Extensive use of discourse in the classroom is a key practice to support the learning of English while learning mathematics. English learners are in varying stages of English language development, and discourse will increase their productive (oral and written) and receptive (listening and reading) language functions in addition to their comprehension of mathematics concepts. The Standards for Mathematical Practice expect students to reason, construct viable arguments, and critique the reasoning of others among other practices. Thus, classroom teachers need to provide support for students’ English language development to engage in these practices. In this webinar, Mathematics Education Consultant Dr. Susie W. Håkansson shares the rationale for using discourse in the classroom, the role of productive and receptive language functions in the learning of mathematics, as well as examples of how to increase discourse in the classroom.

1. Use Discourse to Access Language
and Mathematics for English Learners
Monday, February 13, 2017
Join the Blended Learning community: http://www.edweb.net/blended
Presented by:
Dr. Susie W. Håkansson
Mathematics Education Consultant
and Immediate Past-President,
TODOS: Mathematics for ALL

2. • For better audio and video, close other applications that use bandwidth
• If you are having audio or connection issues, try the “Switch to Phone”
option by clicking “More” at the top of the screen
• For a larger view of the slides, hover over the top-right side of the screen to
access the “Maximize” button
• Please post your questions in the chat box
• If you’re tweeting today, use the hashtag #edwebchat
• If you have any problems, staff from edWeb are standing by to assist you
Here are some webinar tips …
Tweet using #edwebchat

3. Please join the free community!
Blended Learning: Extending Classes Online
 Invitations to upcoming webinars
 Access to recordings of past webinars
 Online discussion forums
 A CE certificate for each quiz you take
Use this link to join the community: www.edweb.net/blended
You’ll receive the following benefits:

4. If you logged in live with your email address:
Your certificate will be emailed to you the next business day.
If you joined by phone or if you’re watching this as a recording:
Take the CE quiz located in the Webinar Archives.
To get your CE Certificate:
Thanks for Attending This Webinar!
Presented by edWeb.net
___________________________________________________________________________
Name
All requirements for this in-service program have been completed.
Number of clock hours completed: 1
CERTIFICATE OF COMPLETION
You’ll receive a certificate for this webinar within 24 hours!
edWeb.net is a free professional social and learning network.
edWeb.TV is a premium subscription service from edWeb.
To take the CE quiz:
Join the community at www.edweb.net/blended
You’ll find a CE quiz in the Webinar Archives

5. Dr. Susie W. Håkansson is Immediate Past-President of TODOS:
Mathematics for ALL. She taught high school mathematics, served
as a faculty advisor for pre-service students, was a lecturer in the
UCLA Department of Mathematics, and has over 30 years of
experience providing professional development to PreK-16
mathematics teachers. She was the executive director of the
California Mathematics Project (CMP) and a site director prior to
that, collaborating with others to design and implement
institutes, workshop series, and school site programs for teachers,
administrators, parents, and students, particularly programs that
focus on providing access to high quality and rigorous
mathematics for ALL students, particularly English learners. Dr.
Håkansson has been a monitor and evaluator on Improving
Teacher Quality and NSF Grants. She is a recipient of the TODOS
2013 Iris M. Carl Leadership and Equity Award, the California
Mathematics Council 2009 Walter Denham Memorial Award, and
a UCLA 2009 Distinguished Teaching Award.

6. Use Discourse to Access
Language and
Mathematics for English
Learners
By Susie W. Håkansson, Ph.D.
Immediate Past-President, TODOS: Mathematics
for ALL
Mathematics Education Consultant
February 13, 2017

8. Description
This session will provide the following:
 Rationale for using discourse in the
classroom
 Role of productive and receptive language
functions in the learning of mathematics
 Examples of how to increase discourse in
the classroom.

9. Outline
 Challenges in Learning English
 Using Discourse
 Language in the Mathematics
Classroom
 High Cognitive Demand
Mathematics Tasks
 Examples of Discourse in the
Classroom
 Equity and Excellence

10. Challenges in Learning
English
 Access to the English language
 Access to the language of mathematics
 Access to the mathematics content
 Expectations
 Self-efficacy
 Opportunity gap

11. Why Is English So Hard?

12. Why Is English So Hard?
Upon seeing the tear in the painting, I shed a
tear.

13. Why Is English So Hard?
Upon seeing the tear in the painting, I shed a
tear.
After a number of injections, my jaw got
number.

14. Why Is English So Hard?
Upon seeing the tear in the painting, I shed a
tear.
After a number of injections, my jaw got
number.
A minute is a minute part of a day.

15. Why Is English So Hard?
Upon seeing the tear in the painting, I shed a
tear.
After a number of injections, my jaw got
number.
A minute is a minute part of a day.
The soldier decided to desert his dessert in
the desert.

16. Why Is English So Hard?
They were too close to the door to close it.

17. Why Is English So Hard?
They were too close to the door to close it.
I did not object to the object.

18. Why Is English So Hard?
They were too close to the door to close it.
I did not object to the object.
We must polish the Polish furniture.

19. Why Is English So Hard?
They were too close to the door to close it.
I did not object to the object.
We must polish the Polish furniture.
The farm was used to produce produce.

20. Why Is English So Hard?
They were too close to the door to close it.
I did not object to the object.
We must polish the Polish furniture.
The farm was used to produce produce.
The bandage was wound around the wound.

21. Why Is English So Hard?
There is no egg in eggplant and no ham in
hamburger.
How can a slim chance and a fat chance be
the same, while a wise man and a wise guy
are opposites?
Did you say thirty or thirteen?
Did you say two hundred or two hundredths.

