Dufferin-Peel Catholic DSB Lesson Study #2

Debrief: Introduction to the Protractor

by Nina Bekanovic, OCT, Michaela Ferracci, OCT, Shannon Jordan, Natasha Moore, OCT, Athena Prosdocimo, OCT

INTRODUCTION (Athena Prosdocimo)

Observational Notes

• We all agree that the lesson went smoothly, had a good flow and was effective.
• One issue that came up was the time limitation. An extra five or 10 minutes would have allowed more opportunity to list the specific steps in constructing a right angle. This would have been very helpful for Individual Education Plan (IEP) students.
• Seating Student C (an IEP student) directly in front of the Smartboard allowed him to become more involved in the lesson. Next time we change the seating plan, keep this in mind and seat students who are having difficulty closer to the front of the classroom.
• Avoid asking questions that can be answered in unison.
• If we had not tailored this lesson for the Level 1 students, they would likely have been left out, and the lesson would not have been effective for them.
• Keep the instructions (how to draw a right angle) basic and provide visuals. Example: Provide an anchor chart with steps to which students can refer.
• Ensure that all of the students have a clear view of the Smartboard. During the lesson, we had to move one table group back because group members did not have a clear view.

Next Steps

For our next lesson we will briefly go over the steps for drawing right angles and then do an activity in which students draw as many acute angles as they can in a specific amount of time and list the measurements of each angle. We will then go through the lesson with the class and talk about how the students drew their angles.

We have decided to laminate an H-chart for each group on which group members can write the “three steps” for any activity they may be working on. This gives them a visual cue to which they can refer.

It may be necessary for IEP students to individually explain the “three steps” to the teacher before beginning the activity. This way, the steps will have been presented three times: once by the teacher, once by the students when they are writing the steps on their H-charts, and once by the IEP students when they explain the steps to the teacher.

Student Profiles

Student A: Grade 5 female, Level 1/2

This student openly dislikes math and often has difficulty understanding mathematical concepts. She is difficult to motivate and does not seek assistance when she doesn’t understand a task or concept. In term one, she received a D in number sense and a C in measurement.

Student B: Grade 4 male, Level 2

This student appears eager to learn math concepts at times and will ask for assistance when he needs it. He was absent on more than 12 days this term and received a C in both number sense and measurement in term one.

Student C: Male IEP student, Level 1

This student has been diagnosed with a learning disability. He receives modifications in math, language, science and social studies and is working at a Grade 3–4 level in math. According to his IEP, his areas of strength are computer literacy and artistic expression.

His areas of need are listed as organizational skills, behaviour management and attendance. He often has difficulty staying focused on a given task and requires extra time to complete a variety of written activities. With modifications, he received a C in both number sense and measurement on his first-term report card.

Student D: Grade 5 female IEP student, Grade 2 expectations, Level 2

This student has been diagnosed with impaired receptive and expressive language skills. She requires the use of wrist and left-foot splints and receives biweekly occupational therapy. She is currently working at a Grade 2–3 level in math and has shown great improvement when integrated with the whole class during math lessons. She has difficulty following multi-step instructions and requires assistance to complete most assigned tasks. With modifications, she received a C in both number sense and measurement.

The observational focus for this lesson was students who express and experience difficulty grasping basic mathematical concepts. These students were encouraged to participate throughout the lesson, and observational notes were taken.

Student A Observations (Nina Bekanovic)

The slides were presented on the Smart Board. Student D began listening by resting her head on both of her hands, however, when the teacher stood beside her, she corrected herself and sat upright. When Slide #2 was shown, the teacher asked, “What do these symbols mean?” Student A raised her hand but was not picked to answer. While the teacher was asking for volunteers to list more attributes of the square, Student A was drawing a square in the air with her finger. When the teacher asked, “Who can point out any angles in the square?” Student A put her hand up halfway and then put it down almost immediately.

Student A tilted her head to either side. Her view of the Smart Board could have been visually obstructed from where she was sitting. When the teacher and other students were speaking, Student A continued to face the Smart Board as opposed to looking at the speaker. Student A nodded when the teacher asked if students could see the protractor on the board.

