Assistive supports – specialised equipment, technologies, medical or physical devices, and other resources that help students
Remediation – strategies that teach students specific, usually prerequisite, skills to help them master broader curricular, scope and sequence, or benchmark objectives
Accommodations – change conditions that support student learning – such as the classroom setting or setup, how and where instruction is presented, the length of instruction, the length or time frame for assignments, or how students are expected to respond to questions or complete assignments.
Modifications – involve changes in curricular content – it’s scope, depth, breadth, or complexity
If target students don’t respond more significant or complex approaches from the next areas may be needed:
Strategic interventions – focus on changing students’ specific academic skills or strategies, their motivation, or their ability to comprehend, apply, analyse, synthesise, or evaluate academic content and material. Strategic interventions typically involve multidisciplinary assessments.
Compensatory Approaches– help students to compensate for disabilities that cannot be changed or overcome
According to The National Council of Teachers of Mathematics (NCTM) publication ‘Principles to Action: Ensuring Mathematical Success for All’ (2014) the 8 high leverage teaching practices that support meaningful learning are:
Similarly the 2012 National Research Council report Education for Life and Work identifies the following essential features of instruction:
Focus on rigor defined as a balance among conceptual understanding, procedural skills and fluency, and application with equal intensity.
Mathematics instruction should be intentionally designed and carefully orchestrated in the classroom, and should always focus on impacting student learning. Start with appropriately challenging learning intentions and success criteria. Teachers need to be clear about where their students are, where they need to go, and what achievement of learning milestones looks like. Good mathematics learning is embedded in discourse and collaboration – both with teachers and among peers – and is orchestrated around appropriately challenging tasks. Students should be doing more of the thinking and talking than the teacher. Must be partners in understanding with metacognition (thinking about their own thinking).
Surface, deep and transfer learning
Surface – initial development of conceptual understanding, procedural skills, and vocabulary of a new topic
Deep – begin to make connections among conceptual ideas, and practice and apply procedural skills with greater fluency. Plan, investigate, elaborate on their conceptual understandings and begin to make generalisations. Can facilitate transfer.
Transfer – ability to more independently apply deeply understood concepts and skills to new and novel situations
These strategies come from an article: Assessment for Understanding by Janelle Wills, published in Assessment into Practice: Understanding assessment practice to improve students’ literacy learning. PETAA edited by Heather Fehring, 2017
Students complete a 3-2-1 exit slip before leaving the room or at the end of the learning episode. For example 3 things I learned, 2 connections I made, 1 question I still have.
The 3-minutes pause provides a chance for students to stop, reflect on the concepts and ideas that have just been introduced, make connections to prior knowledge or experience, and seek clarification:
Each student in the class is assigned a different letter of the alphabet and they must select a word starting with that letter that is related to the topic being studied.
Pose a question to a group or class of students and pause for 30-60 seconds. Ask students to write an answer to the question using note cards, sticky notes or scrap paper. Students share responses with each other using a process such as Give One, Get One (Lipton &Wellman, 2010)
Present students with a analogy prompt: (A certain concept, principle or process) is like _____ because __________.
In response to a cue, all students respond verbally at the same time. The response can be either to answer a question or to repeat something the teacher has said.
At the end of a lesson, students respond to the following questions in a daily journal log:
Compare and Contrast
Identify the theory or idea the author is advancing. Then identify an opposite theory. What are the similarities and differences between these ideas? This process demonstrates the depth of understanding a student has attained.
Compare and Contrast
Create a two-column table. Use the left column to write down 5-8 important quotations/ points. Use the right column to record reactions/ explanations to the quotations/ points.
Create a two-column table. Use the left column to write down 5-8 important points from a learning episode or text. Use the right column to create a non-linguist representation of the key idea or concept.
1. Select a topic students have been studying (ie. democracy)
2. Write the topic on two charts
3. Divide the students into two teams
4. Each team lines up behind a chart
5. On signal, a student from each team goes to the chart and write a phrase associated with the topic. The phrase must start with the 1st letter of the word (ie. ‘d’ for democracy – distribution of political power in the hands of the public. Then, the next letter ‘e’ – eligible citizens participate equally and ‘m’ and so on).
6. After the first student finishes, the next student comes to the chart etc.
7. When both teams are done the charts are compared and shared.
Similiar to an exit card. The ticket out the door is to list at least two important ideas they have learned from the lesson and specific EVIDENCE regarding this learning.
Exit cards are written responses to questions posed at the end of a class or learning activity or at the end of a day.
Find someone who
Students circulate to find others who can contribute to answers on their worksheet. They give answers and receive answers for purposes of review and showing gaps in ethic learning. (Kagan & Kagan, 2009)
Students rotate around the room stopping at posted posed questions, or pieces of learning, quotes, concepts, etc. As they stop at each chart, students have discussions with each other, write responses on poster charts or sticky notes or they pose questions that they have as a result of viewing the gallery walk material. (Lipton and Wellan 2011)
Generic question to guide self-assessment
Students quickly draw pictures to show what they know. They then explain their drawing to a partner.
