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Teacher Training with Blackboard

- by
- Renan Sezer

- In the two teacher training courses offered at

LaGuardia Community - College for future elementary students

blackboard component was added. - In the first course the Blackboard component

helped students investigate such topics as

career goals, education and board certification

requirements, expected salary etc.

- In the second course web inquiry based learning

component was added through Blackboard

assignments in order to investigate the opposing

views of what is generally known as Math Wars,

i.e. teaching mathematics through reform

curricula vs. a traditional approach.

Blackboard assignments help students by

- drawing shy students into class discussion
- starting an ongoing exchange of ideas
- exploring different view points and not being

tied to one source of information - increasing student authorship

BlackBoard Assignment 1

- Please answer each question individually. 1)

How many years ago were you in elementary school?

2) Did you go to elementary school in the U.S.

or in another country? 3) Think back to your

elementary mathematics education and respond to

the following questions a) Was it a

teacher-centered or student-centered classroom?

b) What was the interaction between students

during the mathematics classroom? c) What kind

of activities were you assigned as mathematics

homework (e.g. drill questions, word problems,

writing assignments, exploration activities etc.)

- 4) As a future elementary school teacher, you

need - to be able to explaining the reasoning behind

basic mathematical operations and the steps

required to do them. (For example you need to

explain why when you multiply the denominator of

a fraction by a number you multiply the numerator

by the same number to keep the value the same.

You must be able to explain why when adding and

subtracting fractions you need to find common

denominator and when you multiply and divide you

do not. The reasons behind them are much more

than saying Because it is the rule.) You will

also need to be able to tackle a variety of word

problems. With these in mind, write how

confident you are in your mathematics knowledge?

Do you have a solid mathematics back ground?

Please be very honest.

- 5) Based on your answer to question
- 4, what pedagogical styles of
- teaching would have prepared you better in

terms of your mathematics knowledge? 6) If you

had a child going to elementary school, what kind

of things would you want him/her to learn and do

in mathematics class?

Sample Student Respond

- It has been about eight years since I have been

in elementary school. - I attended school in the U.S.
- 3) a) I recall each classroom experience was

different. The dominate form of teaching in the

classroom was teacher-centered. There was very

little student to student interaction. A great

deal of student-teacher interaction was practiced

as well as long extensive notes to take which

mostly made the classroom too silent for me

personally. The teacher was always standing in

front of the class or even sitting at the desk

delivering the concept that was to be learned

during a given time. I remember even one lesson

was nothing but note taking without the teacher

saying anything, only as a student was I told to

review the notes for that evening as

homework.

- 3b) A typical mathematics session in my classroom

was - that all of the guided learning was directly

drawn from the text book. Each chapter or lesson

was approached step by step as it was given in

the text book. These steps were often dictated by

the teachers who would give examples and as a

class we would answer them. After being

introduced to the lesson, the students were then

given problems to solve individually. Then the

class would come together with the teacher and go

over the problems. There was rarely any

interaction among the students themselves. Group

assignments werent really practiced except for

science projects. - 3c) The homework tasks that were assigned were

always directly from the text. They mostly

consisted of drill question and numerical

problems. Word problems were seasonally assigned.

They were assigned mostly when word problems were

introduced as a lesson. I cannot recall

exploration activities. My elementary school was

not an expeditionary learning center. It was

dictated text, lots of writing, and memory

competition.

- 4) First and foremost I am not comfortable in

mathematics in my own knowledge at the top of my

head. Often I have to refresh my memory, but I am

looking forward to learning to a point where the

information is already their and that I can

retrieve it from memory. I doubt myself and my

abilities when usually I am right or on the right

track in solving a problem. I also have a bad

habit of confusing certain laws and rules in

math. My given mathematics background would be

more solid if I had learned differently also upon

my own efforts. - 5) What wouldve helped me best is more

interaction. I am a visual and expeditionary

learner. Usually, anything with hardcore

statistics and facts do not impact my learning

ability as much as. It is through given examples

and discussions that trigger understanding and

what I learn to memory. More of this rather

than dictation would have helped.

