EDU 4407 Final Project

André Monnéy
EDU 4407 Secondary Curriculum
Instructional Unit
4/27/2011

Introduction

This spring semester I am in the midst of completing my first semester of student teaching at

Nathaniel Bowditch Middle School in Foster City, CA. Nathaniel Bowditch, more commonly known as

“Bowditch,” is Foster City’s sole 6th – 8th grade public middle school in the San Mateo-Foster City School

District and is home to about 935 students. While the school is large in population and size, the student

population seems to get along well with their teachers and administrators. There have been numerous

times where I walk through the halls and have students (who I do not have in either of my periods) say

hi to me in the hallways. Having attended San Mateo county schools all my life, Bowditch was always

known as being a very academic oriented school that provided students with other avenues of

expressing themselves (generally through sports, clubs and other school electives and activities). Now

that I am on the other end of the table, it is obvious that all the teachers at Bowditch are very

enthusiastic about their students.

Currently, I am teaching two Algebra classes to mostly eighth graders and a few sixth graders

with the Holt Algebra 1 Textbook. The classes meet four days a week for 45 minutes, and one day a

week for 35 minutes. Amongst the eighth graders, the students are split up into three different courses:

Eighth Grade Math, General Algebra, and HS Algebra. In order to make it into the Algebra course,

incoming eighth graders must have passed their seventh grade math classes with a B+ average or higher

and score well on their Algebra readiness test. Those who score moderately well on the Algebra

readiness test are placed into the General Algebra course, while those who score proficient in test are

placed in the High School Algebra course. The sixth graders who are in my class were required to pass

the sixth grade math curriculum test, seventh grade math curriculum test and the Algebra readiness test

in order to make it into the Algebra course.

André Monnéy
Instructional Unit
4/27/2011

Of the two classes I teach, one class is a General Algebra course and the other is a High School

Algebra course. While both classes are technically advanced math classes, the difference in these two

classes is that the High School Algebra course will complete the text book and have the opportunity to

take Geometry if my master teacher feels they are prepared. The General Algebra course may

potentially complete the book but are involved in a curriculum that serves more as an introduction to

Algebra. The General Algebra students commonly make a number of computation errors and are

generally uncomfortable with the material at first, but warm up to it afterwards. They will likely retake

Algebra in high school. Since there are different underlying objectives for the classes, the depth of the

material covered and time spent on the material varies.

Curriculum Integration & Learning Characteristics

According to Kellough and Carjuzaa’s research, my classroom would fit the description of a Level

1 integrated curriculum. The curriculum is solely developed by my master teacher as she is the only

Algebra teacher at Bowditch and involves no student collaboration. The class curriculum also does not

involve any integration with other disciplines. Occasionally, the science influenced question will pop up

in the textbook but aside from those few mentions, there is no integration. Despite there being no

formal integration, I commonly make it a point to use vocabulary that the common eighth grader should

become familiar within their middle school years to prepare them for the language arts classes and

vocabulary they will experience once they are in high school. My master teacher is supportive of my

“mini vocabulary lessons” and she allows me to introduce new words during my Systems of Equations

Unit as long as it pertains to what the class needs to do.

In regards to the learning characteristics of both my classes, none of the students have 504

plans, IEPs or are identified as English Language Learners; however, there are a number of students who

speak other languages at home which is part of the reason why I emphasize extra vocabulary that these

André Monnéy
Instructional Unit
4/27/2011

students will undoubtedly cover in other classes. I also make it a point to try to correlate the math terms

that we learn in class to the students common knowledge of school and/or life (for example, I remind

the students that they already under the property of substituting a number into a variable because it

closely relates to the concept of a substitute teacher).

When it comes to the students opinions towards math, most of these students are generally

successful and feel they are successful. There are a few students who struggle with minor calculation

errors and confusion in rules in the high school Algebra course, while the students in the General

Algebra class make more errors and take a while to warm up to the material. Within my General Algebra

course, I have a few students who generally show a lack of effort in their work and in their study habits

for quizzes and tests. A number of these students do not find the need to put the effort in now

considering they will “retake” the class in high school or later in their middle school career. This makes

teaching the class relatively challenging at times, but once they have warmed up to the material they

find it easier. Since the General Algebra students have so much trouble getting warmed up, I feed them

a lot of positive reinforcement during our lessons. I am constantly telling them how smart they are and

that all these methods and tools are helping them develop a skill set that will help them out in their later

classes and in work force. The students generally respond well it and a few (particularly the ones who

show a lack of interest in the material) admit that they are smart and capable.

