Geometry and Measurement for Math Specialists

MAPD 602

Teacher Observation and Coaching Analysis

Kristie Chandler

February 23, 2020

Phase 1: Co-Planning

The coach met with a second grade classroom teacher to plan for an

upcoming geometry lesson. This would be an introductory lesson, followed by

multiple days of practice and developing a deeper understanding of the

concepts. The classroom teacher asked the coach for suggestions on things to

use during the lesson and/or ideas for presenting the concepts. Learning goals

for the lesson would focus on Virginia SOL 2.12.

2.12 The student will

a) draw a line of symmetry in a figure; and

b) identify and create figures with at least one line of symmetry.

The student will use problem solving, mathematical communication,

mathematical reasoning, connections, and representations to

• Draw a line of symmetry in a figure. (a)

• Identify figures with at least one line of symmetry, using various concrete

materials (e.g., mirrors, paper folding, pattern blocks). (b)

• Determine a line of symmetry that results in two figures that have the

same size and shape and explain reasoning. (a, b)

• Create figures with at least one line of symmetry using various concrete

materials. (b)

Due to the lesson being introductory, important geometry terms would be

reviewed and introduced (plane figure, side, vertex, angle, line, mirror image,

symmetry, horizontal, vertical, congruent, etc.) as well as lots of examples and

visuals for the concepts.

There are 19 students, nine boys and ten girls. None of the students are

ELL. Five of the students have an IEP (speech, autism, and learning disabilities)

and one student, who struggles the most in math, does not have an IEP. A

special education teacher works with the classroom teacher during most of the

math block. Three to five of the students benefit from challenging tasks. After a

whole group introduction of the concept, the students would be grouped based

on formative assessing of their understanding. Emergent students would meet

with the special education teacher, proficient students would meet with the

classroom teacher, and advanced students would work with a partner.

The classroom teacher informed the coach that most of the students really

struggle with folding paper. The coach decided to look for ways to manipulate

items to investigate symmetry that require little to no folding. Our new math

series has a “Dig-In” section to begin a lesson. The classroom teacher stated

she would most likely use that with the Smartboard to start instruction. Parallel

teaching occurs sometimes between the classroom teacher and the special

education teacher, but most of the time they teach together during whole group

time. After the whole group portion, students usually work in small group or with

a partner, depending on their level of mastery. The handouts used will be

reviewed by the classroom teacher before the next lesson in the unit.

The coach researched and reviewed journals and classroom resources

from NCTM for symmetry. She then contacted the classroom teacher with the

following ideas:

• face symmetry – the coach took a straight forward image of Barack

Obama and cropped to have just the left side and just the right side, then

flipped those images to create his "symmetrical" face. The coach offered

to make more and show the classroom how to make them. The coach

also shared that the kids could see the actual flip happen, that could help

to develop the understanding of the concept. (see Activity 1)

• heart symmetry – the coach offered to give these out already cut and

folded and this could be a place for the students to "take notes" on

symmetry (heavily guided of course!), which could be drawings or just key

words or use them for just something for them to have in their hands that

relates to the concept.

• mirror words - these words contain letters that do have lines of symmetry;

since not all letters are symmetrical, the coach offered to bring mirrors to

use with the alphabet, especially as an option for those who need

additional support. (see Activity 3)

• shape mirror symmetry - these include the lines for placing the mirror to

check for symmetry; could be used for those who would struggle with

trying out different placements of the mirrors to see if the reflected image

creates the rest of the shape. (see Activity 2)

After reviewing the coach’s ideas, the classroom teacher created the following

lesson:

Lesson Plan from Classroom Teacher

Co-teach- team teaching and small group

Objective: TSW identify at least one line of symmetry in figures.

• TSW fold paper and cut out a heart shape. Open it up to see the heart.

• TSW trace the fold line with a crayon, and label it the line of symmetry.

o Sometimes objects can have more than one line of symmetry. Have

students try to fold their heart a different way to see if a heart has

more than one line of symmetry. (There is only 1)

o TTW cut out a square and show the different lines of symmetry.

• TTW explain that symmetry: When an object is the same on both sides.

o Ask the students if they can think of other things that are

symmetrical.

o Show pictures of butterflies, Eiffel tower, Taj Mahal, pumpkin and

flags as examples of lines of symmetry.

• On their whiteboards have students try to write as many capital letters that

are symmetrical. Project the letters of the alphabet, if needed.

• Show a picture of Barack Obama. Show how a face is symmetrical.

Assessment: TSW complete activity sheets, one sheet they be identifying

whether certain lines are symmetrical and the other they will draw the lines of

symmetry on shapes.

