Assignment 1 Diagnose, Plan for further learning and Teach in the area of Understand Operations. Assessment Criteria, worth 40%, Due 4pm Wednesday 19th AprilThis assignment addresses National Graduate Teacher Standards: 1.2 Demonstrate knowledge and understanding of research into how students learn and the implications for teaching.2.1 Demonstrate knowledge and understanding of the concepts, substance and structure of the content and teaching strategies of the teaching area.3.6 Demonstrate broad knowledge of strategies that can be used to evaluate teaching programs to improve student learning.

The extent to which you justify your selection of Understand Operations tasks for the child, carry them out correctly and identify what the child understands and can do in terms of the Understand Operations mathematics focus of the task.

Did you clearly understand the purpose of the tasks and did you give the child the opportunity to demonstrate what they knew in relation to the purpose of the task? Did you focus on the Understand Operations aspect of the task rather than how the child calculates?

(10 marks)

The extent to which you used evidence from the interview and relevant sources of information to decide what the child knows and can do and also what the child needs to learn next.

Have you included relevant parts of work samples?

Do you make effective use of the readings and the Western Australian Curriculum: Mathematics to support your decision? Have your analysed the problem types that the child can represent and solve and the problems types that the child cannot represent and solve

10 marks)

The extent to which you detail appropriate learning experiences which focus on the mathematics you want your child to learn.

(10 marks)

The extent to which you have reflected on the effectiveness of the learning experiences in engaging the child and bringing about some of the learning intended. If this child was in your class what would they still need to learn about this aspect of mathematics? What would you focus on next with that child?

(10 marks)

You should attach a duly completed Parent Consent Form. Your assignment should not be more than 2 000 words. Your work should be relatively free of spelling, punctuation, grammar and referencing errors. Failure to comply will result in penalty marks of up to 2 marks being deducted.

Total obtained out of a max of 40 marks

Assignment 1: REPORT: Diagnose, Plan for further learning and Teach in the area of Understand Operations. BRADLEY LEE 32533011

Student Profile (OVERVIEW)

The child that I will be analysing throughout Assignment One is my son, Kobe. He is

currently six years of age. Previous school reports have indicated that Kobe is a

quiet and gentle student who is beginning to interact during class learning

experiences. He is currently in Year One who sits within a satisfactory number level.

He has a sound knowledge of Year One Mathematics. Below is what I had already

known.

I believe that Kobe will struggle understanding some components within the

Quantifying Phase, in particular understanding and solving a range of story problems

and/or open number sentences, however, by undertaking this assignment, will give

me a greater insight into his mathematics abilities and will allow me to plan and

experiment with activities that will enhance his level of thinking.

The first step, is to determine is his level of understanding in relation to the way he represents a range of addition and subtraction problems, as well as multiplication

and/or division problems. For this, I will be using the following diagnostic tasks;

- He has entered the “Quantifying Phase,” as per the Diagnostic Map for Number; outlined within

the First Steps in Mathematics (Number).- He can recall the sequences of numbers well into

double digits.

-

- He knows how to count a number collection by manually touching and feeling quantities.

- Kobe can make a group of objects to match a spoken number up to ten and beyond.

- Kobe can create a two or three step pattern- He understands that the last number spoken, is

the count. - He can share by dealing out an equal

number of items.

- Can understand the difference between two collections, and which one is larger.

- He uses realistic objects, blocks and counters to complete simple addition and

subtraction.

What I already know about Kobe

How Does Kobe represent a range of addition and subtraction problems and/or multiplication and division problems?

Addition; Problem Type: CHANGE

When participating in the Kangaroos activity, he was able to draw a collection of

kangaroos, and count each by pointing. He can solve addition problems when there

is a specific action or relationship suggested in the problem situation in which he can

directly represent or imagine (First Steps, Number, 2013). Kobe is starting to write

number sentences that match how he thinks about the story for small addition

problems, however in this case, the “result unknown” was unknown. I asked him,

“What is the story asking you Kobe?” And, “What is it about?” He answered, “There

were some kangaroos at a river and then more came up, so I need to find out how

many are now there.” I asked, “Well, can you please show me how you could do

that?” He started drawing Kangaroos to make meaning to the numbers. Once he

drew three, he then drew another two. Finally, I asked him how he could show this

with numbers and written symbols. Below was his reasoning;