To give you an idea on what the two schedules look like side by side, I have attached the dates it

took our General Algebra class to review the material and the dates it took for the High School Algebra

class to complete the material:

General Algebra HS Algebra

André Monnéy
Instructional Unit
4/27/2011

2/8-2/9/2011 Section 6.1 Solving Systems of 2/8/2011 Section 6.1 Solving Systems of

Equations by Graphing Equations by Graphing
2/10-2/11/2011 Section 6.2 Solving Systems 2/9/2011 Section 6.2 Solving Systems

by Substitution by Substitution
2/14/2011 Chapter 5 Review/Practice 2/10/2011 6.1 – 6.2 Review

Test
2/15/2011 Chapter 5 Test 2/11/2011 6.1 – 6.2 Quiz
2/16/2011 6.1 – 6.2 Review 2/14/2011 Section 6.3 Solving Systems

by Elimination
2/17/2011 6.1 – 6.2 Quz 2/15/2011 Section 6.4 Solving Special

Systems of Equation

(Perpendicular & Parallel

Lines)
2/22-2/23/2011 Section 6.3 Solving Systems 2/16/2011 6.1-6.4 Review

by Elimination
2/24-2/25/2011 Section 6.4 Solving Special 2/17/2011 6.1-6.4 Test

Systems of Equation

(Perpendicular & Parallel

Lines)
2/28/2011 6.1-6.4 Review 2/22/2011-2 Word Problems: Coin & Digit,

/25/2011 Mixture, Travel
3/1/2011 6.1-6.4 Test 2/28/2011 Word Problems Quiz
3/2-3/3/2011 Section 6.6 3/1/2011 Section 6.6
3/4/2011 & 3/7/2011 Section 6.7 3/2/2011 Section 6.7
3/8/2011 6.6-6.7 Review 3/3/2011 6.6-6.7 Review
3/9/2011 6.6-6.7 Test 3/4/2011 6.6-6.7 Test

My Unit: Systems Of Equations

Now that the students have worked with linear equations, we are moving onto to our Systems

of Equations unit. Most of the assessments in this unit will be comprised of diagnostic and informal

André Monnéy
Instructional Unit
4/27/2011

assessments such as homework assignments and in class work and formal assessments which include

quizzes (diagnostic assessments to see what materials I need to better review, etc.) and tests. Since the

High School Algebra course moves at a much faster pace and covers the material more in depth, they

will spend some extra time working through word problems that can be solved using systems of

equations. Although we were only supposed to submit 3 lesson plans, I am actually submitting 5 lesson

plans so that you can see the difference in how the material is covered differently between the two

classes.

The first four lesson plans split up solving systems of equations by substitution and by

elimination among four days. The High School Algebra class would have covered these four lesson plans

within two days and reviewed a lot more extensive material during their review day.

André Monnéy
Instructional Unit
4/27/2011

Lesson Plan #1
Teacher: André Monnéy Subject: General Algebra

Central Focus: Solving Systems Of Equations By Substitution Grade Level: 6th-8th Grade Date: 2/10/2011

Rationale:
- Now that students have learned that systems of equations can be solved, today we will focus on the easier form
of solving systems of equations, substitution. I will stress to the students that although they can continue to use
graphing to solve systems of equations, substitution will be much simpler and will help find those difficult
fraction and decimal answers.

State Adopted Academic Content Standards:
- 9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the
answer graphically.

State Specific Goals and Objectives for the Lesson:
- Prior to the lecture, students will identify Standard Form as Ax+By=C with 100% accuracy.
- Prior to lecture, students will identify slope-intercept form as y=mx+b with 100% accuracy.
- Prior to the lecture, students will identify a solution to a system of equations as an ordered pair (x, y) with 100%
accuracy.
- After the lecture, students will be able to solve a system of equations using the substitution method with 80%
accuracy.

