C&Pa Professional Relationships [1]

Achievement Objectives provide direction for the different learning areas and are specific to each discipline. Each learning area has its own set of specific Achievement Objectives and you will be engaging in each of these throughout the year to guide your planning, learning and teaching.

Learning Intentions & Success Criteria

The ‘intention’ was to give a strong purpose to the learning for children and ensure that they knew what the focus was.  I am often heard saying– “AOs are for teachers and LIs are for students”.  Clarke’s (2003) reading really underpins this.  A child should know exactly what the focus for their learning is from the LI. 

A cautionary tale:  Whilst we do want you to perfect the art of writing Learning Intentions we do not want you getting caught up in every piece of learning has to have a LI or as many of you would have seen in schools – WALTS (We are learning to…).  It should not be laborious, with children or teachers having to write out LIs on every page.  Think of it as a focusing tool.  You might see schools use a ‘focus’ for the lesson.  What matters is that ākonga understand the purpose of what they are learning to do and we deliver this with clarity. 

Success criteria is also another factor in planning.  Simply put, how will ākonga know they have been successful with a task? Teachers will often co-construct the success criteria with ākonga in the beginning phase of the session (in children’s language, obviously) – this is the ideal scenario.   The SC needs to reflect the LI (purpose) and demonstrates how the learner will be successful.  This is why there needs to clarity.  One to three SC is more than enough.  It is very important that we do not ‘add’ in additional SC – for instance, spelling or other editing skills unless that is the focus of the lesson. 

Literacy

In C&P A we tautoko Loane & Muir’s (2010, 2017) quest to become joyfully literate. This quest is championed by finding a voice through literacy – having ‘something to say’ and being able to express it powerfully.  As Calkins (cited in Loane, 2010) says “The teacher of writing triggers memories of life experiences through literature so that the child ‘feels the blood rush to his cheeks because he has become so filled with his life story’.”

Read Alouds

…at the heart of reading is the sharing of stories and the connections we make with these to our own lived experiences as well as connections and themes across multiple media.  

Mem Fox celebrates read-alouds by recognising the importance they have in the classroom by stating: “The more expressively we read, the more fantastic the experience will be.  The more our kids love books, the more they’ll pretend to read them and the more they pretend to read, the more quickly they’ll learn to read.  So, reading aloud is not quite enough – we need to read aloud well” (Fox, 2001, p. 163).

Read :

Read

Comprehension Strategies

We can think of comprehension as the different kinds of thinking readers do before, during, and after reading to gain meaning from a text. Comprehension is a complex set of associated skills and concepts. Tompkins et al. (2019) identify 11 comprehension strategies:

1. Activating background knowledge: what the reader already knows
2. Connecting: text to self, text to world, and text to text.
3. Determining importance: noticing big ideas and relationships between them
4. Drawing inferences: reading between the lines with clues in the text and background knowledge
5. Evaluating: both the text itself and the experience of reading the text
6. Monitoring: checking own understanding
7. Predicting: guess and confirm
8. Questioning: literal, inferential, and critical
9. Self-correcting: identify and solve issues related to meaning
10. Summarising: readers paraphrase the big ideas
11. Visualising: readers create mental images

A Complex Mental Process:  Drawing Inferences

Tompkins et al. (2019) recommend that teachers engage children in a 4-step process to promote the development of inferential comprehension.

1. Activate background knowledge (What does the reader bring to text that might be helpful in comprehending? For instance, what are their lived experiences? Strategy: Prompting ākonga with a text-to-text; text-to-self; or text-to-world connection is a great place to start to activate prior knowledge and lived experiences).
2. Look for author’s clues – what is the author trying to tell us?
3. Ask questions that prompt whakaaro, tying together 1 & 2 (Strategy – I wonder…).
4. Draw inferences by answering questions.

Consider these pedagogical approaches:

• how will you launch your lesson?
• Engage and hook in ākonga?
• A place for korero?
• What will the body of your lesson look like? 
• How will you round it all up (closure)?

Pāngarau: Mathematics

To kick start the year, in our first module we ask who are our ākonga in Mathematics and how do we build professional relationships and connect with them in their mathematics learning? We will explore different ways that diverse ākonga can be supported to show their mathematical strengths and capabilities,  we will disrupt the traditional deficit views that abound in mathematics education for some of our ākonga and explore the pedagogical aim of mathematical practices through the use of talk moves, an ethic of care and communication to engage diverse ākonga. 

Our mathematical focus will be early number, and we will be introduced to planning for a mathematical warm up lesson, quick images. 

