## NRICH - Mathematics Resources for Teachers, Parents and Students to Enrich Learning

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## Primary and EY Teachers

Find more rich tasks, with teacher support, at the Primary and EY teacher homepages

## Secondary Teachers

You can find more rich tasks, with accompanying teacher support, at the Secondary Teacher Homepage

## Your Solutions

## Exploring Problem-Solving in Early Years Mathematics | EYFS/KS1

Webinar Duration: 46 minutes (approx.)

- Understanding how to introduce learning in mathematics which supports children’s ability to problem solve and improve critical thinking skills.
- Recognising successful techniques that can be used in the classroom which improve reasoning in mathematics.
- Appreciating the importance of making problem-solving learning tailored towards the needs of children and ensuring continuous sharing and evaluation of different methods used.
- Understanding what is meant by ‘problem-solving skills’ and how to nurture an environment which encourages curiosity and positive attitudes.
- Building a culture which supports teaching and learning through playing and exploring, active learning and creative and critical thinking.

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## Maths problem-solving activities for Early Years settings

● finding ways to solve problems;

● finding new ways to do things;

● making links and noticing patterns in their experience;

● developing ideas of grouping, sequences, cause and effect;

● planning, making decisions about how to approach a task, solve a problem and reach a goal;

● checking how well their activities are going;

● changing strategy as needed;

● reviewing how well the approach worked.

## Role of the adult

You can effectively support children’s developing problem-solving strategies through:

## Problem solving possibilities

## Going, going, gone

## Camping out

● Materials to construct a tent or den such as sheets, curtains, poles, clips, string.

● Rucksacks, water bottles, compass and maps.

● Oven shelf and bricks to build a campfire or barbecue.

● Buckets and bowls and water for washing up.

● Some distance away, builders’ buckets filled with damp sand and large gravel.

● Bucket balances and bathroom scales.

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## Reception maths

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## Early Years Guide

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## Introduction

- What do we mean by Early Years?
- What does learning look like in the Early Years
- Why is Cognitive Load Theory so important?
- What mastery strategies are available for Early Years?

## What do we mean when we talk about Early Years?

## Areas of learning

The EYFS framework outlines seven areas of learning :

- Communication and language
- Physical development
- Personal, social and emotional development
- Mathematics
- Understanding the world
- Expressive art and design

## Mathematics in EYFS

- Understanding and using numbers
- Calculating simple addition and subtraction problems
- Describing shapes, spaces, and measure

## Revised guidance

The DfE published revised guidance in March 2021 to take effect in September 2021.

The mathematics component now incorporates many elements of the mastery approach.

Specifically, the revised framework says:

## Early Learning Goals

The latest framework has the following early learning goals for mathematics:

Children at the expected level of development will:

- Have a deep understanding of number to 10, including the composition of each number
- Subitise (recognise quantities without counting) up to five
- Automatically recall (without reference to rhymes, counting or other aids) number bonds up to five (including subtraction facts) and some number bonds to 10, including double facts

## Numerical patterns

- Verbally count beyond 20, recognising the pattern of the counting system
- Compare quantities up to 10 in different contexts, recognising when one quantity is greater than, less than or the same as the other quantity
- Explore and represent patterns within numbers up to 10, including evens and odds, double facts and how quantities can be distributed equally

## Learning in the early years

According to the NCETM, there are:

## Six key areas of mathematical learning

Cardinality and counting, composition.

Looking briefly at each in turn:

Comparing numbers involves knowing which numbers are worth more or less than each other.

## Shape and space

- The one-to-one principle: children must name each object they count and understand there are two groups: the one that has been counted and the one that hasn’t yet been counted
- The stable order principle: children must know how to count in the right order
- The cardinal principle: children need to understand the last number in the set is the total amount
- Counting anything: children need to realise that anything can be counted, not just objects that can be touched, but also things like claps and jumps
- Order of counting doesn’t matter: children need to understand that the order of counting in the set is irrelevant and will still lead to the same amount

## How do children develop counting skills?

## Activities to boost number sense in Reception Year

## Crowd control

## Grouping straws

## Fastest 10 frames

## Everyday questions to develop number sense

Practice using the terms more than, fewer than and as many as by asking:

- Are there more grapes than tomatoes?
- Are there fewer tomatoes than grapes?
- Are there as many plates as people eating?

Remember to practice each sentence:

- There are more grapes than tomatoes
- There are fewer tomatoes than grapes
- There are as many plates as family members eating

## Number Rhymes

- Counting back and counting forward
- “No” or “none” (Five little ducks went swimming one day)
- Counting in pairs (two, four, six, eight, Mary at the cottage gate)
- Counting to five, 10 and beyond

## Problem solving, reasoning and numeracy

## Foundations

## Mark making

## Developing understanding with careful questioning

- I have made a pattern. What’s your pattern?
- How many blocks taller is my model compared to yours?
- How do we know this area is full?
- I have three cars, how many do you have?
- Do you have more?
- How do you know?

## Adding maths talk activities to your daily routine

The following activities can get you started:

## How many children are at school?

- How do we know this 10 frame is full?
- How many children are absent?
- What can you tell me about number seven?

## Sorting and grouping objects as a class

## Vote for a story

## Pattern Awareness

## What is mathematical pattern awareness?

- Shapes with regular features, such as a square or triangles with equal sides and angles, and shapes made with some equally spaced dots
- A repeated sequence: the most common examples are AB sequences, like a red, blue, red blue pattern with cubes. More challenging are ABC or ABB patterns with repeating units like red, green, blue or red, blue, blue
- a growing pattern, such as a staircase with equal steps

## Why is pattern awareness important?

Pattern awareness has been described as early algebraic thinking, which involves:

## Repeating Patterns

## Foundations — Your Reception Solution

## Cognitive Load Theory

## What is Cognitive Load Theory and why is it important?

The answer is simple — new skills demand more attention.