Pre-Assessments Connecting To Prior Knowledge/Prior Learning:
- Read off answers from the homework from the night before. Answer 2-3 questions (key points using two points
to find slope and the linear equation in slope intercept form).

Identified Academic Language to be addressed:
- Standard Form – Ax+By=C
- Slope Intercept Form – y=mx+b
- Ordered Pair – (x, y)
- System of equations – y1=m1x1+b1, y2=m2x2+b2

Learner Characteristics:
a. Special Needs – There are no special need students in my class.
b. English Language Learner – There are no ELL students in my class; however, there are some in the 7th
period class. To ease their stress, I would highlight key words on the word problems so they could follow
along a little bit easier. I would also provide them with a paper with common words they will need to know
to solve the problems (elimination, substitution, etc.) as an aid.
c. Other – Not applicable.

Lesson Delivery:
 Introduction-connection of content to previous learning – 5 mins
 Review Homework: Pg. 332-333 # 9-17, 23-25, 28-30
 Answer Questions. Encourage students to ask each other how to solve questions. Have a few
students dictate the work while the other scribes.
 Instruction
 Re-introduce solving systems of equations: - 3 mins
o In these examples, we’ll have two linear equations.
o The solution will always be an ordered pair (x, y).
 Three methods to solve systems of equations: - 1 min

André Monnéy
Instructional Unit
4/27/2011

o The three methods are graphing, substitution, and elimination. Today we’ll review
substitution.
 Solving a system of linear equations by substitution – 30 mins
o Steps to using substitution
• Step 1: Solve for one variable in at least one equation, if necessary.
• Step 2: Substitute the resulting expression into the other equation.
• Step 3: Solve that equation to get the value of the first variable.
• Step 4: Substitute that value into one of the original equations and solve for
the other variable.
• Step 5: Write the values in an ordered pair: (x, y).
o Work Ex. #1a & Ex. #1c on pg. 336-337 and Ex. #2 using the distributive property
(do Ex. 1b if time is available).
o Give 1b, 1c, and 2 on pg. 337-338 for students to work (do Ex. 1c if time is
available).
 If Times Allows: Work through a word problem like example #3 pg. 339, if not review
tomorrow.
 Assessments (e.g. diagnostic/formative/summative, formal/informal)
 Formative/Diagnostic Assessment:
o I will grade the student’s homework with them. (Informal)
o I also like to check in with a “thumbs up” after they’ve worked the problems: Are
they getting it? Answer with a thumbs ups. Are you confused? Answer with a
thumbs down. (Informal)
o Are there any final questions? (Formal)
 Summative Assessment:
o Homework: Pg. 340 # 1-7 (all), 8-24 (even)
o Give students time to do their homework – 5 mins
 Closure
 How can we check to see if a point is a solution for a system of equations? Plug and chug
 Ask students what are the two methods we are using to solve the systems of equations?
Graphing and substitution
 Which method is slowest? Graphing; Which is quicker? Substitution.
 What will the answer look like? An ordered pair, (x,y)

André Monnéy
Instructional Unit
4/27/2011

Lesson #2

Central Focus: Systems Of Equations: Solving by Substitution (Cont) Grade Level: 6th-8th Grade Date: 2/11/2011

Rationale:
Now that we have been introduced to substitution, today we are going for accuracy and speed. Stay focused on all
the computations because inevitably, there are bound to be some errors if you are not careful! Don’t worry, even
your teachers make computation errors, bit if you learn from your mistakes its bound not to happen again.

- 9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the
answer graphically.

- Students will identify Standard Form as Ax+By=C with 100% accuracy.
- Students will identify slope-intercept form as y=mx+b with 100% accuracy.
- Students will identify a solution to a system of equations as an ordered pair (x, y) with 100% accuracy after I
ask them verbally.
- Students will be able to solve a system of equations using the substitution method after our lecture with 90%
accuracy.

- Read off answers from the homework from the night before. Answer 2-3 questions (key points using two points
to find slope and the linear equation in slope intercept form).



