Saturday, January 16, 2016

The MTBoS, Week 1

I know that I usually don't post to the blog on Saturdays. But I have a tradition -- near the end of every semester, I make at least one post to discuss the Math Twitter Blogosphere, or MTBoS.

And so what is going on at MTBoS? Well, it's the 2016 Blogging Initiative:

The above website belong to Sam Shah, a New York high school teacher. (I've linked to Shah's own blog, "Continuous Everywhere but Differentiable Nowhere, back in October.) As part of the 2016 Blogging Initiative, make teachers make four posts, once a week, in response to one of two prompts.

I've said before that I like to consider myself a member of the MTBoS. But I believe that I'm not worthy to be a full member of the MTBoS until I become a full math teacher. Still, even though I'm just a substitute teacher, I want to make the four weekly MTBoS posts anyway.

For week 1, we may choose either Option 1: "Keep a lookout for the small good moments during your day and blog about them," or Option 2: "We thought blogging about a day in your lives would be a great way to start getting to know each other!" I couldn't decide which one to write about -- so I choose both of them. I will write about a day of subbing -- yesterday, to be precise -- but I'll point out all the good moments that happen along the way.

And so, here goes nothing...

A Day in the Life of a Math Sub

7:30 AM -- I arrive at the middle school, expecting to be placed in a special ed class. Indeed, I'd taken the call for the special ed class Monday evening. Then the next day, I took a call to cover an English Language Development class at the same school for Thursday -- a teacher who would be out both that day and Friday. So I was wondered whether I'd stay in the ELD class a second day or be placed in the special ed class for which I'd been originally called.

Instead, subs more qualified to cover both special classes have been found. And I end up being placed in class for which I was more qualified -- an eighth grade math class. This is much to my delight, because math is my subject.

7:55 AM -- First period is the teacher's conference period. As it happens, I see the regular teacher for the class, on his way to a training meeting. I tell him that I've subbed for his class once before in September, and he replies that he recognized me from subbing other classes around campus.

The teacher tells me that he is having the students take a quiz. First, I am to pass out a worksheet labeled "Skill Builder 5" and "Skill Builder 6." This is copied from MathLinks: Grade 8 (Student Packet 3), a Common Core curriculum the district purchased last year. He warns me not to spend more than 20 minutes going over the worksheet, because they'd need at least 30 minutes to complete the quiz.

After the teacher leaves for his meeting, I decide to go to the classroom where I subbed the previous day, in order to establish continuity with the second sub for the ELD class. When I was in that class a day earlier, the students were supposed to divide into the three reading groups to which they had previously been assigned. Instead, they'd split into two large groups. One girl had informed me that the others weren't in the correct groups, as well as how to find out what the correct groups were.

So on this day, I tell the second sub about the correct reading groups so that she can group all the students properly. Then I thank the girl for telling me about the groups, and even gave her a yellow reward card for being so trustworthy. Finally, I return to the math classroom and prepare for the students to arrive.

8:55 AM -- For second period, the teacher has a special Math Lab class. It's common at many middle schools for the weaker math students to be assigned a second math class -- indeed, I will see many of these same students in Periods 3-6 later that day.

In many ways, the name "Math Lab" is a misnomer, since there's no "lab" involved. But this class really was a "lab" -- a computer lab, that is. In the era of Common Core and computerized tests such as the SBAC, many classrooms have a class set of laptops. The carts contains room for 40 laptops, but one slot is empty before the class starts -- the laptop probably went missing weeks earlier. So I knew I was responsible for 39 laptops.

I decide to use the seating chart to keep track of the laptops. As each student takes a laptop, I write down the laptop number next to the student's picture. I also use the seating chart for attendance. There are no absences during this period, but one boy is not in the seat listed on the seating chart -- he should be in the second row, but instead he is in the front row in the corner. Naturally, he claims that this is his real seat. I tell him that there's an 80-90% chance that he is lying, and that I'd have to write his name on the board, intending to write it in the note I was leaving the teacher. Sometimes I wonder whether sitting in the wrong seat is worth leaving his name for the teacher, or perhaps he's telling the truth about his seat -- but I know that I must be extra strict with the seating chart on days when there are laptops out or the students are taking a quiz.

The students are supposed to complete two assignments for the class, but it is difficult for me to determine whether they are really working on them or not. Back in September, they were all working on the same assignment, and when it was completed, the computer reported the percent correct -- so as soon as I saw that percent, I knew that they were finished. But this day, they're all working on different personalized assignments, some of which reported percent correct and some didn't. So all I can do is make sure that they aren't going to other websites besides the Google classroom. I catch a few students going to a shoes website, and some students linger on YouTube instead of choosing a song quickly and going back to the math site. Other than that there are no problems -- I see some students playing games, but these are actually on the math site, a reward for completing assignments.

