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Reading strategies for math statements

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Michelin Ammar, Vanessa Boily and Giovanna Salvagio, Pedagogical Consultants

PRESENTED BY

The development of cross-disciplinary skills for problem-solving

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By the end of this workshop…

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You should be able

To have a better understanding of reading strategies and how it applies to mathematics;
To be aware of some digital resources/tools to support students reading.

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AGENDA

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Opening remarks
Collaboration
The use of error as a teaching tool
Inclusion and problem-solving

Problem-solving and language barriers
Suggested activities to consolidate reading strategies
Technology in support of reading strategies
Closing remarks

Reading strategies for math statements

BREAK

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Facilitate and support students’ learning

Foreword

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Change requires a great deal of collaboration

We must not give in to the pedagogical obstacles that our learners encounter. Instead, we must help each other transform these pedagogical obstacles into didactic solutions.

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Facilitate and support students’ learning

The educational obstacle by excellence

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I understand the problem, but I don’t know what to do!

« Isn’t that what characterizes a problem? At least at the beginning, before a potentially successful strategy has been identified. Even there, you always allow yourself the right to take a step back. »

France Caron (Associate professor, UdeM)

Translated from French

Solving a real problem is rarely a straightforward process; it should not be perceived as a mere exercise by the individual involved.

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Facilitate and support students’ learning

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Flat tire!

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What does it remind you of ?

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Complex Task

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Characteristics of a Complex task

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Authentic, relevant and engaging
Can be represented in many ways
Connect previous knowledge to new learning
Can be solved in many ways (the use of different strategies)
Finding a solution that makes sense and can be explained or justified by the student

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Plan for complex tasks (CT)

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Establish a behaviour to search for meaning and self-regulation in problem-solving

Identify any educational obstacles

CT1

CT(i-1)

CT2

Exam

Remark

N = number of credits
i = number of complex tasks
2N < i < 3N

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Plan for complex tasks

Question yourself before administering CT…

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How does the learner connect the various skills to adequately respond to the task?
Does the learner have the necessary knowledge?
Does the situation allow the learner to develop a new strategy independently?

Can the learner read the proposed situation?
Can the learner relate the given information in the problem to solve it?
Does the learner master the processes, strategies and approach to accomplish the task?

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Plan for complex task

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Who should be responsible for

Reading strategies?

In your opinion …

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Error – a teaching tool

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Errors concerning the processing of the instruction is one of 7 types of mistakes students make, and are opportune teaching tool/moments.

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Errors concerning the processing of the instruction

Error – a teaching tool

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	Types of instruction	Examples
If the instruction is	Too long	The learner is lost in what they are expected to do.
	Too complicated	What is required of the learner is outside their skill level, outside the proximal zone of development.
	Under-taught	Multiple tasks, where it is necessary to perform several tasks successively or simultaneously, and the learner is cognitively overloaded.
	Not recognized	The vocabulary, the task, does not resemble what the learner knows.

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Errors from processing the instruction

Error – a teaching tool

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Provide short and concise instructions;
Ask to rephrase the expected task;
Remember to leave a written record of the instruction to allow the learner to come back to it during the task if necessary (on the board or on the handout);
Avoid implied antecedent with the use of pronouns. Prefer repetition.

Remedies

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What do good readers and good mathematicians have in common?

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Characteristics of Good Readers	Characteristics of Good Mathematician
They call upon their prior knowledge to make meaning from text.	They call upon prior knowledge to understand concepts and solve problems.
They are fluent readers.	They are procedurally fluent.
They have a mental image of what they are reading.	They create multiple representations of mathematics concepts and problems.
They use multiple strategies to understand and interpret text.	They use multiple strategies to understand concepts and solve problems.
They monitor their understanding as they read.	They monitor their understanding as they solve problems.
They can clearly explain their interpretation of the text to others.	They can clearly explain their mathematical thinking to others.

Adapted from Minton 2007)

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The guide for piloting learning situations

Prepare for the complex task

Read	Mathematics
Read the problem Rephrase in their own words Determine what is requested Activate your prior knowledge	Identify what are you looking for/question; Select and organize information that will help solve the problem; Predict/anticipate the solution to answer the question; Think about which appropriate approach/strategy to apply; Make links to prior situations.

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The guide for piloting learning situations

Implement a process to get the answer

Read	Mathematics
Relate the content of the text to the knowledge; Select important ideas and data; Identify relationships between parts of the text (inference); Create mental images, visualize the situation; Ask themselves questions; Choose strategies to overcome obstacles (re-readings, going back and forth within the problem, solving backwards, etc.).	Verify your initial prediction; Identify and eliminate extra information; Recognize implicit or missing information; Identify relationships between parts of the text and mathematical concepts; Model the problem; Identify the sources of difficulties (procedures, strategies, approaches, etc.).

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The guide for piloting learning situations

Validate your approach

Read	Mathematics
Re-read of the complex task	Check your solution (process and result); Confirm your prediction; Validate your solution; Communicate your solution.