Lesson Delivery:
 Introduction-connection of content to previous learning – 5 mins
 Review Homework: Pg. 340 # 1-7 (all), 8-24 (even)
 Answer Questions
 Instruction
 Re-introduce solving systems of equations: -3 mins
o In these examples, we’ll have two linear equations.
o The solution will always be an ordered pair (x, y).
 Three methods to solve systems of equations: - 1 min
o We’ve learned graphing, which form did we learn yesterday? Substitution. Today
we will review substitution some more.
 Review the steps of solving a system of linear equations by substitution – 2 mins

André Monnéy
Instructional Unit
4/27/2011

o Steps to using substitution
• Step 1: Solve for one variable in at least one equation, if necessary.
• Step 2: Substitute the resulting expression into the other equation.
• Step 3: Solve that equation to get the value of the first variable.
• Step 4: Substitute that value into one of the original equations and solve for
the other variable.
• Step 5: Write the values in an ordered pair: (x, y).
o Work Additional Examples 1 on page337 Do 1 & 2, let them try 3 (do this one if
they still need guidance). – 25 mins
o Class will work on Additional Examples 2 on page 338. – 3 mins
 Work through a word problem like example #3 pg. 339. – 3 mins
o I also like to check in with a “thumbs up” after they’ve worked the problems Are
they getting it? Answer with a thumbs ups. Are you confused? Answer with a
thumbs down. (Informal)
o Are there any final questions? (Formal)
o Homework: Pg. 340 # 9-23 (odd), 26, 36-38, 43-51
o Give the students time to work on their homework. – 3-5 minutes
 Closure
 How can we check to see if a point is a solution for a system of equations? Plug and chug
 Ask students what are the two methods we are using to solve the systems of equations?
Graphing and substitution
 Which method is slowest? Graphing; Which is quicker? Substitution.
 What will the answer look like? An ordered pair, (x,y)

André Monnéy
Instructional Unit
4/27/2011

Lesson Plan #3

Central Focus: Section 6.3 – Solving Systems by Elimination Grade Level: 6th-8th Grade Date: 2/22/2011

Rationale:
Our substitution skills have now been perfected after taking our little quiz. Now that you’ve learned two of the
methods for solving systems of equations, we move onto the final method: elimination. Don’t worry; a lot of the
steps are the same as in substitution so you already know how to do parts of it. In some cases elimination is faster so
it’s important to pay close attention.

- 9.0 Students solve a system of two linear equations in two variables algebraically.

- After the lectures, students will identify the 5 steps to solve a system of equations using the elimination method
with 90% accuracy.
- After the lecture, students will learn how to solve a system of equations using the elimination method with 80%
accuracy.

- Students will start with the warm up on page 343 to become familiar with the elimination process.
- I will remind the students that there are three ways of solving a system of equations: 1) graphing, 2) substitution
and 3) elimination, which is what we’ll learn today.



Lesson Delivery:
 Introduction-connection of content to previous learning
 Students will do the warm up problems on page 343 to become familiar with how elimination
works. – 3 mins
 Instruction
 I will introduce the steps on how to solve using elimination: - 5 mins
1. Write the system so that all your variables are on one side and your constant is on the
other (that like terms are aligned).
2. Eliminate one of the variables
3. Solve for the variable that wasn’t eliminated.
4. Substitute that variable into one of the original equations and solve for the other variable.
5. Write your answer in an ordered pair.

André Monnéy
Instructional Unit
4/27/2011

 Elimination using addition (Example #1 pg. 344). Work through both examples on the pages.
Post additional examples (pg. 344) on the board for the students work. – 10 minutes
 Elimination using Multiplication First (Example #3 pg. 345). Work through Example #A, B,
3a & 3b. Post additional example #3a & 3b for students to work. – 20 minutes
 Consumer Application (Example #4 pg. 346) – 3 minutes
o I will check in with the students to gauge their comfort level with the elimination
process.
o Homework: Pg. 347 # 1-19 (odd), 24-29 (all)
o Give the students time to start their homework – 5 minutes
 Closure
 Don’t forget about your homework: Pg. 347 # 1-19 (odd), 24-29 (all)
 Remind students that we are now reviewing the final method to solve systems of equations:
elimination. The answers can be checked by using one of the other methods.
 What are the other two methods? Substitution and graphing.

André Monnéy
Instructional Unit
4/27/2011

Lesson Plan #4

Central Focus: Section 6.3 – Solving Systems by Elimination (Cont) Grade Level: 6th-8th Grade Date: 2/23/2011

Rationale:
We’ve now learned all three ways in which you can solve systems of equations; however, we still need to practice
the elimination method. Remember, you can use either elimination or substitution when you solve these questions
on your tests, but you should know how to solve using both methods in case you want to double check your answer.

