Reading Strategies in Mathematics Statements
2021-2022
Vanessa Boily, Giovanna Salvagio and Micheline Ammar
Presented by
2021-22
Agenda
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By the end of the workshop, you will…
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New DED
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Essential Knowledge
5173
5163
4273
Geometric transformations
Course
Equivalent figures
Initially …
Aligned with FGJ
Statement of a problem
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A mathematics problem consists of a set of information...
… being the subject of a question or an instruction...
… which requires inquiry or action…
… which implies the use of mathematical notions and tools.
The presentation of this information can be in the form of: Text, table, drawing, diagram, graph, etc.
Questioning of this sort is often explicit, but the problem solver can also take on such responsibility.
We must build a path to reach a solution.
The mathematical uniqueness of a problem appear through the concepts and tools used in its solution.
Problem-solving activities
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The mathematics problem and its intentions
Verify the learning of new knowledge
Introduce a
new concept
Provoking inquiry and decision-making
Where does the problem come from?
What is the format of the questions?
Arithmetic
Algebra
Geometry
Probability and statistics
Text
Table
Drawing
Graphic
Oral
Characteristics of a written problem statement
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Written problem statement
It is an instructional text: a request for action or a response to be to formulate.
It uses writing: informative, narrative, descriptive, etc.
There is an instruction (a question or a request) that is implicitly or explicitly given.
Information is provided through various means, such as writings, diagrams, drawings, tables, etc.
The instruction in the problem statement
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The directive part of the statement is the instruction to execute
The instruction can be an order
The task expected of the student is explicit, at least in part, in the instructions.
The task expected of the student is implicit in the instruction.
The instruction can be a question
Calculate the price...
Draw the graph...
Describe the figure...
What is the price of two items?
Can Paul buy his dream house?
What errors are present in this graph?
Understanding a problem statement
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Understanding
of the problem
Construction or utilization
of a mathematical model
From the features of the text:
From the reader's knowledge :
Types of reading of a problem statement
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Narrative reading
Informative reading
Prescriptive reading
The student must imagine and represent the story told in the problem statement, drawing on his or her experience or knowledge.
From the imagined and understood story, information must be sought and organized.
The type of problem asked must be determined. The student must select the information and process it according to the instructions given.
Cognitive skills involved in problem-solving
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Solving a problem is...
Giovanna
Vanessa
Micheline
Intervention 1
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Reading and complex tasks
Reading a complex task.
Reading, a complex task!
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Kick-off activity (CCBE)
The Aviary
Michel and Micheline share an aviary. Michel has three birds: a duck and two swans. Micheline has two canaries, three lemurs, six partridges, four parrots and a kiwi.
Reading Strategies in Mathematics (Macceca et Brummer)
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1 - Enriching vocabulary
2 - Activating prior knowledge through vocabulary
3 - Activating and reinvesting 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
Observable behaviours of effective readers
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Active Reading
Set reading goals and validate them as they read
Do a pre-reading (structure)
Make predictions
Selective reading
Build and question the meaning of the message
Determine the meaning of unknown words and concepts
Make inferences based on prior knowledge
Consider their knowledge of the author
Check their understanding of the text
Evaluate quality/value of text
Read texts differently depending on their type/genre
Write and review summaries
Think about the text before/during/after reading
Feel satisfied by reading
The aviary
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
To better target reading Interventions: Four distinct reader profiles
https://www.youtube.com/watch?v=cZ9CWN8s2xU
What if we listened to them read? Reading fluidity
https://www.youtube.com/watch?v=wzfqNTIqpq0
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
The use of text structure
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By using their knowledge of the structure and characteristics of the text, students can more easily decode the meaning of the text.
Text Structure
Text Format
External structure of the text: title page, credits, table of contents, images, titles, subtitles...
Internal structure of the text: type of text, main and secondary ideas...
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Task 3 (MTH-4151) Home Cinema!
Reading’s intention : text structure analysis
Answer key to the workbook, p. 62
Task 3: Home Cinema!
Leonie and Abdul are passionate about movies and have recently set
up a room in their basement specially designed to optimize sound and
comfort. They are now ready to buy a new Smart television to complete
their project.
So they go to an electronics store and talk to the salesperson, and he
offers them a great promotion on the purchase of an 85-inch smart TV that ends in eight weeks.
Leonie and Abdoulaye need to save as much money as possible to pay for the TV, which costs $4523.99, including taxes.
Here's how they plan to pay for this purchase: - Leonie can put aside $100 per week, and she already has $1750 in the bank; - Abdul already has $1200 in a savings account, and he can put aside $75 per week.
The salesperson offers them a 10% discount on the total price with taxes if they manage to pay for the smart television two weeks before the promotion ends.
Will Leonie and Abdul be able to take advantage of the 10% discount offered by the seller? If not, how could they change their savings plans, knowing that it is easier for Leonie to save money than for Abdul?
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Task 4 (MTH-4273) Lepage Route
Reading intention : Text structure analysis
Task 4: Lepage Route Answer key to the workbook, p. 62
A newly installed radar is placed on Lepage Road to identify drivers who exceed the speed limit of 70 km/h on Lepage Road. All cars passing on this road between points P and Q are subject to radar detection. The radar is placed at point R on the diagram and measures the time it takes for a vehicle to pass between points
P and Q. The chart below shows the number of demerit points and the
amount of the fine for drivers who violate the 70 km/h speed limit.
What is the risk of getting a ticket to a driver on Lepage Road if the radar has detected that he/she has passed between points P and in 3.63 seconds?
From KM
to KM
Demerit point
$
This type of text may include:
consequences, cause/consequences, problem/causes, problem/solutions);
explanatory devices:
KEY CHARACTERISTICS
The explanatory sequence is the dominant sequence in an explanatory text it contains :
Text with an explanatory content is used:
Purpose
Textual sequence
The text with predominantly descriptive nature serves:
Purpose
This type of text includes:
MAIN CHARACTERISTICS
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Types of texts
Did you notice a connection between the different types of texts and the tasks requested or the mathematical skills required?
Task 3 Home Theater, narrative text, algebraic modeling
Task 4 Lepage Road, informational or explanatory text, geometric modeling
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Types of texts
Feedback on the activity
Type of text | Frequent treatment |
Narrative | Algebraic modeling |
Informative (explanatory) | Algebraic modeling |
Descriptive | Geometric modeling |
This allows us to make predictions even before the reading...
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Inferences
Definition
Inference is a logical operation of deduction which consists of clues present in the text, in making explicit and implicit information (evoked or supposedly known).
FORMATIONS NATIONALES MATHÉMATIQUES
Task 9 (MTH-4152) Ekaterina and Milan's students
What inferences will students have to make?
Task 9 Ekaterina and Milan's students
Ekaterina and Milan are special education teachers. This year, they are working mainly with students who have learning difficulties in school subjects. Here are the results obtained by their students in French, Math and English.
*Results obtained by Ekaterina's students Student
Results obtained by Milan's students (in alphabetical order)
In French: 44%, 48%, 70%, 66%, 76%, 52%, 74%, 62%, 51%, 38%
In Mathematics: 66%, 69%, 54%, 79%, 36%, 80%, 74%, 48%, 85%, 41%
In English: 65%, 60%, 78%, 42%, 33%, 69%, 87%, 55%, 52%, 40%
Ekaterina and Milan believe that students who have difficulties in French also have difficulties in English. They also think that students who have difficulties in mathematics also have difficulties in French.
Do the results obtained by students with learning difficulties represent what these two special education teachers think?
Students
French
Math
English
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Inferences
Activity
Task 9 in MAT-4152
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Reading strategies
BEFORE | DURING | AFTER |
Reading intention | Make connections (with our previous knowledge...) | Synthesis or summary |
Overview | Identify (then analyze) the question or task to be performed | Confirm or deny our initial hypotheses |
Predictions (e.g., structure or type of text) | Check your understanding | To verify the realization of our reading intention |
| Select important information | |
| Make inferences | |
| Identify sources of difficulty (e.g., vocabulary - unknown word) | |
| Questioning oneself/the text | |
| Mental imagery (representations) | |
FORMATIONS NATIONALES MATHÉMATIQUES
Task 4 (MTH-4271) The bed of the Chaudière River
Modeling: before, during, after
Answer key to the workbook, p. 52
Task 4 The Chaudière River Bed
Every year, in many parts of the world, rainfall varies, and the height of the riverbed threatens to flood neighbouring areas. This water level is of great concern to municipal authorities.
The amount of precipitation directly impacts the water level, and this is particularly true of the Chaudière River in Lévis, on the south shore of Quebec City. Every 30 mm of rainfall raises the river's water level by 0.5 cm.
The table below presents the alert level associated with the height of the water level.
Knowing that the height of the riverbed was 0.147 m and that 162 mm of rain fell this week, what is the alert level?
Noto: Consideróroz that the height of the riverbed behaves as an integer function.
The height of the river bed (mm)
Alert level
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Inclusion in mathematics at the CONTENT level
Oral Code
Mathematical Code
Written Code
Break …
Reading strategies to develop
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Knowing...
To consolidate reading strategies
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Ways to explore
To consolidate reading strategies
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A short guide to good practice
Progression of activities to consolidate reading strategies
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Depending on the diagnosis, some activities can be included to develop strategies for reading mathematical statements to solve a problem.
Progression of activities to consolidate reading strategies
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Progression of activities to consolidate reading strategies
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Examples of ways to explore
SECTION 1
Progression of activities to consolidate reading strategies
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Section 1
Identify a problem statement
The cherry tree in my garden was 153 cm tall last year. It produced 2 kg of cherries. This year it grew and produced 3 kg of cherries. Now, how tall is my cherry tree?
IS IT A COMPLETE PROBLEM?
I ate at the restaurant with my family. My father and brother choose a $15 menu. My mom gets a salad for $9, a grilled lamb chop for $7, and a dessert for $4. I ate like my mom but chose a $5.50 dessert. My dad paid with a $100 bill. How much do we give him back?
IS THIS A COMPLETE PROBLEM?
Progression of activities to consolidate reading strategies
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Section 1
Start a glossary of polysemic words.
Progression of activities to consolidate reading strategies
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Examples of ways to explore
Section 2
Progression of activities to consolidate reading strategies
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Section 2
Associate a statement with its question
1. A soccer stadium can hold 8,000 people. For the last game,
there were 4,256 spectators.
2. Last Monday, the gas station owner brought in 5,000 litres
of gasoline for his customers. Three days later, he finds that he has 890
liters left.
3. The school principal received $2,500 from the town hall to buy school
supplies. He orders $595 worth of books and $1,240 worth of
materials for manual work.
4. Mr. Abot sells his car for $8,500 and his trailer for $6,400. He goes to the bank
to borrow the money he needs.
5. The space shuttle has travelled 18 times around the Earth, which is 40,000
km.
A. Will the manager still be able to buy a printer worth $700?
B. How far did it travel in total?
C. How much gasoline have customers purchased since Monday?
D. How many empty seats were left?
E. How much money will he borrow?
Progression of activities to consolidate reading strategies
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Examples of ways to explore
Section 3
Progression of activities to consolidate reading strategies
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Section 3
Invent several questions to a single statement
A. In a parking lot, there are 175 cars on the first floor, 225 on the second floor and 115 on the third floor and 115 on the fourth floor.
B. The track of the Palais des Sports in Grenoble is 250 m long. A racing cyclist
wants to ride precisely 10 km on this track.
C. Patrick found that by taking 400 steps, he covered 300 m. To get to his friend Julien's house, he counts 1200 steps.
D. Mr. Martino is in charge of putting 160 bottles into racks that can hold 15 bottles each.
E. Cyril watches television from 5.50 p.m. to 6.30 p.m. daily every week except Saturday and Sunday.
F. The student cafeteria at a school contains four rows of six tables with eight seats.
Progression of activities to consolidate reading strategies
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Section 3
Invent several questions to a single statement
A. On Monday, Jennifer sold 18 raffle tickets. On Tuesday, she sold 2 packs of 25 tickets.
B. In a parking lot, there are five rows of 15 cars on the second floor. There are 45 cars on the second floor.
C. On the first shelf of the library, there are 54 books. There are two sets of 42 books on the second shelf.
D. For her birthday, Sophie bought two 6-packs of fruit juice and three 12-packs of soda.
E. Mom buys four 12-packs of yogurt at $3.10 a pack.
F. Mark buys five records at $9.25 each. When he leaves the store, he noticed that he has 4$ left.
G. At the library, there are two shelves of 40 books for kindergarten and five shelves of 30 books for
elementary.
H. At the canteen, there are three large tables that seat 8 and 9 small tables that seat 4.
I. On his way out of the store, Eric noticed that he has $10 left in his wallet . He has bought 3
CDs at $11.30 each.
J. Eric is reading a 125-page book. He read 38 pages in the morning and 24 pages in the
afternoon.
K. After the rain, Marc and Pascal went to pick up snails. Pascal collects 127 snails, and Mark collects 13 more than him.
Progression of activities to consolidate reading strategies
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Section 3
Find the middle question
For each of the following problems, write the question that a student must answer before finding the final solution.
A merchant receives three cheques: one for $212.25, a second for $488 and a third for $453.50. After depositing these three checks in the bank, her statement shows a net credit balance of $2,388.35.
Three friends go to spend a weekend at the lake of Nantua. The trip costs $122, the food $105 and the camping $25. They had planned a budget of $275 for this trip. If they share the expenses equally, what will be each one's share?
How much money did she have in her account before cashing these three checks?
How much will be left in the planned budget?
Progression of activities to consolidate reading strategies
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Examples of ways to explore
Section 4
Progression of activities to consolidate reading strategies
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Section 4
Write the answer to a solved problem
For each problem, 3 solutions are proposed. Choose the one that seems to be the right one, then write a sentence.
At the hardware store, Lyly and I buy two boxes of nails worth $2.50 each pack. What is the total cost?
A. $4.50
B. $5.00
C. $50.00
Progression of activities to consolidate reading strategies
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Section 4
Write the statement corresponding to a given calculation
The train will be delayed by 22 minutes.
Progression of activities to consolidate reading strategies
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Examples of ways to explore
Section 5
Progression of activities to consolidate reading strategies
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Section 5
Reconstitute a disordered statement
Progression of activities to consolidate reading strategies
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Section 5
Reconstructing the scenario from separate and mixed statements.
Progression of activities to consolidate reading strategies
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Examples of ways to explore
Section 6
Progression of activities to consolidate reading strategies
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Section 6
Find missing data
When Sophie takes the 10:15 a.m. train to Paris, she has €50 in her wallet. She eats her meal in the restaurant car and, on arrival, she has only €15 left.
What time does she arrive in Paris?
A. total expense
B. arrival time
C. travel time
Progression of activities to consolidate reading strategies
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Section 6
Completing a missing statement
A concert hall we can accommodate 500 people. Currently, _______ rows of 25 people each are fully occupied and there are also ______ single spectators. Each spectator has paid _______ for his or her seat.
What is the revenue of the day?
Progression of activities to consolidate reading strategies
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Section 6
Distinguish between useful and useless data
To build a fence around his house, Mr. Smith hired three masons and paid them $19 per hour for 24 hours. This fence will measure 18.50 m long and 1.80 m high. We want to use cinder blocks 50 cm long and 20 cm tall. We know that a truckload of 3 m3 of sand at $5 per m3 to fill 12 bags of cement of 50 kg each, purchased at $8 per bag.
How many cinder blocks will be used?
Progression of activities to consolidate reading strategies
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Examples of ways to explore
Section 7
Progression of activities to consolidate reading strategies
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Section 7
Reduce a statement by removing unnecessary information
Delete unnecessary data and reformulate the problem
Yannick is ten years old. He likes to take care of his favourite stamps collection. Every night, warm in his bed, he studied each stamp carefully until 9 o'clock. His grandmother and
mother gave him a beautiful red album that cost $6. On each page of the album, there are six rows. On each row, Patrick places five stamps. He picks them up and puts them carefully with tweezers to not damage them. Despite this, last week, he tore three of them. He had to throw them away, which made him a little sad. He is still proud of his collection because he has already filled ten pages!
How many stamps did Patrick put away?
Progression of activities to consolidate reading strategies
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Section 7
Order the steps of a solution
Rewrite in order the different steps to solve these problems.
A class of 28 students rents a bus for a field trip. The transportation company charges $1.04 per kilometer travelled. The group also pays for the driver's meal for $11.00. When the bus leaves, the odometer reads, indicating 129 699 km, and on the return trip, it reads 130 019 km. The school pays $63.80, and the students pay the rest.
What is the share for each student?
The total amount to pay is (in $): 343.80 - 63.80 |
Each student pays (in $): 280 ÷ 28 |
Total expense is (in $): 332.80 + 11 |
The amount paid to the bus company is (in $): 1.04 x 320 |
The bus travelled (in km): 130 019 - 129 699 |
Intervention 3
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Intervention 3
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Quizzes:
Vocabulary Flash cards:
We were…
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Reading Strategies in Mathematics Statements
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Thank you !
2021-22