- 6) If I had a child in elementary school, in

contrast to my experience, I would want the child

to learn basic mathematics. Without the basics it

would be impossible to advance in higher levels

of mathematics. As they learn in a mathematics

class I would like my child to have the ability

to practice the math in the classroom. In a

classroom Id want my child to be able to learn

mathematics to a point of being able to calculate

accurately. Id want my child to obtain the

concept and information where they can openly

discuss it and the problem solving procedures. If

the child can openly discuss mathematical

concepts, the child is then capable of helping

others who do not understand.

Another (Jin Weis) Response

- I was in elementary school 50 years ago.
- 2) I went to elementary school in China.
- 3) a) It was a teacher-centered classroom. b)

The students did their work independently. They

couldnt talk and discuss. c) All the

activities of the students were under the

teachers control. - 4) I am a paraprofessional in PS226 . I dont

want to be an elementary teacher in the future. I

had been a high school English teacher for more

than 20 years. Now I am studying in the college

to learn the teaching method of maths because I

am interested in maths and to earn 6 credits

that the Department of Education requires. - I think I have a solid maths back ground.

- 5) PS226 is the public school for special

education. Most of students are in Autism. Their

speaking abilities are delayed. They can know

some numerals and simple addition. It is

difficult for them to work out the problems by

using subtraction and division. Of courses I will

do my best to help them to understand the basic

concept of maths. - 6) If I had a child going to elementary school I

would want him/her to listen attentively in maths

class and do his/her work by himself/herself.

Only doing that he/she would master the basic

theory of maths and have the solid

maths back ground.

A Response to Jin-Wei

- HI Jin-Wei you metioned that you would like

your kids to work by themselves, i disagree

because students need to work together. i believe

that when students wotk together they learn and

understand the lesson better. Students have the

ability to explain their solutions to there class

mates. Also you said you have a solid

mathematics background, eventhough you were in

elementary school 50 years ago. tell me how did

you manage to still remember your basic math.

probably your teacher had a eficient way of

teaching her students.

Blackboard Assignment 2

- 1) Review your response and those of your

friends to question 6 in Blackboard assignment

1. (You do not need to write anything for this

step. 2) Suppose you had a child in elementary

school. Write a detailed letter to your childs

mathematics teacher telling him/her a) What your

child should be learning in class b) What your

child should be doing in mathematics class (For

example should the class be mostly in lecture

form or group discussion form? What percent of

the class time should be spent in doing basic

skills and what percent should be spent on

problem solving and exploration activities?)

- c) Should your child be allowed to use

technology in the classroom or doing homework? If

so what kind - of technology and when?
- d) What kind of homework do you think your child

should be assigned (Do not give too much

homework is not the answer I am looking for

here. Some things you should reflect and write

about are whether the homework should be based

on what is taught in class, should it have more

drill or more word problems, could it have

problems not done in class but given to them for

exploration and challenge, should it involve

projects where they are asked to investigate

open-ended questions, should it have writing

assignments in it?

Ramy Guzmans Response to 2nd Assignment

- Dear Ms. Brown,
- My name is Ramy Guzman, mother of Melanie

Guzman. I am concern about what Melanie will be

learning in your class. I know that in order for

her to understand and do well in math she needs

to learn the basic skills. This is why I want you

to please explain her each and every problem you

assign, also show her various way of doing the

problem and getting the right answer. I would

like you to let her participate in class and also

to give her challenging problems when you think

she has learned the skills. This way Melanie can

feel more confident when is given a problem. In

my opinion you should give them a chance to

explore what they have learn, after giving them

the lecture you should assign them to small

groups.

- Give them some problem and letting them use

manipulative so they can see the difference in

solving a problem with pencil and pen and using

manipulative. They should spend an equal amount

of time in basic skills and problem solving,

exploration activities should be given every once

in a while in order for you to know how much they

know. - Students shouldnt be able to use technology

during mathematics class, because math is a

subject of thinking and finding solutions. In my

opinion because of all the technology we have,

students dont have the chance of thinking.

Students shouldnt be able to use technology

during mathematics class, because math is a

subject of thinking and finding solutions. In my

opinion because of all the technology we have,

students dont have the chance of thinking.