- 9.0 Students solve a system of two linear equations in two variables algebraically.

- Students will be able to figure out whether a point is a solution to a system of equations or not.
- After the lectures, students will identify the 5 steps to solve a system of equations using the elimination method
with 95% accuracy.
- After the lecture, students will learn how to solve a system of equations using the elimination method with 90%
accuracy.

- Students will review last night’s homework and will continue to review more question in class regarding the
elimination method.
- I will remind the students that there are three ways of solving a system of equations: 1) graphing, 2) substitution
and 3) elimination, which is what we’ll review today.



Lesson Delivery:
 Introduction-connection of content to previous learning
o Review homework with the students: Pg. 347 # 1-19 (odd), 24-29 (all) – 5 mins
 Instruction
 I will re-introduce the steps on how to solve using elimination: - 3 minutes
1. Write the system so that all your variables are on one side and your constant is on the
other (that like terms are aligned).
2. Eliminate one of the variables
3. Solve for the variable that wasn’t eliminated.
4. Substitute that variable into one of the original equations and solve for the other variable.
5. Write your answer in an ordered pair.

André Monnéy
Instructional Unit
4/27/2011

 Elimination using addition (Example #1 pg. 344). Work through both examples on the pages.
Post additional example #1 (pg. 344) on the board for the students work.
 Elimination using Multiplication First (Example #3 pg. 345). Work through Example #A, B,
3a & 3b. Post additional example #3a & 3b for students to work.
 Consumer Application (Example #4 pg. 346)
o I will check in with the students to gauge their comfort level with the elimination
process.
o Homework: Pg. 347 #2-20 (even), 22-23, 33-34
 Closure
 Don’t forget about your homework: Pg. 347 #2-20 (even), 22-23, 33-34
 Remind students that we are now reviewing the final method to solve systems of equations:
elimination. The answers can be checked by using one of the other methods.
 What are the other two methods? Substitution and graphing.

André Monnéy
Instructional Unit
4/27/2011

Lesson Plan #5

Central Focus: Section 6.1 – 6.4 Review Grade Level: 6th-8th Grade Date: 2/28/2011

Rationale:
- Today’s lesson will help the students prepare for their quiz on systems of equations. Since the students seem to
be familiar with the three procedures (graphing, substitution, and elimination), the majority of our review will
review the 5 steps in our procedure and will involve team work to solve the problems given. I will review the
problem to verify everyone gets the correct answer.

- 9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret them
graphically.

- After the review, students will identify slope-intercept form as y=mx+b with 100% accuracy.
- After the review, students will be able to figure out whether a point is a solution to a system of equations or not
with 100% accuracy.
- After the review, students will identify the 5 steps to solve a system of equations using the substitution and
elimination method with 100% accuracy.
- After the review, students will identify systems of equations with no solution and with infinite solutions and
classify them properly with 100% accuracy.
- After the review, students will learn how to solve word problems involving systems of equations with 95%
accuracy.

- Review homework with students. Review at least one example of substitution and elimination.



Lesson Delivery:
 Introduction-connection of content to previous learning – 5 MINUTES
 Review homework with the students: Pg. 353 #8-11, 20-22 (all), 23-31 (odd), 33-34, 37-44
 Answer any last minute questions on the homework.
 Instruction – 35 MINUTES
 I will allow the students to have a review period through the game secret path.
 The class will split up down the center into two teams, one sits on each side of the tarp (secret
path).

