Mathematics CPD
2019 - 2020
JCT Mathematics Team
ronan.heavey@jct.ie
aedamar.frawley@jct.ie
emer.brady@jct.ie
barry.tiernan@jct.ie
brenda.murtagh@jct.ie
caitriona.cronin@jct.ie
shane.flanagan@jct.ie
Timeline
Developed based upon teachers’ Feedback
2021
-22
CBA 2 / SLAR
& AT 2020
2020
-21
Developed based upon teachers’ Feedback
CBA 1 & SLAR
2020
2019
-20
Planning for Teaching, Learning & Assessment
Professional Learning & Discussion
Webinar
x2
2018
-19
Teaching, Learning & Assessment in Junior Cycle
Mathematics
Classroom rollout
09/2018
Webinar
Teaching, Learning & Assessment in Junior Cycle
Mathematics
2017
-18
SEC
Exam 2021
Webinars
Learning Intentions
Explore the role of collaborative planning and formative assessment on students’ experience and learning of Mathematics
Examine the use of authentic data and the Statistical Enquiry Cycle to motivate students’ learning in statistics
Explore the role of professional discussions and departmental collaboration in developing a shared understanding of the quality of students’ work
Morning Session
Explore the role of collaborative planning and formative assessment on students’ experience and learning of Mathematics
Planning for Teaching, Learning & Assessment
Teaching, Learning and Assessment
Concept
Key Learning
Ongoing Assessment
Key Learning
Student Context
Ongoing Assessment
Learning Intentions
Success Criteria
Ongoing Assessment
Learning Intentions
Success Criteria
Formative Feedback
Student Experience
Planning for Learning
Collaborative Planning
Collaborative Departmental Planning
‘The specification is underpinned by the conception of mathematics as an interconnected body of ideas and reasoning processes that students negotiate collaboratively with teachers and their peers and as independent learners.’
Mathematics Specification page 4
Sample Unit of Learning
Learning Log
Page 3
Notes / Reflection
Essential components
Formative Feedback given may inform these
Learning Experiences
Designed or sourced and adapted to Student Context
Ongoing Assessment
Ongoing Assessment is directly linked to the
Key Learning
The focus is on what is to be assessed rather than how the students will be assessed
Key Learning
The focus is on what it is the student should understand
This does not mean that content is unimportant
Key Learning and Student Experience
Key Learning
UNDERSTANDING
Students should understand that there are a variety of mathematical representations that can be useful when solving problems, including:
Excerpt from sample unit of learning
Key Learning Impacts Students’ Learning Experience
Concept then Content
Supporting Student Learning using Formative Assessment
Task - Fencing an Enclosure
Learning Log
Page 4
Emily has 20 metres of fencing. She needs to form an enclosure in the garden for her dog. What is the maximum area she can enclose if all the fencing must be used?
Justify your answer.
Sample Solutions to Enclosure Task
Making the Learning Clear
A Learning Intention is a statement that describes what pupils should know, understand and be able to do by the end of the lesson or series of lessons.
Success criteria are linked to learning intentions. They are developed by the teacher and/or the student and describe what success looks like. They help the teacher and student to make judgements about the quality of student learning.
Adapted from NCCA Focus on Learning Series: Learning Intentions & Success Criteria
Enclosure Task with Learning Intentions and Success Criteria
Learning Intention:
We are investigating maximising the
area of 2D shapes
Success Criteria:
I can explain my reasoning mathematically
I can compare a variety of shapes in the context of the problem
I can use the most appropriate mathematical representation in my answer
Emily has 20 metres of fencing. She needs to form an enclosure in the garden for her dog. What is the maximum area she can enclose if all the fencing must be used?
Justify your answer.
Sample Solutions to Enclosure Task
Why are Learning Intentions �and Success Criteria Important?�
Learning Intentions:
WHAT and WHY
Formative Feedback:
HOW to progress students’ learning
Success Criteria:
HOW to recognise successful learning
If students are to take on more responsibility for their own learning, then they need to know what they are going to learn, how they will recognise when they have succeeded and why they should learn it
NCCA, Focus On Learning Series (2015)
Benefits of Learning Intentions and Success Criteria�
Benefits for the student:
Benefits for the teacher:
If students are to take on more responsibility for their own learning, then they need to know what they are going to learn, how they will recognise when they have succeeded and why they should learn it
NCCA, Focus On Learning Series (2015)
What Makes Feedback Effective?