Professional relationships with ākonga

Ethic of care

This ethic of care in the school setting is founded on the seminal work of Nel Noddings. Noddings encourages us to think about schooling a diverse group of ākonga in a caring way and to see our ākonga as unique individuals. The key idea is not to view diversity from a deficit perspective, but to acknowledge ‘good’ classroom practices that should benefit all ākonga regardless of differences in cultural backgrounds, language, abilities and qualities, backgrounds and experiences, gender and disabilities.

Strengths based approach

Commonly the focus for teachers is on what ākonga can’t do in mathematics and plugging these gaps before ākonga can progress.

…consider an alternative perspective; an ākonga who has strengths as a mathematician may have dispositional strengths (perseveres, asks good questions, uses creative strategies or approaches….), strengths in processes and practices (explains their strategies and thinking, creates varied representations, makes connections between concepts and procedures, identifies patterns….) and lastly strengths in mathematical content (uses number sense, converts measurements, knows their basic facts….) (Kobett & Karp, 2020, p.8).

An introduction to Mathematical practices

Kaiako need to ensure that all ākonga explain and justify their mathematical thinking, inquire into, and explore the mathematical thinking of others, and justify and challenge the thinking of others when appropriate. Mathematical practices are grounded within collective practices. 

Mathematical explanations are statements that commence from well-reasoned conjectures. These conjectures, although provisional, are statements that present a mathematical position the explainer is taking. They make visible and available for clarification, or challenge, aspects in the reasoning that may not be obvious to listeners. The criterion for a well-structured mathematical explanation includes the need for explainers to make explanations as explicit as required by the audience, relevant to the situation, and experientially real for the audience. Explainers also have to supply sufficient evidence to support the claims. This may require that the explainer provides further elaboration or re-presentation of the explanation in multiple and rich relational ways. Concrete material or graphical, numerical, or verbal contextual support may also be needed. In other words, it is the explainer’s job to make sure others understand their explanation. 

Mathematical justifications; Explanations become explanatory justification when explainers are required to provide further evidence in order to address disagreement or challenge to their reasoning.

To develop justified claims, it is important to construct classroom cultures which provide participants in the dialogue with space for extended thinking. 

Mathematical generalisations; The need to validate mathematical claims through explanation and justification scaffolds the development of generalised models of mathematical reasoning. 

 Kaiako need to support their ākonga into assuming a ‘mindful’ approach to recognising patterns, combining processes, and making connections at an elevated level of awareness. Generalisations evolve through cycles of reflective pattern finding as theories are publicly proposed, tested, evaluated, justified, and revised. 

Numerous studies have shown that explicit focusing of ākonga discussion on the relationships between numbers properties and operations resulted in their powerful construction of generalisations.

Mathematical representations: Concrete material and problem situations grounded in informal and real world contexts potentially provide a starting point to develop multiple forms of representation. These serve as reference points which are then mathematised— progressed toward abstraction and generalisation. 

Mathematical languages and definitions: Ākonga who display mathematical literacy are able to use the language of mathematics to maintain meaning within the context of its construction, in its form or mode of argumentation and matched to audience needs.  Gaining fluency and accuracy in mathematical talk requires a shift from an informal use of terms and concepts to a more narrow and precise register (Meaney & Irwin, 2003). Meaney and Irwin maintain that “if ākonga are not encouraged to use mathematical language (both terms and grammatical constructions) then eventually their mathematical learning will be restricted” (p. 1). 

• Read: Van de Walle, Karp, & Bay-Williams (2015) Chapter 3: Teaching through problem solving (pp. 54-80) 

Socio group participatory norms

Tamariki need to be explicitly taught how to engage productively in the practices outlined above in collaboration with their peers in their learning communities. Developing new social norms for productive collaboration is challenging and takes time. Sharing the responsibility for one another’s learning and having high expectations of each other go hand-in-hand. It is important that the group take responsibility for ensuring everyone can explain and justify the group’s thinking – there should be no hitch-hikers and no-one left behind.

• Read Hunter, R., & Anthony, G. (2010). Developing mathematical inquiry and argumentation. (pp. 197-206) in Averill & Harvey (2010). As you work through these topic notes, think about how you might explain what these practices are and how they are important. This chapter will help you to make sense of the practices and their role in mathematics learning.

• Read BES Exemplar 1: Developing communities of mathematical inquiry – available here. Reflect on how the metaphors of “whanau” and “friendly arguing” are used to promote productive participation in important mathematical practices.

Collaborative Learning through Problem Solving:

Learning through problem-solving is fore fronted in recent research nationally and internationally as an effective pedagogical approach for the teaching and learning of mathematics and statistics, it is also highlighted in the New Zealand Curriculum document (2007). Problem solving demands an understanding of numbers and mathematical context in order to make sense of a problem and to find a solution. When giving tamariki problems to solve, it is important that they first understand the problem, they can then focus on finding a solution to the problem. Tamariki should be encouraged to articulate the problem solving process and when necessary they should be allowed to use equipment to model the process.