(Slide #4) The teacher modelled how to line up a protractor to measure a right angle and then asked students to measure all the angles on a sheet to see if they were right angles. Student A had not brought a protractor and had to share with a classmate in another group.

Student A lined up the protractor correctly for each angle and placed a checkmark inside each angle to show she agreed that these were all right triangles. To measure the angles that were rotated sideways or upside-down, Student A rotated the paper to measure each angle. After completing the task quickly, she offered to help another classmate who was having difficulty measuring the angles.

Student A bit her nails and continued to tilt her head. When the teacher asked her directly how she had solved the problem of measuring an angle that was turned around, she replied, “I turned the protractor around.” However, it was observed during the activity that Student A had measured the angle by turning the paper, not the protractor.

The teacher moved Student A’s table group so group members would have a better view of the Smart Board. When the teacher asked the students to draw a six-centimetre line in their math notebooks, Student A raised her hand to ask a question but did not address it to the class. When asked what her question was, she said, “Do we draw the line vertically or horizontally?” although a horizontal line was presented on the Smart Board. It was great recognition for constructing her triangles later in the lesson.

When the teacher showed a triangle on the Smart Board and asked the class where the 90-degree angle was, Student A did not raise her hand but did use her pencil to trace the angle in the air. When the teacher asked Student A directly, “What kind of triangle do I have?” Student A correctly identified an isosceles triangle. Her face went quite red before answering.

For the next slide, Student A pointed out the triangle with her finger, tracing it in the air, but did not raise her hand to answer the question.

As more slides were shown, Student A sat slouched in her chair with her head still tilted to one side or the other. When the teacher checked for the class’s understanding, Student A nodded her head yes.

(Slide #10) All students were asked to copy down the instructions for the task. It was getting very close to recess. Student A copied down all the instructions before the teacher finished explaining them. She was the first student to complete the copying and the first to get up from her chair for recess.

Suggestions for Improvement

• When assigning seating arrangements, seat this student closer to the Smart Board.
• Continuously prompt her to answer questions, especially if you see her tracing with her finger.
• Check her work to ensure that she is not just quickly completing a task, but that she truly understands it and can provide a verbal/written explanation of her work.
• Build her confidence in math by continuously providing positive feedback and suggestions for improvement.

Student B Observations (Michaela Ferracci)

Student B appeared tired at the beginning of the math lesson. He removed his protractor from a pencil case but did not take note of the image on the Smart Board, preferring to examine the protractor, his chin resting on his hand. He seemed bored with the topic of right angles. As facts were given about the square, Student B looked over at his peers and continued to play with the protractor.

The teacher asked the students for the characteristics of a four-centimetre square. Information given by other students was recorded on the Smart Board. Student B did not offer any suggestions. He did not copy the information into a notebook and did not make an effort to seem interested in the topic. He was now using the protractor like a magnifier and looking through it at objects in his pencil case and on the desktop.

A square and a protractor were shown on the Smart Board. Having marked the screen with a measurement, the teacher asked the class, “Can you tell me what this is?” The teacher then assigned the question to Student B, who was unable to give a response. The teacher asked a prompting question, “Can we properly measure the image if the protractor is off the line? Is this the right way to measure?” Student B correctly answered and was praised.

The teacher then asked for a volunteer to show the correct way of lining up the protractor. Student B raised his hand, was selected, and proceeded to the Smart Board. Student B appeared more interested in the lesson from this point onward.

(Slide #4) The students were asked to measure nine separate angles on a worksheet, using a protractor to ensure that each angle was 90 degrees. The teacher gave the instructions orally, and a visual was provided on the Smart Board. Before beginning the task, Student B asked the teacher, “If it is 90 degrees, can we just put a checkmark beside the angle?” The teacher said, “That is a very good question. Yes! It is okay.” Student B completed the page quickly. He seemed pleased with all his answers. He managed to turn the paper upside-down to measure the angles properly, but not knowing if this procedure was acceptable, he watched his peers to see if they were using the same strategy. Student B seemed sure of the answers but continued to check with the others in his group for reassurance.