- So I prefer my daughter to get less technology

in the classroom and more problem solving, also

at the end of - class you should give them a couple of open

minded - questions this will give you a sense of what

they learn and what they are confuse in. homework

should be based on what was taught in class, but

you can also give them one or two challenging

problems which you will explain in the next

class. By doing this you have a sense of which

student are prepared for the next lesson and

which students need more practice.. It should

have some writing assignments this way students

can explain there solutions. I am looking forward

to hear from you I hope you take into

consideration some of my advices and comments. If

you have any questions please let me know. I want

to be as much as possible involved in my

daughters education all for Melanies best

success. Sincerely, Ramy Guzman

Response to Ramys Posting

- Dear Ramy, Your suggestions are vital to the

basic math skills.However I think that although

calculators should not be allowed the use of

computers is vital.This is so because in today's

society everything is being computerized.The

child should gain hands on experience with the

use of computers.If the child is able to use the

computer and access information which is

necessary to complete his assignments he would

gain self confidence.This would help the child to

be capable of using the computer for other

assignments as well. I hope this response would

help you to think thoroughly about the advantages

and disadvantages of the use of computers.Being

able to use the computer is very different from

using the calculator.I totally disagree with the

use of calculators when teaching basic math

skills!

Blackboard Assignment 3

- NCTM STANDARDS This assignment is related to the

assigned reading of the following websites

NCTM http//standards.nctm.org/document/appendi

x/numb.htm In the above document click on

Principles or go to http//standards.nctm.org/docu

ment/chapter2/index.htm Then Standards

http//standards.nctm.org/document/chapter3/index.

htm Then Pre K-2 http//standards.nctm.org/docum

ent/chapter4/numb.htm Then 3-5 (Overview of

Standards 3-5) http//standards.nctm.org/document

/chapter5/numb.htm W. G. Quirks

website http//www.wgquirk.com/Tr

uthK12.html http//www.wgquirk.com

/Genmath.html http//www.wgquirk.c

om/HMathStd.html

http//www.wgquirk.com/chap3.html

http//www.wgquirk.com/chap4.html

- 1) Please use VERBS that indicate the kind of

mathematical activity that takes place in a

classroom that is described by NCTM Standards.

Shortly describe the kind of activities that

takes place in such a classroom. (You are NOT

asked to list the Standards but synthesize your

reading of the Standards and visualize a

classroom based on NCTM Standards.) 2) Please

use VERBS that indicate the kind of mathematical

activity that takes place in a classroom that is

described by W. G. Quirk. Shortly describe the

kind of activities that takes place in such a

classroom. (Try to visualize a classroom based on

W. G. Quirks website.) 3) If you were an

elementary school student, from which of the two

classes would you have benefited more? Explain in

detail why? (I do not want TWO WORD answers.)

4) a) What are some of the advantages of being

in an NCTM friendly mathematics classroom? b)

What are some of the advantages in being in a

mathematics classroom described by W. G. Quirk?

Dianas Response to 3rd Assignment

- 1) The kind of activity that takes places in a

classroom that is described by NCTM standards

substitute math appreciation content for

traditional K-12 math content. NCTM believes that

traditional K-12 math is too difficult for most

children. Their version of math reform omits

the essence of traditional K-12 math, including

standard computational skills, symbolic

manipulation skills, and mathematical reasoning

skills. 2) The kind of activities that take place

in the mathematics classroom as described by W.G.

Quirk is more teacher centered than

students. Students learn with the teacher

instruction. W.G Quirk teachers are giving out

their daily plan for the day.

- 3) I f I was in elementary school I would like to

take benefited - the NCTM because it give me more benefits as

student. It is - more fun because I use visual and make me more

confident with math - because I use more creative ideas. The other

method I dont like - because the teacher is the center of the class

and it make me distrait - and make me bored.
- 4) a) The advantage of being in an NCTM friendly

mathematics - classroom are teachers and students made a good

relationship with - students feel comfortable in ask question and

receive well explanation - for their teacher. Also students have the

opportunity to interact with - other classmates and learn with their ideas or

mistakes. Teachers - help students recognize that the challenge of

genuine math are - exciting and rewarding in ways that go well

beyond the math must be - fun and easy
- b) The advantage of being in a Quirk guide

mathematics classroom are - that the teachers teach their specific topics in

math. Teachers use - the curriculum.
- It must be coherent, focus on important

mathematics, and well - articulated across the grades. Students are focus

in what the teacher teach in classroom.

Teachers dont have time for students

ask question.