Start Unknown (Correct), Change Unknown (Correct), Result Unknown

(Incorrect)

ADDITION AND SUBRACTIONKangaroos: To see how Kobe represents a

range of small number addition and subtraction problems

ADDITION AND SUBTRACTIONComparing Bananas: To see how Kobe

represents a range of small number addition and subtraction problems

MULTIPLICATION AND DIVISIONStory Problem 1: To find out how Kobe

represents number sentences , diagrams, materials and role play

MULTIPLICATION AND DIVISIONStory Problem 1: How will Kobe represent

number sentences?

Diagnostic Tasks

Start Unknown (Correct), Change Unknown (Correct), Result Unknown

(Correct)

Start Unknown (Incorrect), Change Unknown (Incorrect), Result Unknown

(Incorrect)

Subtraction; Problem Type: CHANGE

I found that Kobe did not have any trouble with simple subtraction problems as he is

quite familiar with having to give away personal items to his little brother at home.

“Taking away” was a common chore for him. He understands selecting either

counting on or counting back for subtraction problems depending on which strategy

best matches his situation (First Steps, Number, 2013). I asked him how he could

take away five biscuits from nine, his response was, “by drawing them.” Using

strategies such as drawing nine biscuits and then crossing out, or taking away five

cookies gave him the answer of four. His number line representation was excellent.

In this activity, he was competent representing the start, change and result unknown.

When asking him how he came up with the answer in the rabbit activity, his reply

was simple, “Dad, I drew nine rabbits, and then drew seven carrots, leaving two as

the answer.” Again, adding numbers and symbols to complete the number line.

Start Unknown (Correct), Change Unknown (Correct), Result Unknown

(Correct)

Multiplication/Division; Problem Type: REPEAT EQUAL QUANTITIES/ MAKE ARRAYS and COMBINATIONS

Kobe is starting to develop the idea that constructing a fair share, requires splitting

the whole into equal parts without changing the total quantity. Kobe had to revert to

using realistic objects that he could touch. He had to role play the scenario, whereas,

he separated the twenty four emus into small paddocks and then count each. The

first activity, Kobe demonstrated that he can lay out groups to represent

multiplicative situations, but he does not use the groups to find out how many

altogether, counting by ones instead. And, in regards to division, he can represent

division-type situations by sharing or forming equal groups, but then becomes

confused about how or what to count to solve the problem, often choosing to count

all the items individually.

My questions

Kobe’s responses

What is the story telling you

Kobe?

Excellent. And how many emus are to be put into

each paddock?

I have to separate 24

emus

Six. So I need to put six blocks in

each group.

Partitioning; The process to answering a question;

What does Kobe know and understand about part-part whole in relation to addition and subtraction problems?

Throughout his addition and subtraction tasks it was evident that he demonstrated

the part-part whole relationship through pictures, however when asked what it was

and how it was to be used, he was unsure how it was connected to his reasoning.

When explaining the part-part reasoning to him, including examples, he could not

grasp the idea. I did not want to push the idea as he was getting slightly anxious. I

was happy enough to see him grasp the ideas of addition and subtraction through

pictures.

Kobe counted blocks first, then

subtracted six blocks at a time

and put them into six separate

paddocks. Each block represented

emus.

Kobe counted six Lego men to

represent visitors for a BBQ. He then

gave every Lego man three blocks

each which represented a

sausage.

He had to use realistic objects to

make meaning, whereas, he could draw and count on mental strategies with Addition and

Subtraction

NOTE: I asked him how many blocks were there first?

He then counted 24 emus one by one.

Physically touching them. He then

counted six at a time to divide them into 4 equal groups

What does Kobe know and understand about using and array to represent multiplication and division problems?

Kobe has some understanding of an array. When asked to divide six emus into

paddocks he demonstrated an array in rows of six. The same can be said about the

BBQ scenario. Each of the Lego men had three sausages each. Again, put in rows.

These rows were used by Kobe to represent multiplication and division. Abstract

arrays would not be considered because of his age. I attempted to make it very

simple so he could put the objects in rows for himself.

What does Kobe know about choosing equivalent number sentences to find unknown quantities?