Since I have nothing else to do at this time, my eyes linger to the back board, where the teacher has posted student grades for each class, from highest to lowest, with ID numbers rather than names. On each list, there's an orange line separating those earning C's or better from those with D's or F's. I notice that of all the classes, third period has the worst grades, with about half of the students below the orange line. Of these, half are earning 55-69%.

Just before the class ends, an administrator enters the classroom in order to escort a student who's been assigned snack detention by another teacher. Of course, it's the boy sitting in the wrong seat. I know that if he's the type of student to be assigned snack detention, then he's also the type of student to lie about his seat. And so I feel that it's proper to write his name down for the teacher. I also keep his name written on the board -- sometimes I feel that it's wrong to embarrass students by keeping their names on the board. But I see that the regular teacher writes names on the board all the time, so I'm only doing what the teacher normally does.

9:55 AM -- It's snack time. I usually don't eat during snack, preferring to wait for lunch. So instead, I write a note of warning on the board for third period. Even though I know that the grades list hasn't been updated since before Thanksgiving break, I write that they should take the grades seriously. The semester will end next week, and it's likely that the quiz they're about to take may be the last chance they have to raise their grades before the end of the semester.

10:15 AM -- Third period arrives, and they see the note about the quiz. I pass out the worksheet, and the students begin working on Skill Builder 5.

Whenever I leave a note for the teacher, I like to leave good names as well as bad names. So this counts as my first One Good Thing -- it's good that some students are able to figure out the answers to the questions quickly. This lesson on Patterns and Linear Functions is something that was not previously emphasized -- Algebra I teachers often skipped this chapter altogether. But now it's emphasized under Common Core. So I am glad when some students are able to tell me that if the number of toothpicks follows the pattern 5, 8, 11, 14, 17, ..., the recursive rule is to start with 5 toothpicks and add 3 each step. If you asked my eighth grade self what a "recursive rule" is, I couldn't have told you, so I'm glad that these students are able to understand such a challenging concept.

One of the most challenging parts for any teacher -- especially a sub -- is transition. As we all know, students waste so much time during transitions. I have to make a major transition from going over the review worksheet to giving the quiz. Many students are still confused by many of the questions on the worksheet, yet I know that I have to start the quiz. So I just quickly show the students the answers on the document camera so the quiz can begin.

Of course, many of the students run out of time and don't finish the quiz. I feel guilty about this -- here I am, a math teacher who can help them pass the quiz, but instead all I'm doing is showing them the answers, which they copy without learning anything. And of course, they will complain to their teacher on Tuesday that I didn't give them anywhere near enough time for the quiz.

It's difficult for the students to complete both sides of the worksheet and for me to go over the answers all within a span of twenty minutes. Still, I understand why the teacher assigned this. He couldn't be sure that he'd be assigned a math sub. If a non-math sub had to cover the class, all that sub would be able to do is just show the students the answers, so the teacher wanted to make sure that they had sufficient review work, rather than finish the quiz with too much time remaining.

I wonder whether back in first period when I saw the regular teacher, I should've informed him that yes, I am a math teacher. Maybe he would've had me take the entire period to cover both worksheets and waited until next week to give the quiz. But I didn't want to be so presumptuous -- maybe he gave the quiz that day because the semester is almost over.

Still, I resolve that I would only cover the Skill Builder 5 side of the worksheet to the remaining classes the rest of the day. I often say -- and I write this in my note to the teacher -- that I would rather cover one side of the worksheet right than both sides fast.

11:15 AM -- Fourth period isn't specifically listed as an "honors class." But it's obvious that this group consists of the best math students. First of all, the grades list shows only two of the students below the orange line -- one has a D, and the other has a score of 0%. It's possible that the 0% student is someone who had transferred to the class just before Thanksgiving and didn't have time to turn anything in before the grades were printed.

Furthermore, there is a museum field trip for "scholarship students" -- which I assume refers to the top eighth graders. Recall that no one from the remedial second period class is on the field trip, but fully one-quarter of fourth period is on the trip. And of course, no one from fourth period is assigned to the second period class. So putting all the evidence together, fourth period is the "honors class."

Of course it's easy to find One Good Thing about this class. I like how many of the students in this class answer the question about the explicit rule -- some write "multiply the step number by 3 and add 5," while others say, "multiply the input value by 3 and add 5 to get the output." So these students are able to write it in their own words, emphasizing either "steps" or "input/output," whichever helps them understand the lesson better.

And even though I don't go over the Skill Builder 6 side in this class, naturally many of the students are able to figure them out anyway. I like how one student is able to figure out the answer where the input value needs to be a negative decimal, and another question where the explicit rule is to divide the input by 3, or alternatively to multiply it by 1/3. This latter description will be more useful to them when it's time to learn about slope.