The Dialogue That Follows

- Dear Diana, I have read your posting and it is

very interesting however, I disagree with your

reason for preferring the NCTM method. I don't

think that math is based on creativity. I think

that math is based on facts. Therefore we have to

be taught the facts and concepts as they exist.

We should not try to alter the main idea of math.

Although there can be many fun problems there

must be challenging problems based on the

specific topic. Math lessons should not be based

on how the students feel or what they think

should be taught. Math lessons should be based on

what is essential to build a good basic math

foundation. - Shelisa

- Diana, I disagree that math is in the NCTM class

would be more creative. English class is meant to

be made creative and not mathematics. I couldn't

see how someone would get bored in the Quirk

teached class. Mathematics is not meant to be fun

after the 3rd grade in my opinion. Math is fun

when you're just beginning it. Math is meant to

be learned. If I had a more structed class maybe

I would've learned math better. While I didn't

find mathematics to be very interesting in

elementary schoool I knew that is was something

that had to be learned for my own

future. Albina

- Albina You don't agree with me, I understand,

but it is my opinion. Math is not my favority

subject.I like the idea to learn with NTCM method

because I like to learn with creativity. This

method give children the oportunity to explore

with visual and manipulatives things to made

essay easy their knowledge in math. - Diana

- Diana,
- My question is whoever said
- mathematics was easy? I've never been
- told that math was easy. If I'm a
- woman in my 30's and I find math to be
- headache indusing inducing, I'd hate to
- think how children feel about math today!
- Yes, you are entitled to your opinion.
- Thanks for letting me share mine. Albina

Blackboard Assignment 4

- By now you should have finished reading the

websites listed below if you have not please do

so BEFORE you continue with Assignment 4. In

the http//www.pdkintl.org/kappan/k0111rey.htm1a

website, there is a brief summary of the view

point that supports the NCTM recommendations.

There are many who oppose the NCTM

recommendations (W.G. Quirk was just one of

many.) Below you will find websites that express

these opposing views. Some of these websites were

developed by parents who are trying to get their

voices heard. http//www.educationnews.org/nyc_ma

th_warsnyc_honest_open_log.htm http//www.mathema

ticallycorrect.com/wsj.htm http//educationupdate

.com/archives/2002/dec02/issue/spot_mathincity.htm

l http//www.educationnews.org/math_wars_new

_yorkmath_forum_spo.htm

- 1) Please go to Blackboard Assignment 2 and

review what you and some of your classmates

wanted your children to do in mathematics class

from a parents perspective at the beginning of

the term. (You do not need to write anything here

but just reflect) 2) Having read the websites

listed above, you should know more about parents

perspectives as well as those that are pro-NCTM.

- In your group, half of you will take the

position of parents who are against NCTM and half

of you will take the position of teachers who are

pro-NCTM. As a group you will discuss your

different view points. The outcome of such a

debate can be that either one group convinces the

other or they as a whole reach a more balanced

view on the issues. (During this debate take good

notes on what points each side made and how an

issue or issues resolved or not.) 3) I want you

to make a powerpoint presentation one per

group- listing the original views of both sides

and how those views got modified during the

debate. What conclusions if any did you reach as

a whole group? Please post your powerpoint

presentation on the Blackboard.

Points of the Debate

- Drill / Problem Solving
- Group work /Individual Work
- Does writing has a place in math classroom?
- Should use of technology be allowed especially a

calculator

Comparison of Debates Between Groups

- Group 2
- Where your technology agreement is concerned, our

group arrived at - a similar conclusion with respect to the use of

calculators. Our group - thinks that they should be used only to solve

long, difficult equations. - When it came to the computers, the parents in our

group were - convinced by the teachers of the importance of

computers. They - agreed that the teachers could give assignments

that involved the - computers to access websites assigned by the

teachers and - supervised by the parents.
- When comparing your group discussion agreement

and our conclusion - the views vary somewhat. Your group agreed to

have more group - discussions. Our group decided that there needed

to be a more - balanced approach. Discussions would be part of

the lesson, but - shorter. Also, some would be lead by the teacher

with the class kept as a whole.