Get One, Give One
Students respond to a prompt by writing on a sticky note or card. They then take their card/ note and find a partner; share the information or ideas and then exchange cards. After two or three exchanges, hey return to their table group and share information on their last card. Table groups identify themes and patterns to share with full group. ( Lipton and Wellman 2010)
Ask students to display a designated hand signal to indicate their understanding of a specific concept, principle, or process: I understand____ and can explain it (ie., thumbs up). I do not yet understand (ie., thumbs down). I’m not completely sure about _____ (ie., hand wave)
I have, who has?
Reviw questions and responses are handed out to students on cards. The student with number one card begins the review by reading their question (ie. I have what are words that mean exactly what you say.) and then reads the question also contained on their card ( Who has the definition for figurative language?) and the review continues until all cards are used. (Kalgan and Kagan, 2009)
The teacher creates a spinner marked with four quadrants and labelled “Predict, Explain, Summarise and Evaluate.” After new material is presented, the teacher spins the spinner and asks students to answer a question based on the location of the spinner.
Index card summaries and questions
Distribute index cards and ask students to write both sides with these instructions: (Side 1) Based on our study of (unit/topic) list a big idea that you understand and word it as a summary statement. (Side 2) identify something about (unit/ topic) that you do not fully understand and word it as a statement or question.
Students in concentric circles rotate to face partner to answer the teacher’s questions or those of a partner (via cue cards).
Instruct, insight, internalise
Teacher provides instruction to the students for 5-7 minutes, then says: Take a minute to think and record the key ideas or points you’ve heard so far or any questions you have. Teacher then continues instruction to the next stopping point and repeats the previous directions. When instruction is complete, students pair up and share their insights, key ideas, questions and summaries of what they heard.
Students read different passages of the same text or selection. After reading the passage, they take on the role of an expert for their specified piece of text. The “experts” then share the information from their reading with a specific rotating group or the entire class.
Use a K-W-L chart as a preview activity. Prior to instruction, students complete the ‘K’ (know) and W (want to know) columns. When instruction is complete, students complete the L (learned) column. Collect the organisers and check for understanding (Ogle, 1968)
Pr sent student with common or predictable misconceptions about designated concept, principle or process. Ask students whether they agree or disagree and explain why. (Science resource 2016, assessment.aaas.org/topics
Numbered Heads Together
Each student is assigned a number. Members of a group work together to agree on an answer. The teacher randomly selects one number. The student with that number answers for the group.
Reflect on the things you do not like people to say and do when you are working on maths in a group
Reflect on the things you do like people to say and do when you are working on maths in a group
What stuck with you today?
There is more than one way to do the task.
2,3,4 heads are better than just 1
Everyone can learn maths
Low Floor, High Ceiling – entry points and differentiation for all
Maths needs to be hands on – not sheets – to give children the opportunity to experiment
Planning for differentiation is much easier than we sometimes make it (when the task is well-designed)
Youcubed lesson plans and resources, easily accessible and ‘ready to use’
Great ‘Emoji sorting’ lesson – Will definitely try it out!
How many different ways there are to understand a simple concept like ‘what is half?’ Along with encouraging students to take those risks and make mistakes.
Who would have thought that a simple concept like ‘halving’ would result in rich conversations – growing our learning together.
I’m going to look up Jo Boaler’s Youcubed, Daily Inspiration and try some new tasks as feeling a little like the meerkat in Maths at the moment.
Youcubed week of Inspiration site excellent ideas using Emoji’s. So many things you can do with this one activity, also very relevant for kids current fads.
Importance of developing positive attitudes in maths
Open ended, collaborative maths tasks.
Finding ways of exposing misconceptions/ highlighting understandings, and things we do/ say as teachers which might create misunderstandings.
During today’s activities reinforced how everyone sees the same problem differently. Allowing students to explore and work collaboratively is extremely valuable.
The Youcubed Week of Inspiration in Maths – lesson ideas, videos and resources to use
A great Emoji task to do.
Collaborative dialogue is the key to group feeling successful.
Fun working together if group collaborative
Thanks for sharing – inspiring indeed!
Look at and explore Youcubed, Inspirational maths lessons, continue to inspire students in maths.
I have good ideas but my group has great ideas!
Once you convince yourself …convince others.
Low Floor – High Ceiling Tasks:
1. Open up the task so that there are multiple methods, pathways, and representations.
2. Include inquiry opportunities.
3. Ask the problem before teaching the method.
4. Add a visual component and ask students how they see the mathematics.
5. Extend the task to make it lower floor and higher ceiling.
6. Ask students to convince and reason; be skeptical.
Jo Boaler recommends these sites:
NCTM: www.nctm.org (membership required to access some of the resources
NCTM Illuminations: http://illuminations.ntcm.org
Balanced Assessment: http://balancedassessment.concord.org
Math Forum: www.mathforum.org
Shell Centre: http://map.mathshell.org/materials/index.php
Dan Meyer’s resources: http://blog.mrmeyer.com
Video Mosaic project: http://videomosaic.org/
Estimation 180: http://www.estimation180.com
Visual Patterns; grades K-12: http://www.visualpatterns.org
Number Strings: http://numberstrings.com
Mathalicious, grades 6-12; real-world lessons for middle and high school: http://mathalicious.com
This is a great little video to begin a discussion about good and bad teamwork. I would probably stop the video at the polar bears, because of the advertising.