Reflecting on a one-week journey that has been inspiring...

THREE things I have learned

1) Rebecca DuFour’s 4 Critical Questions

Questions that I need to ask continuously as I focus on student learning:

·          What do we want students to learn?

·          How will we know when they’ve learned?

·          How will we respond when they don’t learn?

·          How will we respond when they’ve already learned?

      A shift in thinking is required – from a focus on teaching to a focus on learning…

2) I can do away with the structured lessons on TIME

It’s common sense really. Why have lessons to teach time when it should really be an everyday occurrence as children learn to connect time to their daily lesson times, routines, etc.

 3)   Language is important

The right terminology should be used to avoid confusion and mislearning. The language that we use must help children to make connections between quantity and number…

Example:

¼ is “one fourth”, not “one out of four”

The questions that I ask can effectively support learning…

Example:

Is there another way to make 10?

What do you notice about all these shapes?

Open questions encourage a variety of responses and allow for differentiation.

TWO questions that I have


1) Maths isn't about speed, it isn't about accuracy.. It's about understanding, reasoning, problem solving....... isn't it?


2) Who is a mathematics teacher?

Technology in the classroom

NCTM’s position statement regards technology as “an essential tool for both learning and teaching mathematics.”

The kindergarten years are preparatory years for learning and our young children should be exposed to different learning experiences. Apart from the many hands-on opportunities we plan for children, technology has its place in today’s classroom and it should be used to help encourage active learning and stimulate interest.

There are many in-store and online programs that can be used in the classroom as well, to support  mathematics teaching. Technology can be used in a fun and educational way. As games usually appeal to children, they will be involved in learning without even noticing that they are.


I am fortunate to have an IPad in my classroom, which I use quite often to support literacy learning. It is high time to check out the dozens of math apps available too..

Lesson 4

It is not new knowledge but certainly an important point that all pre-school teachers must adhere to –
The early years are preparatory years for learning and we should not be overly concerned about content and WHAT to teach. More importantly, we should be giving careful thought to HOW we teach and THE WAY we teach, as we want our children to be diverse thinkers who can see different approaches to the same problem. We want them to eventually be able to visualise situations from different angles.
 
I think that in order for teachers to effectively nurture divergent thinking in children, we have to possess an open mind, value all contributions, and be divergent thinkers ourselves. How else to develop strong thinkers but to be models ourselves..

As I watched Dr Yeap deliver his lessons in an easy-going, candid manner, I saw how important it is to encourage discussion and ask questions like, “Did anyone solve the problem the same way?”, “Who found a different way to solve the problem?”…

Children need to feel safe in expressing their thoughts, therefore it is important to accept all suggestions. We should learn to mediate learning. Our job is not to bring the child to the end point, but walk the path with him or her..

Making sense in their world...

Lesson TWO & THREE - Making (NUMBER) sense in their world...

Number sense is an important skill to teach. Children develop this skill over time based on their experiences in school and out of school. Having number sense helps us to create strategies to problem solve.

What does this imply? As a teacher, I have to provide many opportunities for children to investigate, to think about what they are investigating, gather information, organise it, use information to problem solve, explain their reasoning...

There are plenty of opportunities to develop number sense in the classroom. Some examples would include grouping sets into tens and ones, encouraging guessing (How many broad beans do you think are in this bottle?), playing addition and subtraction games, estimating (How many grapes do you think are in this bunch?), guessing a number (give clues, eg. It's a bigger/ smaller number, it's less than 10 but more than 5..), card games, etc.

In my primary and even secondary school days, I recall that the focus in mathematics lessons was always the answer, the correct one, ideally. However, the focus today, is and should be, very different. It is important for children (and adults as well) to know WHY and not just how numbers work..

Lesson ONE

Wait till I baffle them!

I fell asleep after midnight with the card trick on my mind. I cannot wait to impress my children in the morning. I know I will get a chorus of “do again, do again…” It was fun figuring out the sequence of cards together with my table buddies. Dr Yeap didn’t just tell us how. He urged us to find out, and we did, even though it was after 9pm. Auto shut down had not occurred! 

Problem solving!

It got me thinking about the importance of problem solving and how I should get my children to be fearless thinkers, do-ers, try-ers… I think that the key is to NOT hand out answers but to encourage exploration, trial and error, and to look at situations, activities, and problems from all sorts of angles. Perhaps, importantly, it is how we can pose questions to the children to guide their thinking, to acknowledge every try and accept different possibilities.

Lots of “takeaways”:

Numbers are used in four different ways

·       cardinal numbers refer to quantities, eg. 3 cups, 4 boxes

·       ordinal numbers refer to positions in space, positions in time –

        1^st, 2^nd, 3^rd and so on

·       nominal numbers are numbers as names, eg. bus number 14

·       measurement numbers are standard or non-standard units, eg.

        The box weighs as much as 3 oranges; That man weighs 62kg.

How do I get children to learn mathematics?
Pose problems to promote thinking. Problems can be put forth in different scenarios, in word problems, in a game (like the card trick)

Plan activities to encourage children to investigate, explore, ponder over..

Always remember: CPA

Concrete -> Pictorial -> Abstract
Carefully provide appropriate materials, examples (theory of variability)

Constantly assess and reflect to understand how children learn so that we can provide the appropriate level of instruction, materials, etc.

It’s often about patterns!

The name pattern activity was very interesting. I was very engaged in the process of pattern searching and thought that this is something our naturally curious children are adept at. Already, I see them able to grasp the common patterns (ABAB, ABCABC, etc) easily. I really should bring them a level higher to search for patterns in the environment, patterns in stories, perhaps even patterns in a series of numbers like in the name pattern activity.

Excited about Lesson 2!

Chapter TWO

Learning mathematics with understanding!

I recently introduced the concept of multiplication to my K2s. Apart from using the Montessori materials we have in class (golden beads, stamp game, multiplication board), I also got them to experience the whole idea of multiplication by having them make physical groups with their own bodies. They also created individual art pieces to demonstrate multiple groupings of the same number (eg. 3 vases with 2 flowers each to show 3x2). There are many ways to inject fun and creativity to a maths lesson. Maths doesn't have to be humdrum!

 

Multiplication board

Multiplication with golden beads

Multiplication with stamps (Stamp Game)

When I see that children are engaged in mathematical ideas all on their own, it gives me immense satisfaction that they've got it!


It is best that teachers consciously provide positive and meaningful experiences in mathematics in day to day activities. As they work and play together, the language that we use can help them to make connections between mathematics and its applications, for example, asking, "How many more blocks do you have compared to ....?"


Own learning..


Recently, I introduced graphing to my K2s. We worked on many concrete activities together and I was pleasantly surprised when one of the girls in my class came up to me with a graph on "Favourite Fruits" that she had created on her own. She proceeded to write her own short story about it as well. I took this as an opportunity to invite others to try it too! It was wonderful to see them express their understanding of newly acquired knowledge.

Scaffolding..

Teachers can scaffold learning in group and definitely in one-on-one situations. Learning is enriched further when classroom situations and activities are planned where children can interact, support, and learn from each other.

Being among them.. 

Play is an integral part of learning. I believe that it is important for teachers to mingle and be among the children when they go off to their separate areas, whether singly or in small groups. Being in their midst, we can pick up and capitalize on "maths moments" such as "I need 3 more bricks....", "I don't have enough...", "Mine is longer.." By being alert, we can help to develop thinking dispositions in children.

Chapter ONE

MOST IMPORTANT TOOLS to be an EFFECTIVE TEACHER of MATHEMATICS! 

* My knowledge of mathematics 

* How children learn mathematics

Our classrooms are becoming increasingly diverse, with children from different ethnic and cultural backgrounds coming together, the inclusion of children with special learning needs, etc. In addition, children also have different learning styles.

A teacher’s job is not an easy one. To be effective, we must provide an array of learning experiences and address the diverse learning abilities and styles of the children in class. The teaching of mathematics and any other subject for that matter needs to be differentiated so that children can acquire mathematical knowledge in their own unique ways.

Personally, I feel that it is imperative that teachers reflect a lot more on classroom practices. We need to constantly ask ourselves if we are providing enough, teaching appropriately, catering to the different developmental levels and learning styles, etc.

Knowledge gained from research

+

Leadership of the NCTM

+

Public and political pressure

has led to 

STEADY CHANGES 

in the way mathematics is being taught in the US

These changes were initiated because US students had been underperforming in national and international studies as compared to students from Asia, notably.

The revised NCTM principles and standards

These principles and standards act as a guide and were developed to improve mathematics education in the US. They provide educators with learning goals for students from pre-K through grade 12, serve as a resource for teachers to improve instruction, and help guide the curriculum.

NCTM Principles

* Equity

* Curriculum

* Teaching

* Learning

* Assessment

* Technology

These principles reflect basic perspectives on which mathematics educators should base their decisions. They underline the foundation for mathematics programs by considering the broad issues of equity, curriculum, teaching, learning, assessment and technology.

What struck me most - The Teaching Principle

Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well. (NCTM, 2000, p.16)

I believe that as an educator, I need to plan developmentally appropriate lessons and constantly assess progress and identify areas for improvement. Learning should be maximized for each child within his or her own ‘zone of proximal development’ (Vygotsky, 1978).

I also feel that It is important to keep abreast of current knowledge, constantly learn, practise and reflect in order to teach more effectively.

NCTM Content Standards

* Number and operations

* Algebra

* Geometry

* Measurement

* Data analysis and probability

These outline the specific mathematics concepts for each grade level.

An outline is an important guide to rely on however a teacher's responsibility especially in the kindergarten classroom, is to capitalize on play and everyday activities to promote learning. 


Concepts should be taught in an experiential way. Children should be allowed many opportunities to explore and build their knowledge through concrete manipulations. This brings me back to the basic principles of HOW we teach. The teacher's mindset and attitude makes a world of difference to how much and how well a child learns.

NCTM Process Standards


* Problem solving
* Reasoning and proof
* Communication
* Connections
* Representation

These process standards help teachers to make informed instructional and curricular decisions when teaching mathematics. 

Apart from planning appropriate lessons and creating a supportive environment with meaningful interactive mathematical activities, teachers can help to build process skills by asking questions that would help children to make sense of what they are doing.

We can ask questions like..

Why did you do that?

What would you do if....?

How could you show....?