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The role of reading in problem-solving

What is a reading strategy?

From a teacher’s perspective, a reading strategy is procedural knowledge that is taught to help a learner increase their reading skill.

From the learner’s perspective, a reading strategy is a way to bridge meaning between the language of words and the language of mathematics.

Bulletin AMQ, Vol. XLIX, no 1, mars 2009

The hard part of teaching a strategy is to know when and how to introduce it.

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The role of reading in problem-solving

A reading strategy is…

Bulletin AMQ, Vol. XLIX, no 1, mars 2009

Read with intention; Understand words; Spot the keywords; Observe the prefixes and suffixes; Organize the ideas of the text; Check the information for comprehension;	Gather the information from reading the text; Determine the main ideas while reading; Self-correct; Re-read and verify the information found; Read further or go back; Question the text.

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How to read when solving a problem?

Building reading strategies

Bulletin AMQ, Vol. XLIX, no 1, mars 2009

Read the situation	Different reading methods Read-aloud by the teacher; Read-aloud by the learner; Read silently and share the understanding; Guided reading.

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How to read when solving a problem?

Building reading strategies

Bulletin AMQ, Vol. XLIX, no 1, mars 2009

Mentally represent the situation (elicit, mental imagery, …)	Rephrase the given information in their own word; Search for missing words (fill in the blanks); Focus on understanding the vocabulary used; Mimic the situation; Draw or choose pictures.

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How to read when solving a problem?

Building reading strategies

Bulletin AMQ, Vol. XLIX, no 1, mars 2009

Determine what the question is looking for	Consider the meaning of sentences, words, symbols, syntax, etc.; Understand the instructions, re-read the instruction, understand what to do; Locate the question; Highlight.

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How to read when solving a problem?

Building reading strategies

Bulletin AMQ, Vol. XLIX, no 1, mars 2009

List the information we have	Consider the meaning of <keywords> (for example “as many as”), numerical data, polysemous words (multiple meanings); identify if all relevant information needed to perform the task is provided; Focus on implicit, superfluous or missing data.

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How to read when solving a problem?

Building reading strategies

Bulletin AMQ, Vol. XLIX, no 1, mars 2009

Read to understand and to solve a mathematical problem	If reading difficulty originates from the text Reformulate, shorten sentences; Specify the meaning of words; Re-read; Build own dictionary. From the data: Represent the situation; Take into account essential data and ignore others. From the instruction: Recognize their ability to respond or not to respond to the instruction; If unable to answer, find out why; Say what the end result, the solution or the representation will look like.

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How to read when solving a problem?

Building reading strategies

Bulletin AMQ, Vol. XLIX, no 1, mars 2009

Read to understand and to solve a mathematical problem	From the question: Analyze the syntax of the questions.

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Break anyone???

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Go further

Bulletin AMQ, Vol. XLIX, no 1, mars 2009

Other reading strategies in mathematics
	Read aloud to the learner/class	Read a report with mathematical data (ex. %) Read a weather report Read a label Read a recipe
	Time for independent reading	Any text promoting reflection, logic, reasoning (without numbers or calculations) Finding information (using a lexicon)
	The learner’s choice	Ask the learner where they see math in everyday life

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Inclusion in mathematics

www.isotckphoto.com

www.via9gag.com

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Inclusion in mathematics

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Inclusion of mathematics at the CONTENT level

Use an accessible, sans-serif font: Arial, Century Gothic, Comic Sans MS.
Choose at least a 14 points font size.
Number each task.
Print only on one side of the sheets.
Use 1.5 line spacing.
Leave room between subtasks.

Oral instruction

Mathematics

Written instruction

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Inclusion in mathematics at the CONTENT level

Use action verbs for the task at hand (e.g. Choose, draw);
Favour sentences with the S-V-O construction (Subject-Verb-Object);
Favour repetition instead of synonyms (or anaphoras);
Favour images that will activate visual representation.

Poloskaia, 2021

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Inclusion in mathematics at the PROCESS level

Avoid going back and forth. Detach the appendices from the exam.
Remember the original objectives.
Use manipulative tools and videos.
Have a peer explains the material.
Read it to the learner.
Validate if reading is an overload for the adult learner. Use the text-to-speech function.

Ayres and Sewller, 2005, Cognitive and load theory

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Inclusion in mathematics at the PROCESS level

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Inclusion in mathematics at the PRODUCTION level

Give the learner a choice in how they carry out the learning.
Let the learner know of your expectations.
Allocate time to give constructive feedback on learning, by giving voice messages, using digital tools and cue cards.
Use the answer key as a learning guide (focus on process and less on final answer).
Use the method: THINK-PAIR-SHARE.
Plan evaluation time with student input.
Get the adult learner to speak, while writing down their reasoning.