Effective Formative Feedback… |
|
Providing Formative Feedback on Examples of Student Work
What feedback would you give the student to move their learning forward?
Take some time to examine the student's work you have been given
Share your considerations with your group
Learning Log
Page 5
Looking at Our Schools (2016)
Statements of Practice - Teaching and Learning
Domain 3: Teachers’ Individual Practice
Looking At Our Schools (2016)
Teachers share and co-create success criteria with students so that they can assess their own learning through self-assessment and peer assessment, and identify areas for improvement and strategies to achieve improvement.
Teachers’ plans identify clear, relevant learning intentions that are contextualised to students’ learning needs. Learning intentions reflect a developmental and incremental approach to progressing students’ learning.
Creating Success Criteria
Learning Log
Page 6
Examine the task in your learning log
Co-create Success Criteria for the task
Consider Success Criteria for this task individually
Why are learning intentions �and success criteria important?�
Formative Feedback:
HOW to progress students’ learning
Success Criteria:
HOW to recognise successful learning
Learning Intentions:
WHAT and WHY
If students are to take on more responsibility for their own learning, then they need to know what they are going to learn, how they will recognise when they have succeeded and why they should learn it
NCCA, Focus On Learning Series (2015)
Feedback
Providing effective feedback is a crucial step in using the Mathematical Investigation to support learning in mathematics….Feedback on the strengths of the student’s work, and on areas for improvement can be used to support their future learning.
(Assessment Guidelines page 23)
Morning Session �
Explore the role of collaborative planning and formative assessment on students’ experience and learning of Mathematics
Document Your Learning
Learning Log
Page 7
Take some time to document key learning in the morning section of your learning log
Coffee Break
Using the Features of Quality to Promote Professional Discussions
Learning Intentions
Explore the role of collaborative planning and formative assessment practices on students’ experience and learning of Mathematics
Examine the use of authentic data and the Statistical Enquiry Cycle to motivate students’ learning in statistics
Explore the role of professional discussions and departmental collaboration in developing a shared understanding of the quality of students’ work
Mid-morning Session
Explore the role of professional discussions and departmental collaboration in developing a shared understanding of the quality of students’ work
Student Learning Journey�
The Mathematical Investigation (MI) gives students an opportunity to research a question they have about some phenomena of interest from the world around them or that they have come across in the course of their mathematical studies or their studies in other subjects
Assessment Guidelines page 12
Second Year – September 2019 onwards
Engage with learning outcomes in the Unifying Strand and the Contextual Strands
Learning is supported by formative assessment
CBA 1: Mathematical Investigation
SLAR Meeting
Results of CBA 1 reported using Descriptors
�
Third Year – September 2020 onwards
Engage with learning outcomes in the Unifying Strand and the Contextual Strands
Learning is supported by formative assessment
CBA 2: Statistical Investigation
SLAR Meeting
Results of CBA 2 reported using Descriptors
Assessment Task
(10% of Final Examination mark)
Final Examination
The Mathematical Investigation comprises of four areas of activity: defining the problem, translating it to mathematics (if necessary), engaging with the problem and solving it if possible, and interpreting the solution in the context of the original problem
Assessment Guidelines page 12
First Year – September 2018 onwards
Engage with learning outcomes in the Unifying Strand and the Contextual Strands
Learning is supported by formative assessment
Subject Department Timeline for CBA 1
Classroom-Based Assessment Window
January 2020
May
2020
Before the CBA
Agree the three-week window
Agree the date of the SLAR meeting
Agree the SLAR Facilitator
During the CBA
Collegial Support
Discussion and Advice
After the CBA
SLAR meeting must take place within one month of the CBA
Reflect on Subject Learning
Three-week CBA
Teacher Timeline for CBA 1
Classroom-Based Assessment Window
January 2020
May
2020
Three-week CBA
Before the CBA
Learning Outcomes
Formative Assessment
Rich Tasks
During the CBA
Problem-solving cycle
Ongoing formative feedback to the student
Identify possible samples for the SLAR meeting
After the CBA
Assign provisional Descriptors
SLAR meeting
Reconsider judgement
Report the final Descriptor
�Professional Discussions�
‘Good discussions and rich learning in groups seldom happen by chance. Groups rely on structures, protocols, and routines to guide and focus their learning. Such structures ensure that everyone in the group has a voice, the precious time of the group is well spent, sensitive discussions unfold in a safe manner, and attention is directed where it needs to be for learning to move forward.’