## Working memory

## Intrinsic versus extraneous load

## Supporting the transition to long-term memory

## Focused learning objective

## Activate prior learning

## Present information clearly

## Avoid cognitive overload

## Maths mastery for Early Years

## Early Years and CPA

## C is for concrete

## Spending time with real-life objects

## Early years and number bonds

## How to teach number bonds

## Concrete step

## Pictorial step

## Abstract step

## Early Years and place value

## Progress through concepts systematically

## Use the CPA approach to establish meaning

## Teach the ‘10-ness of 10’

## Progress to 20, then to 40

## Use base 10 blocks for 100 and 1000

## Approach larger numbers the same way

For example, you can identify and complete number patterns or find missing digits on a number line.

And a confident problem solver in maths is a confident problem solver in life.

Well done on making it to the end of our Ultimate Guide to Early Years.

If you’d like to learn more about Early Years, we recommend checking out the following links:

- NCETM: How Early Years children develop mathematical thinking (Podcast)
- NRICH: Early Years Foundation Stage Homepage
- The School of School: Episode 17 Play and early years (Podcast)
- Maths — No Problem! CPA approach

Also, don’t miss our other Ultimate Guides:

- The Maths — No Problem! Ultimate Guide to Maths Mastery
- The Maths — No Problem! Ultimate Guide to Assessment

## School of School Podcast

## Maths — No Problem!

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## Paired problem solving in maths

## Benefits and dangers of group work:

As you watch this video of classroom practice, consider how the teacher:

- Gives clear instructions to the whole class before starting paired work
- Monitors pairs as they attempt tasks
- Provides scaffolds and individual support to pairs

## You need to be logged in to view this video

- Campbell R and Bokhove C (2019) Building Learning Culture through Effective Uses of Group Work. Impact. Available at: https://impact.chartered.college/article/building-learning-culture-through-effective-group-work/ (accessed February 2020)
- Wiliam D (2018) Collaborative Learning. Available at: https://education.gov.scot/improvement/learning-resources/dylan-wiliam-collaborative-learning (accessed February 2020)

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## JSmol Viewer

## 1. Introduction

Upon coming to this class, I began to see math differently, as something creative, something without a right or wrong answer, but rather a means of positive struggle, where I embraced all my missteps as part of a growing experience. I took the growth mindset to heart--not only did I apply it academically, I began going to the gym regularly, taking on a vegan diet, and doing even the little things that used to scare me, such as karaoke night (which, might I add, was extremely fun.) (Michelle, Final reflection)

My relationship with math going in was awful, trash, garbage. I hated it and, to be frank, it didn’t make much sense. The way it had been taught to me hadn’t clicked and it didn’t look like it was going to click anytime soon. I was scared for math in college, and honestly considering going from Chemistry to Linguistics to avoid having to take calculus and physics. I am no longer considering switching. (Ricardo, Final Reflection)

## 3.2. A Shift in Students’ Problem Solving and Collaborative Skills

I was made sure of this today when we approached a problem nearly identical to the one we attempted to solve on the first day. Instead of jumping straight into the concepts we learned in statistics and calculus, my partner and I made visual representations of our thoughts and identified the patterns within the problem. Even as we were doing it, my partner and I realized the differences in our thought processes and how that led to us finding an equation that could represent what we were trying to solve. (Kim, Final Reflection)

This class taught me how to think. It taught me how to make connections within the realm of calculus and with the people around me. Because of this class, I am looking forward to working collaboratively on work, especially math, because I have found that some of the best learning comes from learning with others. (Tasha, Final Reflections)

## 3.3. Centering Mindset through Mathematics Problems: An Example

When we began to engage in more of the hands-on activities, I started to shift my mindset and continue to try things out. The moment that I believe changed me the most was the cube task. In that task, we worked so well together, and the work was distributed pretty evenly. I felt accomplished, as well as did my group surrounding me. (Chantelle, Final Reflection)

The first problem that really helped open my eyes was the lemon problem. My group thought really creatively about the three methods that we tried, and actually physically manipulating the lemon helped me see why the different methods worked well. But it was at the end of it, when we discussed the problem as a class, that I saw all of my groups’ solutions were basically just different ways to perform summation/integration. It was the first time that I saw the integration formula/graph, and it actually made sense to me. Since that problem I have been riding a kind of high in the class. I now feel like if I try hard enough, and if I think creatively enough, then I can genuinely figure anything out. (Esther, Final Reflection)

## 3.4. Students Who Resisted the Messages of the Course

Being forced to learn math at a fundamental level was very frustrating at first because beneath the memorization of formulas and functions, it made me feel like I didn’t actually understand it at all. (Marina, Final Reflection)

## 4. Discussion and Conclusions

Taking this class has been my best decision at college so far. I feel like I will go into my first-year maths courses knowing a secret that no one else knows: Maths does not have to be intimidating. It is not maths’ fault that it has been portrayed to be an evil subject only conquered by "geniuses" and/or white males. With a little love and understanding, maths can be kind, compassionate, and even fun to be around. (Briaunna, Final Reflection)

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to solve problems. Many students currently at U.K. universities undertaking mathematics degree courses have been very successful at school, as measured by

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