Phase 2: Teacher Observation

The classroom teacher introduced the lesson by handing out pink and red

paper to the students and guiding them through a folding and cutting activity.

The heart that was formed was used to introduce the concept of symmetry.

Students investigated symmetry by folding the heart in various ways to look for

“matching” halves.

Questions were asked to guide the students to make connections to

examples of symmetry in their own lives. Some of the students had read a book

recently that discussed the concept and most students were able to identify or

recognize examples of symmetry in nature.

The classroom teacher displayed various images using the Smartboard.

Some images had lines of symmetry drawn on them and were used to further

the discussion of the concept. For certain images, students came up to draw

lines of symmetry. Students appeared to be engaged with identifying lines of

symmetry and using the Smartboard pens.

Most of the students enjoyed being able to cut and fold the heart to

practice the concept. Having something in their hands helped to keep most of

focused. A few students were distracted by what other classmates were doing,

but most of them remained on task.

The classroom and special education teacher prompted the students to

explain how they knew lines they folded or drew were or weren’t lines of

symmetry. This provided the opportunity for the discussion of the difference

between images being reflected versus being rotated.

The overall purpose and goal of the lesson to introduce the topic was

accomplished. The fine-tuning of the definition of the concept would occur in

the following days.

Note: Observations typed on the coach’s laptop.

Observation Notes: • Pink and red paper and students will do a hamburger fold • Given half a heart on cardstock to cut out • Teacher demonstrates how to place the heart on the paper on the folded line to trace • Handles special needs student with patience and kindness • Cut on the traced line • Trace the line down the middle of the cut out heart • Line shows the line of symmetry • Ask what they observe – both sides on each of the folded line are the same • Ask them to fold different ways to see if there are other lines of symmetry • Ask students to make connections for a reading group who had read a book with

examples of symmetry; students gave real life examples of symmetrical things and places

• Coteacher/sped joins class • How do I fold something to see if it is symmetrical? • Items on smart board – flag, building, instrument, etc. • Asks about folding certain shapes like a rectangle – how many lines of symmetry can

they find • Teacher “folds” items and ask what they see • Ask about natural items that have symmetry – tree, leaf, apple, orange, bugs, kiwi,

butterfly • Displayed more flags and talk with a partner about if they are symmetrical or not –

point out not just the shape but the colors and shapes within the flag • Mentioned using a mirror to reflect symmetry • Asking why it works and why it won’t work so the kids have to explain their thinking • Asking what lines up and what doesn’t line up • Face of Barack Obama with left and right symmetry; compared the differences;

discuss how most faces are not truly symmetrical • Quadrilateral’s features – sides, vertices, right angle; students draw line of symmetry

on a square on Smartboard; discuss lines drawn • Handout for checking symmetry – gave reminders of what to look for/check for;

students have the option to come to one of the tables for help with either the teacher or sped teacher or work quietly at their desk; challenging student calls out often, sometimes yelling or screaming; asking guiding questions about handout, offered ruler to help make straight lines; tricky shapes like trapezoid

• Last activity to color a medallion that would be symmetrical • Go on chrome books to math sites

Phase 3: Debriefing

The classroom teacher felt that the goal of the lesson was met. Most of

the students understood the overall concept. Those students who did not were

pulled to work in small groups with an adult for additional exposure and practice.

Students were able to think through the concept through their folding and

drawings.

Some difficulties occurred when using the ruler to draw lines and cutting

and folding due to not following instructions. An adjustment for next time would

be to have the hearts pre-cut and have extra copies, so students could spend

more time investigating the concept and learning from their mistakes. The

classroom teacher shared that in the following lesson, the students struggled

with lines of symmetry for a star, so she felt that was due to some of the

difficulties from the introductory lesson.

The coach offered various considerations for next time. She observed

students needing clarification of lines of symmetry for rectangles. Some

students still did not understand that the image could not be rotated or slid, but

must be reflected for symmetry to be present. Not all of the students fully

understood what needed to happen when folding for a line of symmetry, so

additional examples of different shapes being folded to demonstrate how some

don’t truly match.

The classroom teacher did use the words with mirrors activity in a future

lesson in the unit. Some of the students were able to correctly use the mirrors,

while others watched a demonstration. Both groups were able to verbalize their

understanding of why symmetry was show by using the mirror. Those students

who showed mastery early on even attempted to make their own words to

check for symmetry using the mirrors. Other kids watched a demonstration of

the words with mirrors.

Activity 1:

ORIGINAL LEFT

LEFT SYMMETRY RIGHT

RIGHT SYMMETRY

Activity 2:

Activity 3: