What's maths got to do with it?

Is Numeracy Project really doing its job for us?

Current New Zealand research and results is showing evidence of students not achieving to their best ability.

Is it the Numeracy Project, our pedagogy or content knowledge that needs addressing?

How can we give the teachers more resources to select from and what are the foundation skills our teachers must be addressed?

Are we aligning in our practices across the school?

Prime Maths - could it be an alternative?

Dr Lester Flockton thinks so. He is currently doing research in Christchurch schools which is published on Scholastic website.

I was most concerned about how teachers implement when produced with a text book for every child. However, text books are designed for conversations between two children and teacher.

The lesson format is no different from Numeracy;
- concrete using concrete materials
- pictorial concepts are modeled by pictures representing concrete objects previously used
- abstract using only numbers, symbols, and mental thinking

Planning formats are all done. It includes resources and page numbers for the teacher. Available digitally.
Lestor Flockton has aligned to each curriculum level, ICAN, JAM and Gloss testing.


So;
My next steps;
Shared understanding of what is effective teaching looks like
Criteria of what is needed to raise student achievement
Understanding what teachers know about progressions and content knowledge.
What would support them more?

While these are my next steps,  the move away from Numeracy project, I believe is up to the interpretation of pedagogy and knowing your students, progressions and how students learn.

I guess for me it's finding the way teachers learn best in a curriculum area that may or may not be a comfort zone.

What are math leaders doing? Some important conversations.

What is acceleration? 

- more than expected amount of progress in set amount of time. 

- increase of work and attitude ethic 

-identifying blocks in learning that has held them back in the first place

- gathering data to assist in a new approach to support the ownership of the learning.

- change mindset for success due to low self esteem

- key prior knowledge is pre taught to prepare

- connected to class learning to keep them in the loop and identify where they are at in relation to their peers

-understanding larger concepts rather than parts of each stage

- teachers taking the time to look and listen for the blocks

-targeted actions

 teachers having an explicit moral commitment to excellence and equity 

-students are feeling challenged yet supported

What does it look like in your school?

What's the big deal about math vocabulary?

is required for enabling classroom discussions 

content specific vocabulary 

reading is not enough to build vocab

Strategies to develop language 

planned for direct and explicit teaching

Share your rich vocabulary. Deliberately using more challenging words in classroom discussions. 

amathsdictionaryfor kids.com

Think Boards with; 

word, definition, pictorial representation, everyday language 

Pinterest 

TIP - term, information, picture 

word - definition - example 

clines for measurement, time, weight, etc

discourse cards - could be great for parents at home as well!!

Updates to nzmaths... 

- problem solving section has been revised

- planning sheets revamped

-more modules added to e-ako

-student and whanau task sheets will be linked 

(these would be great for parent workshops) 

Questions for the team

How do we track children - individual / whole school

What questions do you have?

ILE / MLE 

What is working well?

What is providing challenges?

What are the opportunities?

Coverage fitting everything in?

ICT how are you using it in maths? 

So what does a balanced classroom look like?

Check out page 12 in the pink Getting started book. 

Our pink books have rich math tasks. Drop off the end part of the questions and let the children do the thinking. 

How can I improve my understanding of the Number Framework?

The value of number sense, place value, roll over numbers,
The Number Framework Book is the most vital resource we can refer back to. Having a broad range of the whole range.
1. Know the stage number but more importantly the name. (It tells you what the students are doing)

When we solve a problem in real life we have to solve it on our understanding of what we know and interpret from the situation.

When posing problems in maths we ask questions that keep it open - ie: not a specific question of how many or a final question and letting our children make sense of the problems


The difference between stage 6 and 7
The strategies you have applied to whole numbers in stage 6 are the same in stage 7. However they are now being applied to decimals, integers, fractions,
This will highlight any knowledge gaps of place value very quickly and takes time to correctly teach to catch them up.

Pose a problem at stage 4 but scaffold them through to stage six. The strategies build on each other. Don't hold them at a stage until they are completed. Move them through.
KEY IDEAS 
The key ideas are really important - when children struggle they have not grasped these key ideas.

Some vital key ideas we ned to be aware of;
Stage 1
convince them them 7 is 7
Stage 2-3 
7 can be split and rearranged in different ways through loads of experiences This is the beginning of place value understanding
Stage 4
Objects can be counted by creating bundles of 10. Students must develop a solid understanding of Place Value.
Stage 5
Our number system is based on 10.
Stage 6 
The equals sign means balance
Stage 7
10 tens make 100 and 10 hundreds make 1000
Decimal fractions arise out of division.

Next steps
Look, as a team over the progressions of place value
Review visual pathways to ensure these new key ideas have been included accurately.
Are we posing the right problems to develop these key ideas?
If we are wanting children to part whole what equipment will we want them to use.

What are children doing to solve problems at each level?
Level 1
From stage 1 - 4 children count to solve problems
Level 2
From stage 5 - children partitioning around ten to solve problems
Level
From stage 6 - children are solving problems by flexibly using with whole numbers and choosing wisely in their choice of strategy
Level 4
From stage 7 - flexibly using strategies to solve problems wisely in not whole number problems

Allow students to solve problems their way - select student to share their solution they will then see the diverse ways of solving a problem and discussing the most efficient and why.


The Five Practices
Anticipate 
What stages are they at and where do I want to take them

What different materials might children use?
What we might we want to know? see the range of stages we are working with
Sharing and Reflection 
Who shares and in what order
struggling children need to articulate their thinking
What was the best equipment to best represent the opportunity for teaching next step

Literature with math content 

Can we use a Critical Incident Interview Technique to refine our assessment practices during Rich Math Tasks?

This qualitative research technique aligns with my own qualitative ideology of an interview process for reflection time at Action Stations. 

How powerful could this framework become if we applied it to assessment of an observation of a student engaging in a rich learning task. I know many of you who use action stations and rich learning tasks in your classrooms much of this will sound familiar. 

This is my attempt at synthesising CIT with educational teaching practice to consider a different approach to assessment of and for learning. 

The critical incident technique (CIT) is a well-established qualitative research tool described by John C. Flanagan in 1954. It is a flexible set of principles that can be modified and adapted to meet specific requirements. By gathering factual reports made by observers, we can build a picture of the students thinking and capabilities that we are investigating. The CIT format effectively turning anecdotes into data. 

To gather really useful, meaningful information, about how and what students are thinking and feel about their learning, anecdotal information regarding these areas is plentiful throughout action stations. However, the anecdote’s subjective nature makes it difficult to access and credibly analyse using traditional quantitative research methods. 
We need to carefully consider this framework to ensure we are consistent in what we are looking for and how we will navigate conversations to gain this information. 

These steps are essential components of CIT;

Step 1 PURPOSE - Identify what it is that you want to know as the students educator. 
Students actively engaging in  a rich math task are working and applying what they know or seeking ways to solve their problems. Sometimes the decisions and actions performed during learning in context results in "critical incidents" which may be either a success or a failure. This interview technique is used to help identify the specific actions (behaviours), decisions, and information which led to the critical incident. 
Possible purpose of the interview. "We want to learn more about how you make decisions as you work out this rich math task."
They may also be derived from;
- problem solving strategies applied
- number knowledge applied to the learning process
- strategies applied 
- key competencies
- learner dispositions
- areas of strength or interest
- ability to communicate the learning process
- ability to build and construct knowledge with / alongside others

Step 2 Collecting data - Through probing questioning we can help the student to talk about identifying the critical incidences they experienced throughout the task. These are decisions that may have or would likely have resulted in the success or an error in completing the task. It is important that the focus remains on the incident and what led to it.
These should be recorded as close as possible to the time when they occurred. During and throughout the activity. 
Memory of the learning will become improved if they know they have to report / share to an audience. 

During the questioning;

• Ask for clarification, justification, explanation of their thinking and actions. 
• Avoid discussion about things not related to the learning process. 

In Action Stations we record anecdotal notes on a class list for simplicity and ease of access. 

Step 3 Analyzing the data

Often considered the most important and difficult step. With a framework such as this we are able to then summarise and describe the data so it can be used for practical purposes.

