The First Day of School
May 27, 2019
On the first day of school, the teacher begins a training process that conditions students to sustain effort and concentration – the most important catalysts of mathematical learning. To accomplish this, they follow the widely accepted norm of establishing procedures, but veer from this unwritten rule by teaching content while doing so. As a master teacher, they understand that inundating students with routines devoid of academic learning is exhausting, inefficient, and less meaningful than introducing them in lesson contexts.
Through several dozen short tasks lasting between a few seconds and five minutes, the instructor spends 60 – 90 minutes teaching classroom practices and work habits, while facilitating a four-part math lesson. In the ensuing days and weeks, they will repeat this process daily, gradually spending less time addressing procedures and more time teaching content until the former is rarely, if ever, needed. Anchor charts, therefore, are used sparingly. Although the words, tone, cues, and expectations vary slightly depending on the grade level and teacher’s personality, the mathematical goals and tools remain the same.
Before students enter the classroom, the following items are piled neatly on each desk:
Pocket folder
Pencil
Dry-erase marker
Sheet protector stuffed with two pieces of card stock (one white, one red) and a small felt eraser
Marble notebook
Math workbook
As the students arrive, the teacher meets them outside the classroom, funneling each child through the doorway one-by-one. The orderly entry establishes the classroom as a place of work and purpose. Having researched the students’ math skill and comfort in the weeks leading up to the first day of school, they have already prepared a strategic seating chart to maximize learning (see The Sagherian Triangle).
They assign seats and review a few simple classroom rules, the most important of which is maintaining eye contact during instruction. Either mentally or verbally, they vow not to waste an instructional word or repeat directions. Students, in turn, must sit up straight and look at them when they speak. An instructor who uses measured, clear, concise language absent of unneeded words, might seem to be rushing, but this is a false perception. The teacher’s aim is efficiency, not speed. Throughout the class period, they are careful to maintain a pace that all students can keep up with, so long as they are paying attention.
Next, they tell students that the person sitting next to them is their math partner. Conversation rules are as follows:
One person talks at a time.
Speak loud enough for your partner to hear, but soft enough to not distract other groups’ conversations.
Eye contact is expected while talking, listening, and asking questions.
With this established, the teacher stimulates student pairs with short, uncomplicated questions, allowing them to practice conversing, e.g.
Name a few fun activities you did over the summer.
What was the most interesting thing you saw on your way to school this morning?
What is your favorite subject and why?
Each time the instructor notices students breaking conversation rules, they concisely review expectations, trying hard to hide their urgency. Constructively conversing will be vital to learning mathematics this year and class can’t begin until all students hold productive discussions.
Once satisfied, the teacher introduces a call-response protocol with three to five questions that every child in the class can answer correctly. Starting with the phrase Raise your hand if you know, the instructor waits until all hands are raised and then signals for a choral response with a snap or gesture. By selecting problems that every child can confidently answer, they instantly know which students are paying attention and/or which children are purposely resisting participation.
The following dialogue might take place:
T: Raise your hand if you know my name.
S: (Raise hands.)
T: (Waits until all hands are raised.) On my signal, say my name. (Snap)
S: Ms. Davis.
T: (Points at a green piece of paper.) Raise your hand if you know the color of this piece of paper. (Snap)
S: Green.
T: (Raises one hand while pointing at a stapler with the other.) What am I pointing at? (Snap)
S: A stapler.
Gradually, the teacher prompts choral responses with fewer and fewer words. Like a train, the tempo is initially slow but gradually gains momentum as the call-response exchanges continue. When executed well, the rhythm becomes pleasurable, the energy contagious. Along the way, the teacher begins asking easy math questions. Creating a success association with the subject is the first step to relieving (and hopefully reversing) mathematical anxieties and complexes; or, for lower grade teachers, never allowing them to develop in the first place. The following might serve as excellent initial questions:
1st Grade: (Project 2 dots) How many dots do you see?
2nd Grade: (Project a square.) Name the shape.
3rd Grade: What’s 5 + 5?
4th Grade: What’s the value of 5 x 2?
5th Grade: How many tens are in 80?
6th Grade: (Project a half-shaded circle.) What fraction of the circle is shaded?
The teacher then tells students to stand up when only a board and marker are on their desk. “You should be standing in five, four, three, two...one.”