(Ritchhart, 2015)
‘Good discussions and rich learning in groups seldom happen by chance. Groups rely on structures, protocols, and routines to guide and focus their learning. Such structures ensure that everyone in the group has a voice, the precious time of the group is well spent, sensitive discussions unfold in a safe manner, and attention is directed where it needs to be for learning to move forward.’
(Ritchhart, 2015)
Mathematical Investigation – �Features of Quality�
Mathematical Investigation – �Features of Quality
Using The Features of Quality
YES
Award the Descriptor
NO
Award the previous Descriptor
YES
Check for evidence in the next Descriptor
Is there evidence “on balance” to support the awarding of this Descriptor?
Begin with Yet to Meet Expectations
Review the work from start to finish
Descriptor Definitions
Learning Log
Page 9
‘Where it is not clearly evident which quality descriptor should apply, teachers must come to a judgment based on the evidence from the student’s work, to select the descriptor that best matches the student’s work overall. This ‘best fit’ approach allows teachers to select the descriptor that ‘on balance’ describes the work being assessed.’
(Assessment Guidelines page 7)
Working with Features of Quality�Student Example One
Learning Log
Page 13
What are the strengths of this piece of work?
What are the areas for development/improvement in the work?
What feedback would you give to this student?
Individually consider the student’s work through the lens of the Features of Quality
Professional Discussions�
Learning Log
Page 13
4. Continue this process until you arrive at a consensus of where the student needs feedback to move their learning forward
3. If there is sufficient evidence, move to In Line with Expectations and discuss evidence in each of the four areas of activity
2. Starting with Yet to Meet Expectations, discuss the evidence the group identified in each of the four areas of activity
1. Assign a facilitator at your table
Professional Discussions�
‘..we need to bring evidence of student thinking and learning physically to the communal table around which we gather for our learning. This evidence might be a work sample, a video, or notes from an observation. Such evidence helps us de-privatize teaching and grounds our discussions, keeping us focused on student learning. Furthermore, sharing the responsibility for putting something on the table across a group fosters community and commitment.’
(Ritchhart, 2015)
Working with Features of Quality�Student Example Two
Learning Log
Page 14
What are the strengths of this piece of work?
What are the areas for development/improvement in the work?
What feedback would you give to this student?
Individually consider the student’s work through the lens of the Features of Quality
Professional Discussions�
Learning Log
Page 14
4. Continue this process until you arrive at a consensus of where the student needs feedback to move their learning forward
3. If there is sufficient evidence, move to In Line with Expectations and discuss evidence in each of the four areas of activity
2. Starting with Yet to Meet Expectations, discuss the evidence the group identified in each of the four areas of activity
1. Assign a new facilitator at your table
What is a SLAR meeting?
‘Shared understanding of standards within junior cycle will arise through professional discussion in Subject Learning and Assessment Review meetings where staff bring their own examples of student work and compare their judgements with other colleagues, with annotated examples of student work and with specifications provided by the NCCA. Over time, this process will help develop a greater understanding of standards and ensure consistency of judgement about student performance.’
(Assessment Guidelines page 22)
The purpose of a SLAR meeting�
‘Engagement in Subject Learning and Assessment Review meetings will help teachers to develop their own knowledge and skills by developing a shared understanding of national standards and expectations. The meetings will also enable teachers to reflect on the assessment process within their subject overall and support teachers in providing useful feedback to their students to improve their learning.’