- Your group had a writing agreement, where you
- decided to basically eliminate writing for math

class. - Our group addressed the parents concerns about
- too much writing with homework. We agreed that
- word problems and think and write questions

would - be part of everyday homework along with some
- drills. The think and write questions would be

along - the lines of asking the students to write out

in - words the steps they used to solve a particular
- problem. This encourages the student to learn the
- algorithms, but at the same time think for
- themselves and write. They can draw the algorithm
- from their understanding.
- Group I

Blackboard Assignment 5

- In your last Blackboard assignment (4) you

have wrote the view points you have reached after

a debate on what is usually known as Math Wars.

Below are some websites that reflect a more

balanced view on the issue compared with the

previous ones you have read through out the

semester. Read these websites. http//gseweb.harv

ard.edu/ncsall/fob/2000/safford.html

http//www.education-world.com/a_curr/curr071.sht

ml

- The four websites below are the four pages of

the same link and you can go to the next page

simply by clicking next. http//www.ed.gov/admi

ns/lead/math/ms/edlite-slide019.html

http//www.ed.gov/admins/lead/math/ms/edlite-slid

e020.html http//www.ed.gov/admins/lead/math/ms/e

dlite-slide021.html http//www.ed.gov/admins/lead

/math/ms/edlite-slide022.html 1) After reading

the above websites, compare how they are similar

and different than your final position as was

outlined in Blackboard assignment 4.

A Sample Answer

- After finishing debating on what is better for

kids, we have - many similarities and differences on whether the

traditional - or NCTM is better for the kids to learn.
- Some similarities were
- Students understand and show more interest when

taught with - real life math problems.
- Students should learn how to use calculators in

other to solve - higher level math. We agree that students should

understand - the problem in other order to solve it.
- When students are involve in group discussion

they tend to - feel more comfortable. Also students show more

enthusiastic in the lesson. Also students

tend to understand better from their own

peers than from teachers.

- Some differences were
- During the debate we argued about what can be the

best for - the kids. As teachers we believe that the use of

calculators at - an early age should be limited. but students

still need to - understand what is happening in those

calculations Because in - order for a child to understand a problem one

must first know - how to do it with pen and pencil. Others believe

that - calculators shouldnt be used at all.
- Some said that group discussions are good , this

way all - student contribute and it increase their

proficiency. Others - said that students get disturb when working in

groups. - Even though we had many differences we got to an

agreement. - If kids are taught with a combination of both the

traditional - and the NCTM, students will learn the math

concept better. Students will have the

ability to solve the problems more

efficiently.

Blackboard Assignment 6

- Assume you are teaching in an elementary

school that embraces the NCTM Standards. (You may

want to refer to the following websites for the

NCTM recommendations http//standards.nctm.org/do

cument/chapter3/numb.htm, http//standards.nctm.or

g/document/chapter5/numb.htm, http//standards.nct

m.org/document/chapter5/alg.htm. ) However, some

of the parents are concerned that their children

are not spending enough time learning the basics.

(You may want to refer to the following sites for

parents concerns http//www.educationnews.org/ny

c_math_warsnyc_honest_open_log.htm,

http//www.mathematicallycorrect.com/wsj.htm.)

- 1) You are asked to create 2 lesson plans

(the items that need - to be included in your lesson plan are

listed at the end of this assignment for your

reference) on the topic of Adding Fractions with

Different Denominators that you would cover in

two consecutive lessons. (Make sure that you are

really doing only addition and not other related

topics.) In preparing these lessons you want to

take into account both the viewpoints of your

school administration and those of the parents.

Make sure you attach any hand-outs, homework

sheets etc. you intend to give to your students.

Your lesson plans should include ALL the

drills/problems you intend to cover in class.

Assume you have already covered the topic on

Adding Fractions with the Same Denominator and

other prerequisite topics which you should list

in your lesson plan. 2) Write a description of

how your approach addresses the standards and the

parents concerns. Do NOT write what the NCTM

recommendations are or what parents concerns

are. What you need to do is item by item analyze

your lesson plan (the motivational strategy used,

each drill, each problem, the teaching strategy

used, each item in the homework assigned) and

discuss if it satisfies one view or another and

if so why.

LESSON PLAN

- Grade
- Topic
- Aim
- Previous Knowledge Assumed
- Materials Needed
- Teaching Method
- Motivation
- Drills/Problems
- What Can Go Wrong?
- Homework