André Monnéy
Instructional Unit
4/27/2011

On the tarp there lies a secret path that only I know. The students are required to figure out the
path. The first team to figure out the path will get a prize (candy).
 Each team will be presented with one problem at a time. If the team answers correctly, they
will have the opportunity to take a step on the secret path (see the drawing on the second page
after the “Closure” section). See other attachments for Sample Problems.
 If the team gets the answer wrong, the other team will have an opportunity to answer the
question. Both teams will need to solve the problems posted under the document camera in
case the other team misses (it is also a good way to have extra questions to practice when
studying).
 Someone new has to answer the question each time (you can ask your team for help, but once
you are presenting the problem you will need to know how to do it without their help).
 If you get the question right, then you will need to walk us through the problems by first
identifying the method you used and then explaining step-by-step using the 5 steps we have
learned to solve systems of equations.
 There will also be key term questions so be familiar with your key words we went over in
class.
 Assign Homework: Pg. 363 #1-17
o I will check in with the students to gauge their comfort level with systems of
equations using the thumbs up (I feel good with the work), thumbs sideways (I am
still a little confused) and a thumbs down (I am lost).
o Once the game starts, I will check the student’s work and correct any answers that
might be incorrect. I will also pick key students to explain the procedures they used.
(Informal)
o If there is a question answered wrong and the class seems “stuck,” I will solve it with
the class to guide them through the problem. (Informal)
o Homework: Pg. 363 #1-17 (Formal)
 Closure – 5 MINUTES
 Do not forget about your homework: Pg. 363 #1-17
 Tomorrow’s quiz is on Solving Systems of Equations:
 What are the three methods? Graphing, substitution, and elimination.
 Explain the procedures used to complete the 3 methods.
 What are the two types of special systems we see? No solutions and infinite
solutions.
 How would you classify them? Using the table we created in class.
 What are the classifications? Consistent, Dependent and Independent; and
Inconsistent.
 Things you should do before you take a quiz…
 Study using old homework assignments and class notes.
 Practice your favorite method and make sure you have perfected it.
 Also be familiar with the other two methods of solving systems of equations.
 Memorize the classification table for special systems either by having someone quiz
you, visualizing what I said in class, or copying the table as many times as you need
until you’ve memorized it.
 Get a good night sleep.
 Eat a good breakfast in the morning.
 I will be available in the morning for extra help if needed.

André Monnéy
Instructional Unit
4/27/2011

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André Monnéy
Instructional Unit
4/27/2011

PACT Commentary #1

Since I am covering the material over two days, the first day I work each and every sample

problem out one step at a time so that the students can follow along without feeling overwhelmed. By

doing this I have the opportunity to set up scaffolds so that each student knows exactly what to do. As I

continue through the problems in class, I slowly take away each little step and begin asking the students

for their input. I ask students to share their feedback in the following ways: students explain it to me

while I scribe, students explain it to another student and have that student scribe, students can come

up, have the student do the work and explain it while they write it, and place his/her work under the

document camera. Each of these methods touches on a few of Gardners Multiple Intelligences:

linguistic, logical-mathematical, and intrapersonal. Each of these intelligences associates with the

following set of learning traits:

• Linguist Intelligence – The linguistic intelligence includes effectively using language as a mean to

remember information.

• Logical-mathematical intelligence – As part of teaching a math class it is only appropriate that I

not only allow the mathematical students to grow, but also get the rest of my students to this

level. Logical-mathematical intelligence allows for the carrying out of math operations and think

in an overall mathematical format.

• Intrapersonal intelligence – Intrapersonal Intelligence details with the understanding of peoples

intentions, motivations and wants. Keeping these things in mind allows for people to work

effectively and productively with others.

André Monnéy
Instructional Unit
4/27/2011

Using these approaches to answering questions encourages students to verbalize their thoughts

and procedures (an extremely important attribute for people who fall in the “Linguistics” and

“Interpersonal” intelligences). This also forces them to try the problems on their own and feel confident

that they can get the correct answers. As I progress through my lessons, the students have less guidance

through their problems and eventually solve one or two (at least) before they start their homework.

Aside from the scaffolds I give the students, I am also big on getting help from peers. If a student

is confused on a problem I’ll ask them to ask a classmate for help. This is an attempt to practice some of

the social skills needed for those who fall under the intrapersonal intelligence. Those who fall under the

interpersonal intelligence scope are generally people who are very verbal and have the ability to allow

people to work together well1. This also forces them to be able to discuss the material clearly and

effectively for everyone to understand. If the classmate can explain the process and concepts clearly, I’ll

leave it at that and move on in an attempt to increase the amount of student talk that goes on in my

classroom. This is a new incorporation into my lesson planning so it is still in the works, but so far, the

students seem to feel like they are learning from others as well which has eased some of the stress in

the class.