Pre-counting concepts

The development of number sense and learning to count builds on four key concepts— conservation, seriation, classification, and one-to-one matching.

1.     Conservation of number is the ability to determine how many objects there are regardless of spatial arrangement.

2.     Seriation refers to sequencing things in an order. For example, ordering things by length, or volume, or by the number of dots, etc.

3.     Classification (whakarōpungia) refers to the process of putting things into classes (or sets). Classification is a process of logical thinking and of being able to determine whether an object does or does not belong to a particular set. Young children can classify using attributes with which they are familiar such as colour, shape or size.

4.     One-to-one matching or one-to-one correspondence (panga tahi) is the process of pairing off the physical elements of one set with the elements of another set.

The triad model: 

help teachers focus activities and questions

The  three  elements  are  the  model  (some  kind  of visual representation of the concept),  the word (the name of the concept), and the symbol (the specialised abbreviation used to represent the concept).

Links to Literature: Literature can be used to make and enrich connections to many mathematical concepts. Check out the Christchurch City Library ‘Mathematics in Pictures’ section. Many of the titles from the Christchurch catalogue can be found in the Massey Library.

Using Stories to Teach Math

Teaching literacy and math at once helps make the most of class time while deepening young students’ understanding in both subjects. https://www.edutopia.org/article/using-stories-teach-math

1. Use stories to develop number line skills: One of the biggest contributors to math achievement, even into adulthood, is a strong grasp of the number line. While we might be tempted to think the number line is just about counting, it’s also about sequence and spatial relationship. Students who have a firm mental number line are far more able to manipulate numbers and have a better sense of when they’re moving in the right direction in solving math problems.

Strengthening number line language: Using Tuesday, the teacher can ask questions that emphasize sequence. For example:

• What do you think happened before the frogs took flight?
• What do you think happened after the old woman woke up?
• What funny thing happened when the frogs moved forward through the clothesline? Why do you think they didn’t go backward at that point instead?

Strengthening spatial relationship sense: Story train sequencing necessarily creates spatial relationships that allow children to literally see how far the events of a story or poem are from each other. The children can also be asked to count up the events once the train is complete, pointing to each card as they count.

Using stories to promote recognition of conservation of number or fractions: To an adult, it’s obvious that three apples on a table that are moved to a couch are still three apples. Not so to a child, who needs to learn conservation of number. (If the child has to re-count the apples to be sure, we know she doesn’t yet display this math understanding.)

For children who already recognize at a glance that there are still three apples, you can turn this into a fraction conversation. “Oh, look, one-third of the apples are on the left side. Where are the other two-thirds hiding?” Such a conversation won’t necessarily be simple—fractions are famously difficult even for adults—but this is a chance to speak the language and do the math together.

Using make-your-own books to solidify counting skills: It’s hard to believe that counting is a skill so predictive of math achievement even into adulthood, but it’s true: Those who count strong early on often have a lifelong math advantage. 

Such books—which children can color, write in, and eventually read aloud to friends and family—can also include important counting terms such as whole and altogether that relate naturally to the skill of addition.

Early Counting: Learning to count is a more difficult task than many people realise. Tamariki encounter a range of problems, many of which are related to the English language.

Alison’s note – OMG yes, trying to learn to count in either French or Māori is diabolical. I still can’t remember which word belongs to which number, let alone do any form of basic math in either language. It has given me a fuller appreciation for ākonga learning to do early counting.

Developing Counting: a focus on key number knowledge and the process of coming to know numbers.
– includes number identification, number sequence and order, grouping/place value, and basic facts. The emphasis with all our work on number is about developing number sense.

Recognising Groups: Prior to actually counting, most tamariki are aware of small numbers of things.  Many tamariki entering school can identify quantities of three things or less by inspection alone, without actually counting. Group recognition is important in that recognition of the number of objects in a small group is faster than counting each individual member and helps develop more sophisticated counting skills.

Communication to engage diverse learners: Planning for Quick Images: All students

When you read this section of the mathematics BES, consider what research says about the importance of ākonga articulating their mathematical thinking. When ākonga make their thinking explicit, teachers have access to information about what ākonga know and what they need to learn. Ākonga need to learn how to explain their mathematical thinking, and kaiako have a central role to play in this learning.

Teachers don’t need to have all the answers, but when we understand the underlying principales we are able to encourage ākonga to find the answers with us.

Kaiako promote mathematically productive talk through structuring kaiako-to-ākonga interactions and ākonga-to-ākonga interactions and the use of specific talk moves. Talk moves are defined by Chapin and O’Connor (2007) as “simple conversational actions that have the potential to make discussion productive” (p. 119).