The aim is to increase the usefulness of the data without sacrificing comprehensiveness, specificity, or detail

• Know the purpose of assessment
• Used a consistent classification system - national standards, levels, stages, strategies, progression framework, KC's, learner dispositions. 
• Developing a set of success criteria. This can emerge from the observations made and work towards developing next step. In action stations this is developed through KC's every Monday but as an educator and the student as a learner we need to know more than just that - the ability to identify the learning in a task.  
• Placing the observations into the above categories will require experience and judgement from the teacher. 

Step 5 - Interpreting and reporting 

For each decision point before adding to classification register, consider the following:

1. Errors If an error occurred, what was it?
2. Optimal How should the decision have been made?
3. Ambiguous What information could have helped make the decision. Was any information missing?
4. Error Avoidance Could the error have been avoided? If so, how?
5. Environmental Factors What aspects of your environment influenced your decision?
6. Expert / Novice Do (or would) experts and novices differ in their decision making?
7. Information What information was used in making the decision? How was it obtained?
8. Ongoing Training What would you teach them about this kind of incident in the next lessons?

Advantages 

• Information is gathered directly from the students
• Can follow-up on statements in future lessons
• Can interview multiple students for a more complete perspective
• One of the most significant advantages of the CIT is its connection to real-world problems and situations provided through the words of the participant, thus limiting the subjectivity of the researcher (Kain, 2004).
• allows participants a wide a range of responses within one rich task 
• participants freely develop the context using their own perspective, allowing cultural neutrality (Gremler, 2004)
• When recalling incidents, participants openly use their language This can also become a disadvantage if ESOL or difficulty with oral language or self confidence. 
• operates with a flexible set of rules to let themes or theories emerge directly from the data - no preconceived ideas about challenges student may or may not have. 

Disadvantages

• Subject to the interpretation of teachers / students
• Questioning needs to be conducted shortly after or during a task 
• Memory about an incident may be biased or fallible - will require Teacher competency in questioning, recording and analysing of narratives. 
• Some students may be reluctant to talk about certain elements of the process. Requires a relationship of trust, and feel safe to take risks. 

Linking theory to practice is a great way to help define and refine elements that make it work, both being as vital as each other. 

Sources of information 
Journal of Dental Education March 1, 2008 vol. 72 no. 3 299-304
Sourced from: http://www.jdentaled.org/content/72/3/299.full

http://www.hr-survey.com/Critical_Incident_Interview_Guide.htm

http://www.jorgvianden.com/uploads/2/2/7/7/22771362/vianden_2012_cit.pdf

What are interactive math spaces?

Interactive Learning Spaces

Purpose:

1. engaging child centred learning
2. reinforce visual learning pathways
3. create opportunities for developing self directed learning
4. create opportunities for self management
5. displays learning for parents
6. invites learning before school for behaviour management
7. becomes another teacher in your classroom.

Things to consider:

• catering for different learning styles - ind, small group, quiet area, discussion areas.
• clean tidy and represents a love for learning
• looks like fun and inviting
• pathways with furniture to prevent running

Interactive wall space for children to have discussions around, parents to view and understand the language of learning and for maths

Challenge Board - pose a problem for all to solve on a whiteboard

Investigating Book

- an exercise book that children have freedom to explore practice, consolidate their learning in maths, writing, handwriting, art, science.

Rules - no crayons or felts, but can use colour, pens, pencils

must show respect at all times

cannot take home til book is full

Visual pathways for children to know and understand next steps and recognise prior learning

Equipment is organised, accessible to students and managed with respect throughout the day

Are you teaching your children how to learn?

How to use equipment to achieve their goal?

How to test each other?`

How to show their thinking in different ways?

Classroom Number Space

Room for learning on the floor and at tables

Looks inviting, exciting and fun welcoming the exploration of new ideas

Space for exploring and space for working

Math Work Books

• Are they for sharing thinking and  learning or  storing worksheets?
• dated?
• marked?
• celebrate achievements?
• reflects work that inspires further learning, celebration of learning or requires clarification of new learning and understanding? How do the students know this?
• Are they a portfolio of a learning journey in maths?