Student B was paying attention when the teacher asked, “How do we measure when the angle is turned around?” He seemed eager to participate in the discussion. The solution to this problem was to turn either the paper or the protractor around or to use the other side of the protractor. Once the teacher demonstrated turning the paper around, Student B smiled and appeared more confident. He continued to pay attention and seemed to enjoy this portion of the lesson.

The teacher asked the students to draw a six-centimetre line in their notebooks. Student B understood the instruction and completed the task. The teacher asked him, “What did you use to draw the straight line?” Student B answered, “I used my protractor as a ruler.” The teacher then drew a right angle on the Smart Board, drew a connecting line, removed the protractor and asked, “What do I have here?” Student B answered, “A right-angle triangle.”

The teacher moved to a slide showing a six-centimetre line segment and asked, “What other kinds of triangles can I make?” The teacher challenged Student B with this question. He seemed to hesitate. The teacher prompted, “How can I place the protractor differently to create a different-looking triangle?” Student B responded by saying, “Turn the protractor upside-down and measure that way.” The teacher drew another right-angle triangle using Student B’s suggestion. Student B did not copy the examples into his notebook.

The next task was geared towards the Grade 4 students. The students were challenged to draw a quadrilateral using the six-centimetre line segment. Student B did not copy the example but appeared to be listening. He did not ask any questions.

(Slide #10) To conclude the math lesson, the teacher asked each grade to complete a final challenge. Student B copied the grade-level instructions into his notebook. He used his time to copy the instructions rather than beginning the task. The teacher had written steps on the adjacent chalkboard to help the students remember how to use the protractor properly. Student B did not copy the steps listed. When the teacher asked him if he had copied the steps, Student B noted that it wasn’t necessary because he had understood the concept and would remember it.

Student C Observations (Shannon Jordan)

Student C was seated at the front of the class next to the Smart Board, where most of the lesson took place. This allowed him to clearly observe the slides and follow what the teacher was discussing.

As the lesson began, Student C was very engaged. He was listening attentively and aware of new information presented by the teacher and/or the students who were answering questions. He directed his attention to whoever was speaking.

As the teacher erased two sides of a square to create a triangle on the Smart Board, Student C was thoroughly interested. When the teacher posed the question, “What do we notice about this triangle?” Student C immediately raised his hand. The teacher motioned for him to answer, and he responded, “It has a right angle.”

When asked, Student C was able to approach the Smart Board and correctly label the right angle of the triangle in question. He was then asked how he knew it was a right-angle triangle, and he responded, “Because it has 90 degrees.” When asked how he would go about making sure the angle he was referring to was indeed a right angle, he responded, “Measure with a protractor.”

Student C continued to pay close attention as the teacher discussed the correct way to line up a protractor when checking to see if an angle was a right angle. When the teacher asked for a volunteer to approach the Smart Board and line up the protractor with the angle, Student C again raised his hand and was chosen to perform this task. He made a very good attempt at trying to line up the protractor correctly, however, he was a fraction off the spot that would have been exact. He did not seem too bothered by this, and when he sat down he continued to listen attentively.

(Slide #4) Students had been asked to bring a protractor, and Student C was prepared. A worksheet was distributed to each student. The worksheet showed nine different right angles in a random arrangement. The teacher instructed the class to measure each angle to confirm that they were all right angles. On receiving his worksheet, Student C immediately got to work. He began lining up his protractor and labelling each angle in turn. It was clear that he had paid careful attention to what had been taught and modelled earlier in the lesson, and that he was now taking his time and accurately lining up the cross section of the protractor with the corners of the angles. He also wrote “90 degrees” on the appropriate spot on top of each vertical line segment.

(Slide #5) When the teacher asked the class to help fill out a T-chart with the headings “Problems” and “Solutions,” Student C followed along attentively. The teacher asked who agreed with the problem of angles being turned around, and Student C immediately raised his hand to show that he agreed. (It seemed that he wasn’t just raising his hand because it was the thing to do, but that he was in agreement with what was being asked.)

Students were asked to collectively discuss and draw right-angle triangles using a six-centimetre horizontal line. Student C’s attention began to drift as the teacher and class continued to work through the process of constructing the triangles.