Kobe has a very limited understanding of equivalent number sentences. He

represents number sentences via his drawings, but if he was to find the unknown

number in a sentence, then he will struggle. He will often write his number sentences

after he has solved the problem using materials, counting or basic facts. He may be

unable to write number sentences in advance when needed for problems involving

larger numbers (First Steps, Number, 2013).

What types of problems can Kobe represent and solve?

Addition and Subtraction problems seem to be the easiest problems to solve. I

believe that at a year one level, this is one area that his class specifically focuses on.

I love the way he can represent his problems by drawings or by using visual

representations in which he can touch and feel. Through his drawings he is able to

represent number problems.

What types of problems does Kobe need to deepen his understanding?

Kobe needs to understand deeper division and multiplication problems. Through role

play he is able to work out solutions to simple questions, however, I would like to see

Kobe extend his learning beyond the confines of those realistic objects. By drawing

pictures he will be able to represent the correct number line for multiplication and

division. These pictures will assist him finding solutions.

If Kobe was in my class, what does he need to learn next?

Learning Experiences to move Kobe along

RETRIEVED FROM THE FIRST STEPS, BOOK TWO, CHAPTER 3.

Story Problems: Smaller multiplication problems will be set first. This way he can grasp the ideas from the story. Encourage little role play.Once he can find solutions through drawings or mental strategies, then I will proceed with larger numbers. NOTE: this is not about right or wrong answers, but finding ways to come up with alternative ways to find an answer

Multiplication

Story problems: Again, very small numbers will be used to minimise confusion. Kobe still cannot grasp the idea of Divison.He needs to listen carefully to the question and then break it down through drawings. At present calculations are done through using visual objects.

Division

Key Understanding 1Adding and subtracting

numbers are useful when we; change a quantity by

adding more or taking away, think of a quantity as

combined of parts and equalise or compare two

quantities.

Key Understanding 3Multiplying numbers is useful

when we repeat equal quantities, use rates, make

ratios comparisons or changes, make arrays and

combinations, need products of measures.

Key Understanding 5Repeating equal quantities and

partitioning a quantity into equal parts helps us relate

multiplication and division and understand their properties.

Learning Activity One; Picnic Blanket Squares KU 3/5

Purpose: To see how and if Kobe choose to count, add or multiply to find out how

many? when items are arranged as an array. Does Kobe understand the structure of

an array?

Learning Activity Two; How Many? Worksheet Three KU1

Purpose: To determine what strategies Kobe can use to build upon his knowledge

of Multiplication and Division.

Learning Activity Three; How Many? Worksheet Four KU1

Purpose: Kobe needs to identify alternate ways to represent multiplication and

division problems. He needs to move from using visual representations/role play to

blocks, counters, drawings and mental strategies.

Links to the curriculum(ACMNA031) Recognise and

represent multiplication as repeated addition, groups and arrays

Links to the Curriculum

(ACMNA031) Recognise and represent

multiplication as repeated addition, groups and arrays

(ACMNA015) Represent and solve simple addition and subtraction problems using a range of strategies

including counting on, partitioning and

rearranging parts

Links to the Curriculum

(ACMNA031) Recognise and represent

multiplication as repeated addition, groups and arrays

(ACMNA015) Represent and solve simple

addition and subtraction problems

using a range of strategies including

counting on, partitioning and

rearranging parts

Carrying out these learning experiences with Kobe

I began with the Picnic squares activity as I wanted to introduce him to a new way of

multiplication (Making arrays and combinations) through the use of an array rather

than objects. I wanted to get an inside into his level of thinking, on how he would

comprehend the activity chosen. Once I had read the question to him I asked, “Tell

me what they are asking Kobe?” he’s reply was, “How many squares are under the

plates of cookies.” I praised and then asked,

Kobe was becoming extremely anxious with all the questioning. He went ahead and

counted the squares by marking each one with a dot. I asked him again after the

activity and he couldn’t quite get the concept that there were four rows of five in this

array. I asked him if he could tell me what an array was. He couldn’t. I left it there

knowing that this would have to be planned for within his learning journey.

The second learning activity focused on the “repeat equal quantities” component of

mathematics. Once we had read the activities together I asked what the story is

asking. He said, “There are five bags of jelly beans.” I replied, “Well done, and how

many need to go into each of those bags?” He understood and replied, “Three need

to go in each.” In order to complete this activity, he had to draw the bags.