Gardner and Intelligences aside, first and foremost I believe in effective coaching skills and

strategies2. While my General Algebra class is not a sports team, these are the “underdogs” of the

advanced math eighth graders. Most of these kids still make careless mistakes in their homework and if

they focused a little more, they could probably succeed. I have one student in particular that has

checked out of the class, especially knowing that he will take Algebra gain next year. With students such

1
Smith, Mark K. (2002, 2008) 'Howard Gardner and multiple intelligences', the encyclopedia of informal education,
http://www.infed.org/thinkers/gardner.htm (April 2011).

2
Article #418 from Innovative Leader Volume 8, Number 8, August 1999,
http://www.winstonbrill.com/bril001/html/article_index/articles/401-450/article418_body.html (April 2011).

André Monnéy
Instructional Unit
4/27/2011

as this young man, I make sure to remind him how smart he is and share my experiences with the typical

errors I made in my math classes and how I learned not to give up on them. In class, I am constantly

telling my students how smart they are, and how while this work is difficult, they will still manage to

understand it if they invest some time into the class and the homework. I also have them give each

other round of applauses when a students stands up in front of the class to share how to solve a

problem. With students like the one previously mentioned, I make it a point to commit him to answer

one question a day. This forces him to focus on the class lecture and material. As a result, this also

transitions him into more class participation and allows him to begin to realize how capable he is of

doing his work. Using these minor coaching skills has really made a difference in how my students view

their math work and in how comfortable they are in talking with me regarding their work.

André Monnéy
Instructional Unit
4/27/2011

Pact Commentary #2

As I had stated before, none of my students are considered English Language Learners; however,

most do speak other languages at home which can at times cause challenges in the classroom when it

comes to pronouncing words in front of their peers and/or memorizing the subject specific words. When

introducing new vocabulary words to students, I always make it a point to correlate the word to

something they already understand.

For example, with the systems of equations unit, when I introduced the concept of substitution,

I opened the discussion with the concept of a substitute teacher. I explained how the role of the

substitute was equal to that of a regular teacher, but the only difference was that the substitute needed

to adapt to the styles and classroom of the teacher they were currently replacing to have a specific

outcome. Much like a substitute, I explained how a linear equation such as x=4y+1 can actually be equal

to the “x” part of y = 2x +2 and began to show the students step by step how to substitute the equation.

To most students this made sense; however, they tried to identify it in their own terms which by

coincidence completely replaced the word substitution.

All of the sudden the substitution method became known as “the switch thingy” amongst a

group of female students in the classroom. Although I understood what they meant, I told them it was

extremely important to be able to remember substitute and not just their version because if they ever

had to explain the process to someone else, they would thoroughly confuse them. I then asked for a few

of their own examples on how they could remember the substitution property. One of the girls, came up

with the concept of substituting fruits for candies to get the needed sugars in their diets but to also

maintain a healthier lifestyle. I then pointed out how she even used the word “substitute” in her

example and reiterated the importance of knowing the vocabulary for math.

André Monnéy
Instructional Unit
4/27/2011

While this story shared is all anecdotal evidence, it shows that coming up with your own

definition can be very dangerous at times. None of my students struggle with understanding the English

language and therefore try to take short cuts in understanding certain words and definitions. This

particular group of girls is among the lower performing students so I needed to drive the point home

that you cannot take a shortcut before you understand the entire concept which in their case was

substitution.

Aside from connecting to prior experiences and understandings, I will occasionally ask students

to come up with ways to describe the methods or properties in math. For example, with elimination, I

asked my students to tell me what they thought when they heard the word elimination? Most students

responded with getting rid of something. One student said, hearing elimination reminded him of a ninja

sneaking in to eliminate an enemy. All these examples were great and led perfectly into the process of

solving systems of equations through elimination. After hearing my students’ thoughts on what

elimination meant, I went with the ninja example (primarily for comedic purposes) and explained how

we, the mathematicians, were like the ninja and needed to eliminate a variable in order to find the value

of the other variable. Now had I not asked my students what they thought of when they heard

elimination, I may have never had the opportunity to role with one of their examples. By forcing them to

think for themselves, they take more ownership in their education and I am able to demystify a new

mathematical procedure with a little bit of humor and something that engages them.

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