If students aren’t standing in the allotted time, they are directed to sit back down and the process continues until they’ve all met the expectation. Again, the teacher immediately knows who’s focused and cooperating, but this simple classroom management exercise holds deep mathematical implications. Conditioning students to follow concise directions is not only vital to maximizing class time, but also building their powers of concentration. Once a class follows instructions with alacrity the first time they’re given, the ceiling on what can be academically accomplished is significantly raised.
Holding a closed dry-erase marker upside down, the teacher says, “Show me that your marker is capped.” After students mimic them, they introduce two simple rules:
Writing and drawing is only permitted when students are directed to use their markers.
Lids remain capped unless they are writing.
These guidelines are essential for math lessons to go well. Dawdling on dry-erase boards distracts students from lesson content and consumes an expensive school resource. The teacher will perform scores of informal assessments daily, and this isn’t possible if markers aren’t treated as learning tools.
“Sit down when you’ve written the number one on your board. Should be seated in three, two...one.”
When students are seated, the instructor says, “Show me your board.” A sloppy student response invariably follows. Some children hold their boards backwards or point them at sidewalls. Others pinch the corner with one hand and the board flops down, hiding their answer.
“Boards down,” says the teacher, as they pick up a dry-erase sleeve and demonstrate how they expect students to hold them – one hand gripping each side, raised just above their eyes. This position allows the instructor to maintain eye contact with every student and perform efficient informal assessments. Other white board rules include:
Unless otherwise stated, write answers, responses, etc. on the white side of the board.
Show me is a signal to hold up boards as soon as they’ve written an answer.
Red side up means to place the board face down on the desk, hiding answers, until the instructor says Show me.
The teacher continues calling out numbers until all students efficiently write and correctly flash their responses. They then return to asking simple mathematical questions. Projecting the equation 2 + 1 = ___ they say, “Show me the answer.”
The informal assessment reveals two common written responses:
3
2 + 1 = 3
They write down both on the board and say, “I see three and I see two plus one equals three. Which answer is correct?...Turn and talk to your partner.”
In time, a child clarifies that they were directed to write the answer, not the equation. This detail is vital to keeping instruction efficient for two reasons:
Extra writing can be time consuming, especially for students who struggle with handwriting dexterity.
When students write extraneous information, the teacher must pause more often to locate student answers. The small delays accumulate into lost instructional time, but – more critically - a lag in classroom momentum. Feeling the weight of empty pauses, many children become distracted.
The teacher then continues prompting students with fill-in-the-blank problems until all students have met the protocol.
Holding a small felt square above their head, the instructor says, “Show me your eraser.” Once the class complies, the teacher drops it into a dry-erase sleeve. “Slide it on the white side of your board and stand behind your chair when there is nothing but a pencil on your desk.” By the time the class has risen, the teacher is standing in the front left corner of the classroom.
Students are responsible for having a sharpened pencil when math class begins. The instructor points to the pencil sharpener(s) as well as an inventory of spare writing utensils stationed close to the doorway. Then, motioning towards the left side of the room they say, “Raise your hand if you’re the first person in your row.”
Four hands raise and – holding eye contact - the teacher says, “I’m going to place a small stack of papers on your desk. Please don’t touch them.” To hold all students’ attention during the distribution, the teacher might ask simple math questions that preview content on the written fluency sheet.
Back in the front-center of the room, they say, “When I snap I want each row leader to take one paper and pass the rest. Please sit when you have a paper and don’t peek at the problems.” The students are slow to react and the teacher resets the class until they efficiently move papers across their row. Spending several minutes training students to do this well saves hours of instructional time over a school year.
Content with the paper distribution, the teacher leads a written fluency routine. This involves a few procedural instructions that they will repeat over the next few days, but with consistency, they’ll hardly need to say a word next week. Using the choral response and white board protocols that were covered a few minutes earlier, the teacher then delivers a few additional fluency drills.
Students file away their white board tools, take out their notebooks, and write the date in the upper right corner of the first page. The nuances of maintaining notebooks vary from teacher to teacher, but the expectation does not. Students clearly understand where to record their work when they’re directed to do so.
By the time they’re finished writing the date, a word problem is projected. The class reads it chorally and the teacher directs them to:
Draw a picture or diagram of what they read.