(Framework for Junior Cycle page 40)
Teacher preparation for a SLAR
‘In preparation for the Subject Learning and Assessment Review meeting, each teacher will identify one example of students’ work for each descriptor, where feasible, and will have these available for discussion at the meeting.’
(Assessment Guidelines page 22)
What happens after a SLAR Meeting?
‘Following the Subject Learning and Assessment Review each individual teacher re-considers the judgement they made of their student’s work based on the outcomes of the meeting and where necessary makes the appropriate adjustments to the level of achievement awarded to the work.’
(Assessment Guidelines page 22)
‘Students will be informed of the Descriptor they have been awarded once the SLAR meeting has taken place and its outcomes have been processed.’
(Assessment Guidelines page 23)
Mid-morning Session �
Explore the role of professional discussions and departmental collaboration in developing a shared understanding of the quality of students’ work
Document Your Learning
Learning Log
Page 14
Take some time to document key learning in the mid-morning section of your learning log
Lunch
Motivating Students’ Learning in Statistics
Learning Intentions
Explore the role of collaborative planning and formative assessment on students’ experience and learning of Mathematics
Examine the use of authentic data and the Statistical Enquiry Cycle to motivate students’ learning in statistics
Explore the role of professional discussions and departmental collaboration in developing a shared understanding of the quality of students’ work
Afternoon Session
Examine the use of authentic data and the Statistical Enquiry Cycle to motivate students’ learning in statistics
Junior Cycle Statistics�
“…the learning outcomes represent outcomes for students at the end of their three years of study. The specification stresses that the learning outcomes are for three years and therefore the learning outcomes focused on at a point in time will not have been ‘completed’, but will continue to support students’ learning of mathematics up to the end of junior cycle.”
Junior Cycle Mathematics Specification page 13
Group Discussion
…the way that statistics, or data handling, is currently taught in many jurisdictions largely misses the point of studying the subject. Data is not just about numbers – it’s about numbers in context.
Each part of the data handling cycle is influenced by, and contributes to, the understanding of that context ... being asked to represent a set of non-contextualised data in several different ways, without having the information to decide on which kind of diagram would best illustrate it, makes a nonsense of the activity.
McClure (2018)
What opportunities do students have to engage with authentic data in their learning of statistics?
…the way that statistics, or data handling, is currently taught in many jurisdictions largely misses the point of studying the subject. Data is not just about numbers – it’s about numbers in context.
Each part of the data handling cycle is influenced by, and contributes to, the understanding of that context ... being asked to represent a set of non-contextualised data in several different ways, without having the information to decide on which kind of diagram would best illustrate it, makes a nonsense of the activity.
McClure (2018)
Statistical Enquiry – Data in Context
CSO website
www.cso.ie
Learning Log
Pages 15 & 16
You have 10 minutes
www.cso.ie
Statistical Enquiry – Data in Context
The Statistical Enquiry Cycle�
Statistical question
Informal inference
Sampling
Improvements to the investigation
Analyse and interpret data
Displaying the data
Summarising the data
Organise and manage data
Variables
Gathering of data
Reliability
Sample
Identify variables and select reliable methods for gathering data
Formulation of the question
Data collection
Designing the investigation
Possible Considerations
Stage
Semi-Structured Statistical Enquiry
Initial Context is Given
Data Generation
Formulation of Statistical Question
Semi-Structured Enquiry – Hand Eye Reaction
Learning Log
Page 17
Please record your perception of your hand-eye coordination in your learning log
Reaction Timer Experiment
Instructions for the Semi-structured statistical enquiry
www.jct.ie/maths
Instructions for the Semi-structured statistical enquiry
All data collected is anonymous.
1
2
3
www.jct.ie/maths/cpd_workshops_2019_2020
Instructions for the online reaction timer
1
Record your reaction times in your booklet
Learning Log
Page 17
NRICH Reaction Timer
Instructions for the online form
2
Please input your five reaction times along with some other information in the form.