• Revoicing – by kaiako and/or other ākonga.
• Asking ākonga to repeat what another ākonga has said
• Eliciting reasoning – do you agree? Why/why not?
• Asking ākonga to add on
• Kaiako wait time
• Turn and talk

Quick Images

Quick image tasks involve an image (array of dots in this case) flashed for 3 seconds that encourage ākonga to visualize a set of objects and count them quickly by decomposing the image and subitizing. For example the card might look like

How many dots did you see and how did you work it out?

this task can support the sharing of ideas, ways of listening to other children’s thinking, and exemplify how we can support one another within a community of mathematics learners.

To encourage ākonga to actively listen to one another, to participate in the discussion, and to be flexible with responses, the kaiako might ask “Can someone explain what Amanda saw? Show us on the dot card.” After someone restates her thinking, the teacher may then ask Amanda, “Is that how you saw the 4 and 4?”

“Look at all those different ways we made 8. Your brains think differently and we saw the amount in so many ways. How cool is that?!”

Think about how you as the kaiako can probe responses and help supply the words. Quick Images are a useful routine for setting up classroom norms and building a strong community of learners while doing important mathematics at the same time. Think about three reasons why quick images may be a good task for diverse learners.

Providing multiple entrance points, from ākonga who have strong subitizing ability and can recognize the pattern, to ākonga who counted the top line only, being able to work together to not only come up with strategies, but in order being able to understand their own thinking. “I just know”, is replaced with “I have learnt to recognise that when I see a pattern like this it means there are so many symbols”.

Think about how the kaiako is able to use ākonga responses to help her to formatively assess ākonga understanding.

Are they using the right language? Does their working towards a conclusion make sense? Are they able to self-correct when a conclusion doesn’t make sense? Does their working fit other scenarios, showing that they understand the underlying principle?

Think also about how the kaiako reacts to ākonga suggestions—instead of confirming the ākonga solutions you may allow them to prove their answers and asks questions to help them clarify their thinking.

I was taught one way, I have learnt other ways, and yet there are still multiple ways to get to the same answer. In high school maths it is so important to show your working, being able to take this into primary schools rather than just working on rote learning builds a better understanding of the mathematical concepts – and builds confidence. Anyone can do maths, being unable to memorize your times tables doesn’t make you bad at maths, it makes you unable to memorise your times tables!

The “three phase lesson format” is one approach to lesson planning in mathematics :

1. what happens to set up that inquiry (before phase)
2. what happens as they explore (during phase)
3. what happens after the task is solved (after phase)

In mathematics we are interested in the key elements of a lesson plan – the quality of the learning experiences and questions posed – rather than adhering to a particular template. As you become more experienced, lesson plans become more concise. For now, it is important to record detail, especially the key questions.

Learning languages

Learning a new language provides a means of communicating with people from another culture and exploring one’s own personal world.

Languages are inseparably linked to the social and cultural contexts in which they are used. Languages and cultures play a key role in developing our personal, group, national, and human identities. Every language has its own ways of expressing meanings; each has intrinsic value and special significance for its users.

This learning area provides the framework for the teaching and learning of languages that are additional to the language of instruction. Level 1 of the curriculum is the entry level for students with no prior knowledge of the language being learned, regardless of their school year.

Health and physical education

In health and physical education, the focus is on the well-being of the students themselves, of other people, and of society through learning in health-related and movement contexts.

Four underlying and interdependent concepts are at the heart of this learning area:

• Hauora¹ – a Māori philosophy of well-being that includes the dimensions taha wairua, taha hinengaro, taha tinana, and taha whānau, each one influencing and supporting the others.
• Attitudes and values – a positive, responsible attitude on the part of students to their own well-being; respect, care, and concern for other people and the environment; and a sense of social justice.
• The socio-ecological perspective – a way of viewing and understanding the interrelationships that exist between the individual, others, and society.
• Health promotion – a process that helps to develop and maintain supportive physical and emotional environments and that involves students in personal and collective action.

The four strands of the ‘Health and PE’ curriculum are:

• Personal health and physical development, in which students develop the knowledge, understandings, skills, and attitudes that they need in order to maintain and enhance their personal well-being and physical development
• Movement concepts and motor skills, in which students develop motor skills, knowledge and understandings about movement, and positive attitudes towards physical activity
• Relationships with other people, in which students develop understandings, skills, and attitudes that enhance their interactions and relationships with others
• Healthy communities and environments, in which students contribute to healthy communities and environments by taking responsible and critical action.

The seven key areas of learning in the ‘Health and PE’ curriculum are:

• mental health
• sexuality education
• food and nutrition
• body care and physical safety
• physical activity
• sport studies
• outdoor education.