The teacher asked Student C to point to where 90 degrees was on the Smart Board (most likely because she noticed him losing interest and because he was conveniently positioned to point). Student C did not stand up but instead stretched his arm and pointed at the correct spot and said, “90 degrees.”

Student C’s attention faded as the lesson progressed to Slide #8 (featuring more exercises involving right-angles). He fidgeted in his seat and tapped his fingers on the table. When the teacher asked the class to construct a rectangle using a six-centimetre horizontal line, Student C seemed to tune out completely. He most likely detected the incorporation of more Grade 4 math terminology and felt that he no longer needed to devote his full attention to what was being said. He was very occupied with trying to locate his protractor, which he’d misplaced amidst the materials on the table in front of him.

(Slide #10) At the end of the lesson, the teacher asked the students to complete an activity that involved drawing quadrilaterals and right-angle triangles in their math workbooks. She also asked them to finish writing instructions in their workbooks before going outside for recess. Student C wrote the instructions down word for word. Being the student closest to the board, Student C was asked to provide feedback and discussion as the teacher wrote down the three steps involved in constructing a triangle. He did not seem to mind that this kept him indoors during recess.

Overall, Student C remained engaged and attentive for the majority of the lesson. He demonstrated that he understood how to identify a right angle and how to mark “90 degrees” on top of the vertical line segment of a right angle. However, he could not stay completely focused for the entire duration of the lesson and became distracted at times, even though he was seated very close to the Smart Board at the front of the classroom, where the lesson was taking place.

Student D Observations (Natasha Moore)

Student D attempted to participate at the beginning of the lesson. When the teacher asked the class to name a polygon, Student D raised her hand and said, “It looks like a square.” As the introduction progressed, Student D began to bite her fingernails and hide her hands in her sleeves, flapping them back and forth.

Student D continued to play with her sleeves, but when asked to identify a shape on the screen she was able to identify the triangle. Student D noticed that she was being observed and stopped playing with her sleeves. She always answered in unison with the class when asked yes/no questions by the teacher.

The teacher demonstrated protractor use on the Smart Board, modelling how to line up the protractor with the angle. When the teacher asked the class, “What did I just do?” Student D did not offer an answer. The teacher asked Student D to interact with the protractor on the board and repeat the action just demonstrated, but she was unable to line up the protractor correctly. Student D appeared to be more attentive after her participation.

The teacher instructed the class to take out their protractors so they could practise measuring angles. Student D did not follow the instructions until assisted by the teacher.

(Slide #4) Student D did not begin the activity until a teacher assisted. She required reminders to use the protractor correctly and follow the teacher’s instructions. Once assisted, she was able to measure one right angle on the page.

Student D continued to practise measuring the right angles on the page as the lesson continued. As students presented solutions to problems with the protractor, the teacher asked for a show of hands from other students who had used the same strategies. Student D raised her hand to signify her use of one of the strategies suggested, however, there was no evidence that she had in fact used this strategy.

Student D continued to practise with the protractor as the lesson proceeded, with the result that she did not participate in the lesson at the beginning. The teacher modelled drawing a right-angle triangle using a six-centimetre line segment. Student D suggested another way to draw the triangle – by attaching a vertical line segment heading down from the initial line segment. As the teacher drew the right angle upside-down, Student D turned her head almost upside-down in an attempt to see the right angle.

Student D often looked at her classmates in order to mimic their responses when the teacher asked the class to respond to a question in unison.

Student D lost her protractor for a couple of minutes as it was under her book. She required reminders to follow the given instructions. The teacher assisted her in using the protractor as she was unsure what to do first. She was asked what she did during the previous activity but was unable to communicate her ideas.

After receiving assistance with drawing the first right-angle triangle, she was able to draw a second triangle independently. She began drawing squares and rectangles and again required reminders to follow the given instructions. She was ableto complete a modified task with reminders and some prompts.

Overall, Student D seemed to grasp the basic concept of this lesson. She will continue to require assistance and reminders to follow procedures. Her participation in the lesson appeared to aid in her understanding of the selected concept.