So how could you find out?

I am going to start

counting from the top

Ok, so how many are

along the top?

1,2,3,4,5

And how many are down the

side of the blanket

1,2,3,4

OK, can you see how many rows

are on the blanket?

Dad, can I just count

the squares!!

Of course you can Kobe’s. Go

ahead and take your

time.

Again, he had to count each of the jelly beans separately, however came up with the

answer. To keep moving him forward I had to continuously probe him with questions

related to the task, as he would always lose focus throughout each of the activities.

Start Unknown (Incorrect), Change Unknown (Incorrect), Result Unknown

(Incorrect) Kobe had issues completing the number lines for the above activities.

The process was the same for the twelve bags, however Kobe became unstuck with

the count on a few times. He was getting a little distressed so I left it. He came back

again after a short break and the same occurred. Large number counting is an issue,

however on the other hand, I was extremely happy with the process of multiplication

from a year one student.

The final learning experience was another “Repeating equal quantities” activity, this

time focusing on the Division component. Kobe seems to have a distinct way in

which to undergo a task. Similar to the multiplication, he needed to draw the answer.

Again, I asked, “What is this question asking you?” he replied, “There are twelve jelly

beans Dad.” So he drew 12 jelly beans in a single array.

So how many beans go in each bag?

Three Dad

So what do you need to

do now?

Count them all up?

Spot on Kobe’s

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15

OK, so you have 12 jelly beans,

what do you need to do now?

I need to put three jelly

beans in each bag

OK, but how could you do

that?

Put a bag around 3?

(He circles 3)

Yes! Well done Kobe, Do you need to circle

anymore?

Um, Yes, I will circle another

3, then another

A fascinating process to work towards an answer. I was extremely happy that he was

grasping a difficult concept. The second part to this activity highlighted the exact

same tactic. He would draw twelve lollipops in an array and then circle groups of

four. Shown by the examples in both below;

Start Unknown (Incorrect), Change Unknown (Incorrect), Result Unknown

(Incorrect) Samples indicate Kobe could not represented Multiplication and Division number lines

Overall, the work samples completed by Kobe highlights that he is starting to grasp

the concept of mathematics and division. I was extremely pleased because

throughout each of the activities he did not wish to use solid objects or game based

scenarios as highlighted in his learning objectives, but instead draw on his own

mental capabilities through drawings. Large number quantities still trouble him, and

representing multiplication and division in number lines confuses him, however he is

well on track to move through the quantifying and partitioning stages as outlined in

the First Steps.

How effective were those activities in terms of engaging the student and bringing about some learning?

Throughout this entire experience Kobe and I had an amazing time. I was amazed at

how much he did know, and the extent to which his number lines had been written.

His partitioning throughout the activities were evident and even though he had to

draw back on using visual objects/role play at times to answer each question, I was

really pleased with the engagement and positive attitude he had whilst completing all

tasks. The questions and activities chosen made for a tranquil environment, allowing

him to draw upon his own knowledge and prior experiences to find answers.

Personally I believe the techniques I used were relevant to his age and the

demeanour in which I set, allowed for a relaxed, fun and inclusive environment which

I believe, enhanced his learning.

WORD COUNT: 2219

REFERENCES

Department of Education. 2013. First steps in Mathematics: Number - Book 1 Understand whole and decimal numbers; Understand fractional numbers. Western Australia. Department of Education. 2013.

First steps in Mathematics: Number - Book 2 Understand operations; Calculate; Reason about number patterns. Western Australia. Department of Education. 2013.

First steps in Mathematics: Number – Diagnostic Tasks – Student Worksheets. Western Australia. Department of Education. 2013.

Reys, Robert. Lindquist, Mary. Lambdin, Diana. Smith, Nancy. Rogers, Anna. Falle, Judith. Frid, Sandra. Bennet, Sue. 2012. Helping Children Learn Mathematics. 1st Edition. John Wiley & Sons ltd. Australia. Western Australian Curriculum. 2017.

School Curriculum and Standards Authority. Western Australia. Retrieved From: http://k10outline.scsa.wa.edu.au/home/p-10curriculum/curriculum-browser

APPENDICES