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Inclusion in mathematics

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From a linguistic point of view

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Read the complex task and derive meaning from it;
Have a correct global semantic representation of the problem;
Use your reading strategies properly;
Validate the solution in context.

To solve a complex task, you have to…

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From a linguistic point of view

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Part 1 : Provides information about the situation to solve
Part 2: Provides direction for action

The text used in complex tasks has two parts:

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The linguistic characteristics of a complex task

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The scenario

Use a variety of texts: informative, narrative, descriptive, etc.

It is an imperative text: a request for structured actions that requires a response, a recommendation, an analysis, a decision-making, etc.

An instruction, a question or even an order is implicitly or explicitly given.

These texts are presented in various ways: sentences, diagrams, figures, drawings, tables, etc.

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The imperative text in a mathematical problem

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The procedural part of the statement is the instruction to be executed

The instruction can be an order.

The task expected of the learner is explicit, at least in part, in the instructions.

Imperative action verbs are used.

Examples

Calculate the time required to complete a project.
Draw a regression line.
Describe the property of the figure.

The instruction can be a question.

The task expected of the learner is implicit in the instruction.

Infinitive action verbs are often used.

Examples

Can the deadline be met?
What volume will require the least material for its construction?
What options should we choose?

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Model for reading comprehension

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Giasson, 1990

Search for meaning

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Understanding a mathematical question

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Understanding the question

Construction or development of a mathematical model

From the characteristics of the text :

Vocabulary: unusual words, generic terms, etc.
Syntactic and lexical forms: conditional, subject inversion, passive form, interrogative form, etc.;
Complex grammatical structures: for example, the information given in the question (knowing that, etc.)

Based on the reader’s knowledge:

Nature of the information (presence of implicit knowledge unavailable to the reader);
Type of text: the text structure might be unknown;
Overall semantic: representation of a problem.

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Reader’s attitudes

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Aesthetic reading

Pleasure of reading

Comprehension of questions

Practical reading

Perform a calculation

Finding numbers

Studious reading

Complex situation to mobilize resources

Information retrieval and mental network

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Reading strategies in mathematics

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1 – Enrich the vocabulary

2 – Activation of prior knowledge by the vocabulary

3 – Activation and reinvestment of prior knowledge

4 – Predictions and inferences

5 – Thinking aloud

6 - Questioning

7 - Summary

8 – Visual representations and mental imagery

9 – Use of text structure

10 – Multiple strategies

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1 – Enrich the vocabulary

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Case study

Cognitive barrier unknown words rectilinear

Suggested strategies: root learning map and knowledge assessment scale (personal lexicon)

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1 - Root learning map

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rect

(in a straight line)

rectangle

correct

direction

From Latin rectus, straight

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1 - Knowledge assessment scale and lexicon

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Word	Known word	Word seen or heard	Unknown word	Meaning
1. Rectilinear			X	What is in a straight line
2.
3.

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9 – Use of the text structure

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By using his knowledge of the structure and characteristics of the text, the learner more easily decodes the meaning of the text.

Structure of the text

Formats of the text

The text: title page, credits, table of content, images, titles, subtitles...

Internal structure of the text: type of text, main and secondary sequences or ideas…

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Different types of reading for a math question

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Narrative reading

You have to imagine, represent the story told in the scenario, calling on your experience or your knowledge.

Informative reading

Imagine, understand, then seek and organize information from scenario.

Prescriptive reading (order)

Determine the nature of a given problem. The information must be selected and processed from the given instruction.

GOAL

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Effective readers...

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Read actively

Set reading intentions and validate them while reading

Pre-read (structure)

Make predictions

Read selectively

Construct and challenge the meaning of the message

Determine the meaning of unfamiliar words and concepts

Make inferences from their prior knowledge

Take into account their knowledge of the author

Check their understanding of the text

Evaluate the quality / value of the text

Read texts differently depending on their type / genre

Write and review summaries

Think about text before/during/after reading

Feel satisfied while reading

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Ingenious teachers who care about reading skills...

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Take the time to understand each strategy in their own reading

Incorporate explicit instruction in reading strategies into daily or recurring activities

Have learners apply each strategy to a wide variety of texts in different contexts

Group learners differently to teach strategies

Gradually teach learners the responsibility of applying a comprehension strategy

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4 profiles of readers in action

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Poor decoding

Poor comprehension

Good decoding

Poor comprehension

Poor decoding

Good comprehension

Good decoding

Good comprehension

Fluidity

Oral task

Hooray! !

Strategies/Tools

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READING STRATEGIES

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Immersive Reader

Giovanna Salvagio

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Web

LMS

WAYS OF USING IMMERSIVE READER

Cell phone

CLICK HERE FOR RESOURCE

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Let’s review…

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We were able to

have a better understanding of reading strategies and how it applies to mathematics
be aware of some digital resources/tools to support students reading

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Reading strategies for math statements

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… IN CONCLUSION

Pencil it in!

Part 2 will be on March 31, same time same location.

See you soon!