

Journal entry: “Hijacking the class”

February 5

The students reminded me today of the math classroom’s absolute total dependence on verbal skills.  We are studying linear equations, and we just moved from slope-intercept form to point-slope form.  The students are beginning to be comfortable with the instruction, “Write down point-slope form.”

Some of them can use this on their own in response to my prompt, “What do you do next?”

But the book is inconsistent in the meaning of “form,” and the students sense my discomfort.  The template or model equation itself — y – y1 = m(x – x1) — is described as “point-slope form”; at the same time we say that a specific equation — such as y – 5 = 3(x – 4) —  is written in in “point-slope-form.”  I don’t know how I would teach this differently next year, and we’re too far into the process for me to make a big deal out of it right now.  I need to keep looking for these things (and find solutions for them) that make the students whine out loud, “Why does math have to be so complicated?”

February 6

Period 3 had 100% homework today.  All students brought in homework.  I was astonished and praised them way too long.  Some apparently went home with tales of their weird math teacher.  (I even heard of parents who responded to these tales with their own praise of their children.)  It all felt really good.

Students had been showing me a reasonable rate of return, maybe 60-70%, and a few had excuses occasionally.  A few however, were just never bringing in homework and merely shrugged when I asked them why.  A couple weeks ago, I cracked down: no homework → lunch detention; skip lunch detention → official after-school detention.  I found that one total homework abstainer (after he got done complaining about my calls home and his detentions) is now bringing in his homework every day and even seems to be understanding more of what’s going on.

So, I learned from the students that even though they complain about having to work, they also are happy to be learning.  This is what we want, since when they’re learning, they’re engaged and not screwing around.  Plus, they’re learning, since they’re not screwing around.

February 7

The principal visited today on a pre-announced observation.  I was surprised to learn from defiant Frank that not everyone fears the principal.  After a couple reminders to turn and face forward, and then my next classroom-intervention-matrix step of a writing assignment, Frank began complaining about being singled out.  He reached the point of demanding to see the assistant principal and even the principal, whom he knew was right there in the room.  I spoke to him calmly but firmly at each stage, and I think it may have felt to him that he was being singled out.  I believe, however, that this is someone who is usually not denied anything.  Or maybe it’s the opposite, and he feels like the classroom is one place where he can make his own decisions.

Nevertheless, I was forced to deal with his hijacking directly, and eventually I had to ask him to leave.  The other students were complaining about his behavior, and after the class was over, the principal told me I had done the right thing. Regardless, it would have been nice to have an errand to send Frank on that would have allowed him to calm down without having to get in trouble.

February 8

Sean wrote in today’s mini-essay that the lesson hadn’t gone well.  He had trouble focusing (which was reflected in his disruptive behavior) and wrote that this was because he hadn’t gotten enough sleep the night before.  I now casually ask him, nearly every day, if he got plenty of rest last night, as a reminder to him to do so and as a way for both of us to recognize the cause if he becomes belligerent.

I learned to remember that behavior is not spontaneous and usually not premeditated.  I have tried since this discussion to be ready with questions about the students’ preceding 24 hours – enough food?  enough sleep?  enough peaceful opportunities to do homework? – whenever issues begin to arise.  This feels like a great use of my time and worthy investment toward classroom sanity.

February 12

I began using my 30-sided die today for random selection during lessons.  I learned from students today the following: this is a great technique for equity.  The first couple (or ten) times, they think you’re kidding.  Then they begin to figure out that the teacher is serious when he says, “Answer this question.  [Pose question.]  Turn to your neighbor, and discuss this for 30 seconds, and be ready to answer when I roll the die.”  Be sure they learn that you won’t let them off the hook with the response, “I don’t know.”

I’m happy with using this technique in just about any lesson now.  I knew, of course, that many students were hiding behind the hand-raisers and troublemakers and consequently not learning a thing. But I was letting the momentum of a marginally functional classroom keep me from fixing this problem.  So, the random-selection technique is working great.  And students are even learning about probability first-hand: “Yes, ladies and gentlemen, the purple die will give each of you an equal opportunity to show us how much you’ve learned!  And the purple die doesn’t even remember that it chose Maria a minute ago: it might just choose Maria again.  She still has the same chance as everyone else!”

February 13

Terrible day.  My students taught me today, among other things: don’t let them use the stapler (someone stole the rubber feet off the bottom), don’t let them have paper clips (they folded them into dangerous macelike balls), don’t let them out of their seats (they chased each other around), don’t let them have rubber bands or paper (somebody got hit in the eye with a folded missile from across the room).  Probably better not to let them have any freedom at all.