Online Form
Instructions for the spreadsheet
Analyse and
interpret the data
3
Google Sheets
Posing a Statistical Question�
Learning Log
Page 17
With the data available, pose a question that allows you to engage with the statistical enquiry cycle
Designing the Investigation
| Yet to Meet Expectations | In Line with Expectations | Above Expectations | Exceptional |
Designing the Investigation | | | | |
Identifying the Variables of Interest | | | | |
Organising and Managing the Data | | | | |
Analysing and Interpreting Data Summaries | | | | |
Statistical Investigation CBA 2 Features of Quality
Considerations:
Population
Sample
Sample selection
Question reformulation
Bias control
Limitations
Considerations:
Formulation of the question
Data collection
Identifying Variables of Interest
| Yet to Meet Expectations | In Line with Expectations | Above Expectations | Exceptional |
Designing the Investigation | | | | |
Identifying the Variables of Interest | | | | |
Organising and Managing the Data | | | | |
Analysing and Interpreting Data Summaries | | | | |
Statistical Investigation CBA 2 Features of Quality
Considerations:
Variables
Gathering of data
Reliability
Sample
Organising and Managing Data
| Yet to Meet Expectations | In Line with Expectations | Above Expectations | Exceptional |
Designing the Investigation | | | | |
Identifying the Variables of Interest | | | | |
Organising and Managing the Data | | | | |
Analysing and Interpreting Data Summaries | | | | |
Statistical Investigation CBA 2 Features of Quality
Considerations:
Displaying the data
Summarising the data
Analysing and Interpreting Data Summaries
| Yet to Meet Expectations | In Line with Expectations | Above Expectations | Exceptional |
Designing the Investigation | | | | |
Identifying the Variables of Interest | | | | |
Organising and Managing the Data | | | | |
Analysing and Interpreting Data Summaries | | | | |
Statistical Investigation CBA 2 Features of Quality
Considerations:
Statistical question
Informal inference
Sampling
Improvements to the investigation
Statistical Enquiry Cycle Infographic
Considerations:
Population
Sample
Sample selection
Question reformulation
Bias control
Limitations
IDENTIFY VARIABLES AND SELECT RELIABLE METHODS FOR GATHERING DATA
ANALYSE AND INTERPRET DATA
ORGANISE AND MANAGE DATA
INVESTIGATION DESIGN
Statistical Enquiry Cycle
Statistical Enquiry – Data in Context
Data in Context
What evidence can you identify of students engaging with the statistical enquiry cycle?
Design
Identify
Gather
Analyse
St Munchin’s College, Limerick
Click on the image to view a video of a class engaging with the statistical enquiry cycle on YouTube
Data in Context �
What evidence can you identify of students engaging with the statistical enquiry cycle?
Group Discussion
…the way that statistics, or data handling, is currently taught in many jurisdictions largely misses the point of studying the subject. Data is not just about numbers – it’s about numbers in context.
Each part of the data handling cycle is influenced by, and contributes to, the understanding of that context ... being asked to represent a set of non-contextualised data in several different ways, without having the information to decide on which kind of diagram would best illustrate it, makes a nonsense of the activity.
McClure (2018)
Assessment to Support Student Learning
(Classroom Based Assessment)
Assessment to Support Student Learning
�
First Year – September 2018 onwards
Engage with learning outcomes in the Unifying Strand and the Contextual Strands
Learning is supported by formative assessment
Second Year – September 2019 onwards
Engage with learning outcomes in the Unifying Strand and the Contextual Strands
Learning is supported by formative assessment
CBA 1: Mathematical Investigation
SLAR Meeting
Results of CBA 1 reported using Descriptors
Third Year – September 2020 onwards
Engage with learning outcomes in the Unifying Strand and the Contextual Strands
Learning is supported by formative assessment
CBA 2: Statistical Investigation
SLAR Meeting
Results of CBA 2 reported using Descriptors
Assessment Task
(10% of Final Examination mark)
Final Examination
The Statistical Investigation (SI) gives students an opportunity to carry out an investigation that involves varying data. This data may be related to work they have encountered in other subjects or to a question they have about some quantitative phenomena of interest from the world around them.