When it's time to give the quiz, of course everyone finishes the quiz on time. Many of the students complete it early -- and the school policy is that teachers are allowed to let deserving students go out to lunch a few minutes early. This is the first time as a sub that I have ever let the entire class go to lunch early.

12:05 PM -- It is lunchtime. I am caught with only $2 in my pocket -- well, $2 and a twenty-dollar bill, but many school cafeterias don't take 20's. Fortunately, the lady behind the counter is nice enough to let me have a slice of pizza for free. So I use the $2 to purchase some food from the student snack line -- 75 cents for chips and $1.25 for soda. Actually, that's 75 cents for baked chips and $1.25 for carbonated fruit juice, since cafeterias are supposed to serve healthy (or at least healthier) foods.

12:40 PM -- There is an instructional aide for fifth period. Throughout the period, she is able to answer some of the questions that I am unable to answer -- but she admits that she herself is confused with recursive and explicit formulas.

Here is One Good Thing about fifth period -- I like how many students are able to figure out how to solve the following question, "In which step number are there exactly 92 toothpicks?" They've already figured out the explicit rule 3n +5, so the students have to solve the equation 3n + 5 = 92. A few of them are even able to come up with the answer 29 in their heads.

When the quiz begins, some students say that they should be allowed to use notes, claiming that the teacher allows them to use notes on a quiz (as opposed to a test, for which no notes may be used). I check this out with the aide, but she's not aware of this rule either. And so the students have to put their notes away. A few students are confused with a quiz question where they are to use the variables x and y to write the explicit formula, and so I decide to help them out on this question only.

The aide makes sure that the students are behaving -- she tells them that any names left by a sub would receive a severe punishment -- Saturday school! I understand why the teacher would come up with this rule -- he knows that students may want to misbehave when there's a sub, so to deter such misbehavior, he comes up with a stricter punishment.

Now this makes me feel bad about the boy whose name I wrote during second period -- yes, he was not in his seat, but Saturday school seems like a harsh punishment just for that. Still, I've already written his name both in my note to the teach and on the board -- and besides, I think that seeing his name on the board discouraged any students from misbehaving the rest of the day, even before the punishment of Saturday school was announced.

1:45 PM -- Sixth period is usually a challenge for any sub -- especially when it's the last period before a three-day weekend. The transitions in this class are very tough, and students are definitely running out of time to finish the quiz.

Some students place their quizzes in a special yellow folder. This indicates to the teacher that they need more time to finish the quiz. I point out that they are doing so at their own risk -- yes, normally the teacher will give more time to finish the quiz, but this is the end of the semester. He most likely wants to start grading them as soon as possible so that he can submit the final grades. But I'm not sure whether any of the students are listening to me.

2:40 PM -- As the school day ends, I reflect back to think what I could have done better. I'd hate to think that there's a student on the border between passing and failing -- one who might have passed if I had reviewed with them better, but now they are failing and are at risk for missing the eighth grade promotion ceremony at the end of the year.

For example, perhaps I should have brought my lunch back to the classroom and started looking at the completed quizzes from Periods 3-4 -- especially looking at the questions which the weak third period class got wrong, but the "honors" fourth period class answered correctly. Then I could have targeted my review in Periods 5-6 to spend what little time I had to go over the corresponding questions on the Skill Builder Worksheet. Maybe this could have allowed one more student to pass the quiz and ultimately the semester.

This concludes One Day in the life of a Math Sub. Part of the 2016 Blogging Initiative is for me to respond to the last three participants to complete the initiative, on their respective comments page. I don't wish to create a Wordpress account, and so I will choose three Blogspot blogs to respond to, as soon as I click "Publish" on this current post.

Here are the three blogs I've chosen:

Just looking at the blurbs, the first link about is "A Day in the Life," while the other two are about "One Good Thing." I look forward to reading and responding to them.

I'm supposed to complete this first post by the "end of the day Saturday," which I interpret to mean by midnight Eastern Time (since Sam Shah is in New York). This is just barely in time. I hope to make by MTBoS Week 2 post on Wednesday (as I often post MTBoS on the second day of finals). I am still posting the Geometry final on Tuesday.


  1. I enjoyed reading from the perspective of a sub. Your attention to student learning is wonderful. I have a feeling you must be in high demand!! Thanks for sharing.

  2. I enjoyed reading from the perspective of a sub. Your attention to student learning is wonderful. I have a feeling you must be in high demand!! Thanks for sharing.

    1. Thanks for reading! And I enjoyed reading your blog post from the perspective of an instructional coach. I've used algebra tiles in my classes before, but I've never had the oppotunity to use Desmos. It's good when we all can contribute to the MTBoS.