More realistically, I need to do a better job of limiting the choices the classes make (especially my difficult afternoon periods), and I need to simultaneously tie the students’ choices to their freedom.  I have an official “Festive Friday” each week: 20 minutes of origami, music, reading.  I can (and have) taken this privilege away from individual classes for misbehavior during the week; however, it’s been way too subjective.  I need to make yet another system – a numeric scale to tie Festive Friday to various behaviors in the class, including punctuality (see February 12), attentiveness, respect, and homework completion.

I told the class at the end of the period that I didn’t think it had gone well at all and asked them for their opinions.  They agreed by consensus that they had had too much freedom.

Lesson: Cooperative-Group Mathematics Lesson



At the conclusion of this lesson, the student will be able to:

●      Write a linear equation, given various configurations of points, slopes and y-intercepts

Subject and ELL Standards

●      CA State Algebra Standard 7.0: Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.

●      Strategy 5b: Use multiple media to support concepts.


●      LCD projector, with remote

●      OpenOffice presentation software

●      OpenOffice presentation files

●      Overhead projector

●      Transparencies

●      Whiteboard

●      Pull-down eraseable coordinate plane

Introduction (Anticipatory Set)

●      Post slope-intercept form on the board.  Query students in detail on what it means to answer a homework questions which prompt: “Write an equation in slope-intercept form.”  Students should recognize that they are filling in the missing numbers (m and b) and are retaining the variables x and y along with the organization of the equation.

Teacher Activities (Instruction)

●      Introduce “Making the Equation” game.

  1. Four “games”comprise complete set of activities. Fourth game is a culmination of the skills practiced in the three preceding games.
  2. There are three “hands” in each game.
  3. Each team gets a plastic bag containing 24 “resource cards”: colored pieces of paper containing the data needed to create a linear equation.  In the Yellow Game (yellow paper pieces), a resource card contains a slope and an ordered pair; in the Green Game, each resource card contains a slope and a y-intercept; in the Blue Game, each card contains two ordered pairs; in the Pink Game, the cards are a mixture of contents from the three preceding games.  (In this game, students must decide what to do with the resources and what form of a linear equation to start with.)
  4. In each hand, teams pick a resource card, write down the resources in the indicated area, write the template equation – either y = mx + b or y – y1 = m(x – x1) – and then substitute the resources and simplify if appropriate.
  5. At end of each hand, teams trade and grade.

●      Display instructions on LCD projector.  (See attached.)

●      Display sample homemade student worksheet on LCD projector.  (See attached.)

●      Demonstrate sample exercise on LCD projector.Guide students through folding two papers each into four sections: “taco” fold and then “taquito” fold.  Use this folded paper for the worksheets.

●      Guide students through each game.

Accommodations for ELL/SDAIE/Exceptional Learners

●      Use of LCD projector.

●      Use of white board.

●      Use of multiple colors of text on LCD presentation; use of multiple colors of marker on white board.

●      Speak slowly, clearly.

●      Use of gestures/expressions.

Student Performance

●      Students fold homemade worksheets.  Write heading info in top section of first page.

●      Students play one game at a time, selecting three resource cards and writing one equation each. After completing each game (three equations), students stop and await direction.

●      Each hand involves 1) copying resources from resource card to appropriate field on worksheet, 2) writing down template equation (either point-slope or slope-intercept), 3) substituting, and 4) simplifying.  Students box final answer.

●      Students trade papers with neighbor teams and grade each other’s work, using answers on overhead projector.


●      “Trade & Grade.”  (Teams trade with next-door teams and grade work.  Answers are displayed on overhead projector.)

Teacher Reflection

An exercise in frustration for all concerned.  Students used no initiative in deciphering instructions displayed on overhead and generally refused to hear instructions.  Teacher did not allow enough time for instruction, and did not manage time well enough to get through all four games. Teacher did not explain clearly enough that each student should maintain his/her own work, to be turned in and graded.

Many students believed they were done when they found a slope, failing to understand that finding the slope was the first step to substituting and simplifying the equation itself.  I have been working faithfully on the concepts of an equation (as a statement and as grammatical form which requires three parts), but the students are attracted less to abstract concepts than to procedural recipes.  I will continue to discuss this, probably through short-duration, high-frequency “equation? Or not?” drills.

Repeat the game later for better results.  (Students figured out the instructions through trial-and-error and dozens of redundant questions.)

On the plus side, most students were generally on-task, especially considering the distractability of the group in question.