Write a number sentence that helps them solve the problem.
Write a word sentence that answers the question.
Because the instructor’s main focus on this day is to teach students how to work, the content is a grade level or two behind. There will be plenty of time to introduce complexities later, especially when the students’ working stamina has increased. For now, they’re content to create success associations with word problems while introducing (or reintroducing) the Read, Draw, Write (RDW) process. To succeed in mathematics, students need to accurately and efficiently represent information in pictures or diagrams. They also need to justify their work through equations and written responses. By providing simple content to draw and analyze, the instructor sets a fertile track for cultivating the RDW habit and building problem-solving skills.
With two stages of the four-part lesson complete, the teacher begins the first concept development of the school year. They planned the lesson knowing that mathematics is a subject children rarely practice in the summer. Deconditioned to sustain concentration, most students are ill prepared to learn a new, complicated concept on the first day of school. Still, getting through the curriculum is a long journey and suspending the initial lesson for a later date is wasteful.
Considering all this, they selected manageable content to teach. A lesson with four major complexity tasks, for example, might be reduced to two or even one. This modest goal initiates the curricular journey, while creating more success associations with the subject. In the process, it further establishes the classroom as a place of work and purpose. Customized content might include:
1st Grade: Reviewing numbers 1-5 instead of 1-10.
2nd Grade: Place value to 100, instead of place value to 1,000.
3rd Grade: The first five Times Tables of 2 facts, instead of all ten.
4th Grade: Place value to 10,000, instead of one million.
5th Grade: Multiplying and dividing decimals by 10, instead of multiplying and dividing decimals by 10, 100, and 1,000.
Throughout the abbreviated lesson, the instructor engages students with choral responses, white board exchanges, and partner discussions. In the process, they frequently check for understanding and thus have a good feel for what every child does and does not understand.
With ten to 15 minutes remaining in the class period, the teacher ends the lesson and directs the class to an inauspicious dry-erase board on the front wall (see image on right). Pointing at it they say, “Raise your hand if you know the title of this white board.”
Scaffolded independent practice problems match the nature of mathematics. After mastering one complexity, students are ready for a new challenge that stretches their understanding.
When all students have raised their hands, they signal and the class chorally says, “Order of Work.” The teacher then provides the following independent practice guidelines:
Practice will be a part of daily math lessons.
The assignments will always be posted on the Order of Work board.
Ancillary resources, such as Challenging Word Problems, are stacked on a bookshelf in the back right corner of the classroom.
Never expect to finish all of the listed tasks. The entirety of independent practice time should be spent working through incremental challenges.
All projected problems (Problems on the board) should be written in personal notebooks.
If students are confused, they are encouraged to ask their partner questions.
A system of answer keys is posted around the room. The students’ desk position dictates which answer key they use (see image on right).
After completing a task, check your work on an answer key.
Never move on to the next task until your work is completely correct.
Moving on to the next task without correcting and understanding mistakes is not in the students’ best interests, because the ensuing tasks become more challenging.
If students answer a problem incorrectly, they should follow this procedure:
Try to understand the mistake you made.
If you don’t understand why you made the mistake, discuss the problem with your partner.
If you’re still unable to understand why you made a mistake, ask a different classmate or raise your hand and wait for teacher help.
The colored boxes represent desks. Students check their work on the answer key that corresponds to the color of their desk. Thus, there should never be more than five students using the same answer key at once. This evenly spaces students throughout the room, minimizing distractions while maximizing efficiency.
“You’ll be working for three minutes,” says the instructor. “Begin.” They step back and watch the students work.
On this day, they are solely focused on beginning an independent practice system. If the class learns to work well within the outlined parameters, the teacher can assist struggling students when content becomes harder.
The problems on the board are easy enough for each student to complete independently, allowing the instructor to monitor everyone for the entire work period. Occasionally, they remind children to sit up straight, not daydream, or check answers as soon as they’re finished with a task. If students become too loud or don’t move about the room with purpose, the teacher stops class and reviews rules before directing them to resume working.
The final procedure of the day prepares students for the next math lesson (1). They should arrive to class with a pocket folder containing four items that will be used every day:
sharpened pencil
workbook
dry-erase board
marker