Assessment Guidelines page 24
The SI provides an opportunity to display evidence of the development of skills such as posing questions, working with others, designing studies (experiments, surveys or observational studies), conducting studies, generating and recording primary data, processing and analysing the data, dealing with variability in data, making valid conclusions, interpreting conclusions in context and communicating findings to others.
Assessment Guidelines page 24
Conducting CBAs
From an early stage, students should be familiar with and learn/understand how to conduct statistical investigations. This is best achieved when students use success criteria for ongoing assessments throughout first, second and third year. At an appropriate moment in their learning, students should be familiarised with the Features of Quality which will be used to judge the quality of their Statistical Investigation.
Assessment Guidelines page 26
The Classroom-Based Assessment should be viewed as part of teaching and learning, and not solely for assessment purposes. It is envisaged that teachers will guide, support and supervise throughout the process
Assessment Guidelines page 8
Features of Quality – Placemat Activity
Read through the Features of Quality for In Line with Expectations
on the placemat
Features of Quality – Placemat Activity �
Discuss the cards from the envelope and place each one on the placemat where appropriate
Features of Quality Placemat - Completed
| Yet to Meet Expectations | In Line with Expectations | Above Expectations | Exceptional |
Designing the Investigation | | | | |
Identifying the Variables of Interest | | | | |
Organising and Managing the Data | | | | |
Analysing and Interpreting Data Summaries | | | | |
Poses a question that anticipates variability and plans to collect/source the type of data appropriate for the question posed
Identifies variables and develops a measuring strategy for measuring the dependent and independent variable
Displays data in a way that allows patterns to be identified, identifies patterns and describes the data in terms of those patterns
Makes a concrete connection to the original question of the investigation but does not look beyond the data
Statistical Investigation CBA 2 Features of Quality
Uses given statistics question and collection method
Gathers and displays data
Makes statements about the data displayed
No concrete connection back to the original question
Poses a question that anticipates variability and seeks generalisation; data collection plan shows awareness of how variability affects the validity and reliability of the findings
Chosen measuring strategy will provide valid and reliable data
Uses appropriate data displays and describes the data in terms of measures of centre and spread
Reports the findings and the conclusion refers to the original question and attempts to look beyond the data
Poses a question that anticipates variability and seeks generalisation, study design will produce as far as practical reliable and valid results by taking into account variability and confounding variables
Describes relationship between the variables and describes considerations related to reliability and fairness
Use distributions to analyse the data and justifies measures of centre used to describe the data
Interprets the data in relation to the original question; conclusion displays understanding of the limitations of generalising to the population and considers the need to reformulate the original question in light of the findings
Teachers should not assume that the results of a group of students being assessed will follow any particular distribution pattern, as the students’ work is being judged only against the Features of Quality rather than other students’ performances.
Assessment Guidelines page 7
Conducting CBAs
The Statistical Investigation promotes student engagement through:
Assessment Guidelines page 24
Choice about question:
Choice about formats:
Possibilities of student collaboration:
Document Your Learning
Learning Log
Page 22
Take some time to document key learning in the afternoon section of your learning log
Some of Today’s Learning
Statistical Enquiry Cycle
Generation and Use of Authentic Data
Engaging with Features of Quality
Effective Professional Discussions
Professional and Subject Learning
Using Features of Quality
Planning for Learning and Teaching
Concept Before Content
Learning Intentions and Success Criteria
Reflect and Plan
Action Plan | Goal | Action | Who/When | Evaluation Criteria |
Teacher’s Individual Practice |
|
|
|
|
Departmental Collaborative Practice |
|
|
|
|
Learning Log
Page 23
Reflect and Plan
Statistical enquiry cycle
Rich learning experiences
Planning for learning
Unifying strand
Working collaboratively as a department
Problem-solving cycle
Formative assessment
Learning Intentions
Explore the role of collaborative planning and formative assessment on students’ experience and learning of Mathematics
Examine the use of authentic data and the Statistical Enquiry Cycle to motivate students’ learning in statistics
Explore the role of professional discussions and departmental collaboration in developing a shared understanding of the quality of students’ work
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Mathematics Team
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