Linking to Literacy - students who struggle with maths often struggle with reading.

What considerations do you have in place for supporting literacy with numeracy?

How could this be shown in your classroom space?

What's the Problem?

A Mathematical Problem is...

-when you can't get the answer immediately
-unclear about what strategy to use or how to work through a method

A problem should be....
interesting
motivates the need to solve it
context that interests them
uses their name if possible
at the appropriate level
provides a challenge but allows success

Big Ideas 
Work systematically
- organising systematically supports logical and systematic approach to math. Teachers need to model and remind students often about this.

Look at solved problems
Some problems can be solved in similar ways. Comparison of strategy use rather than context.

Solve a simpler Problem
use smaller numbers to demonstrate the strategy then scaffold to larger numbers

Find a pattern
- patterns in math can be easy or complicated. Looking for them is problem solving

Work Backwards
- justify your answer if you know it.


Strategies to teach

Guess and Check - simplest strategy however develops complexity when justifying the pattern

guess is a conjecture, checks are called proofs, a guess that has been checked becomes a theorem

- limited possibilities
- gain better understanding of problem
- might know the answer
- systematically try possible answers
- our choices have been narrowed down by other strategies
- no other obvious strategy to try

Guess and Improve- students use initial guess to improve their next one

Act It Out  - great for demonstrating to class
- problem is about doing things
- aids understanding

Use equipment - should be used by all students of all ages
-may be difficult to keep track of the solution.
-encourage students to keep a record of what they are doing
- supports logical thinking and sequence of events to solve a problem

Make a Table - vary in form
- efficient way of finding number patterns

Make an organised list
- should be in natural order
-categorised under headings

Draw a diagram - anything that is not a picture, more symbolic dots for animals etc

some frequently used diagrams have names - tree diagram 

- physical situation is involved
- geometric figures or measurements involved
- gain understanding
- need a visual representation

Draw a Picture - only drawing enough detail to explain thinking to solve problem

Questioning - scaffolds, creates ownership, directs thinking, empowers the learner, maintains momentum of the learning, encourage ideas, 

Getting Started
- What are the important things in this problem?
- What is the problem asking you to find out?
- What information has been given?
- Can you guess what the answer might be?
-Has anyone seen a problem like this before?
-What strategy might you use to get started?


While working on the Problem
-Tell me what you are doing.
- Why did you think of that?
-Why are you doing this?
-What will you do with the result when you've got it?
-Why is this idea better than this one?
-Can you think of another way to find the answer?
-Can you justify this step?

At the End
- Have you answered the question?
-Have you checked your answer?
- Does the answer look reasonable?
- Is there another answer?
-Can you explain your answer to the class?
-Is there another way to solve this problem?
-Can you make the problem harder /trickier?
-What if....

Need help with your math?

Priceless!

Can I teach maths through inquiry - REALLY?

Inquiry is often seen as a cyclic approach rather than a facilitating approach to the whole classroom. Kath Murdoch challenges the way teaches see and use inquiry in such a thought provoking way. As I sift through her site I stumble upon this fabulous site that you have to check out!

Good grief if only I was taught in this way. 
Creative, accepting of new thinking and ideas, invites thinking processes, extends language, encourages the link of patterns, values student voice, embraces difference! This list could go on. Check out this amazing website - it won't disappoint!

Authentic Inquiry Maths

How can I manage my literacy and maths games on my blog?

Every year we look at updating our online games for our students to consolidate learning.

This year a collaborative team effort, collated all of our best games for teaching and learning numeracy at an Upper Clutha Cluster workshop.

We all worked in our levels of teaching and added links to a symballoo. This displayed the childrens access to games in an organised and attractive way. Each teacher who worked on the symballoo received the embedding code to put on their blog. Now we all have the best games that we all use and the kids have choice!

www.notcot.com

Check out symballoo for organizing your resources for teaching.

I'm beginning one for listening and speaking activities so that it will grow over time as a resource to pull from for teaching a specific skill. It could be used in many ways. Let us know your ideas.