22. “Even”
Social register
The floor is even (smooth/liso)
The picture is even with the window (leveled/nivelado)
Sleep provides even rhythm in our breathing
(regular/uniforme)
The dog has an even temperament (calm/calmado)
If we share equally, we will be even (balance/igual)
I looked sick and felt even worse (comparative/aún)
So simple, even a child could do it
(comparative/incluso)

23. “Even”
Social register
Got even
To be even
Even out
Break even
Not even
Even-steven

24. “Even”
Mathematics register
Number: even numbers (e.g., 2, 4, 36, 58)
Number: even amounts (e.g., even amounts of
flour and sugar)
Measurement: exact amount (an even pound)
Function: even function (e.g., y = 5x2 – 3;
y = cos x)

26. Teachers learn to amplify and enrich—rather
than simplify—the language of the classroom,
giving students more opportunities to learn the
concepts involved.
Aída Walqui, Teacher Quality Initiative

27. Using Discourse
 Receptive Language Functions
 Listening
 Reading

28. Using Discourse
 Productive Language Functions
 Speaking
 Writing

29. Mathematical Practices
MP2: Reason abstractly and quantitatively.
MP3: Construct viable arguments and
critique the reasoning of others.

30. MP2: Reason Abstractly and
Quantitatively
Receptive Language Functions
 Comprehend the meaning of a problem situation
and its relevant quantities as presented through
multiple representations
 Comprehend other’s talk about the relevant and
irrelevant quantities in the problem situation
 Coordinate written texts and multiple
representations

31. Communicate (orally and in writing) about concepts,
procedures, strategies, claims, arguments, and other
information related to abstract and quantitative reason:
 Explain reasoning as it relates to problem situation,
 Create, label, describe, and defend coherent
representations of the problem situation at hand
 Ask questions to contextualize the problem situation
or the quantities of the problem
MP2: Reason Abstractly and
Quantitatively
Productive Language Functions

32. Comprehend oral and written concepts, procedures, or
strategies used in arguments and reasoning, including
 Questions and critiques using words or other
representations
 Explanations offered using words or other
representations by others (peers or teachers)
 Explanations offered by written texts using words or
other representations
MP3: Construct and Critique
Receptive Language Functions

33. Communicate (orally and in writing) using words about
concepts, procedures, strategies, claims, arguments, and
other information related to constructing arguments and
critique reasoning:
 Provide written or verbal explanation of an argument
 Justify conclusions and respond to counterarguments
 Recognize and use counterexamples
 Respond to questions by amplifying explanation
 Respond to critiques
 Critique or support explanations or designs
MP3: Construct and Critique
Productive Language Functions

34. Language in the
Mathematics Classroom

35. Language in the
Mathematics Classroom
 Focus on students’ mathematical reasoning, not
accuracy in using language.

36. Language in the
Mathematics Classroom
 Focus on students’ mathematical reasoning, not
accuracy in using language.
 Shift to a focus on mathematical discourse
practices, move away from simplified views of
language.

37. Language in the
Mathematics Classroom
 Focus on students’ mathematical reasoning, not
accuracy in using language.
 Shift to a focus on mathematical discourse
practices, move away from simplified views of
language.
 Recognize and support students to engage with
the complexity of language in math classrooms.

38. Language in the
Mathematics Classroom
 Focus on students’ mathematical reasoning, not
accuracy in using language.
 Shift to a focus on mathematical discourse
practices, move away from simplified views of
language.
 Recognize and support students to engage with
the complexity of language in math classrooms.
 Treat everyday language and experiences as
resources, not as obstacles.

39. Language in the
Mathematics Classroom
 Focus on students’ mathematical reasoning, not
accuracy in using language.
 Shift to a focus on mathematical discourse
practices, move away from simplified views of
language.
 Recognize and support students to engage with
the complexity of language in math classrooms.
 Treat everyday language and experiences as
resources, not as obstacles.
 Uncover the mathematics in what students say and
do.
Judit Moschkovich

40. High Cognitive Demand
Mathematics Tasks

41. High Cognitive Demand
Mathematics Tasks
Number Line
 Natural Numbers
 Fractions
 Integers

44. 0
1
?
0 1
?
?
1
2
10
g)
c)
k)
?
3
2
?
1
5
?
52
21
b)
d)
l)

45. 3 5
?
0 1
?
?
53
h)
f)
i)
3 5
?
?
52
j)
b)
3 5
?
?
?
53
h)
f)
i)

48. Discourse in the
Classroom
 Number line
 Language rich classroom
 Student questions
 Video

49. Video:
Brandon, Chris, and Nathan use multiple
examples organized systematically

50. Equity and Excellence

51. Equity and Excellence
 Guiding principles
 Best practices for English learners
 Quote
 TODOS: Mathematics for ALL

52. Guiding Principles

53. Guiding Principles
Challenging mathematical tasks

54. Guiding Principles
Challenging mathematical tasks
Linguistically sensitive social environment

55. Guiding Principles
Challenging mathematical tasks
Linguistically sensitive social environment
Support for learning English while
learning mathematics.

56. Guiding Principles
Challenging mathematical tasks
Linguistically sensitive social environment
Support for learning English while
learning mathematics.
Mathematical tools and modeling as
resources.

57. Guiding Principles
Challenging mathematical tasks
Linguistically sensitive social environment
Support for learning English while
learning mathematics.
Mathematical tools and modeling as
resources.
Cultural and linguistic differences as
intellectual resources.

58. Best Practices for English
Learners
Provide high cognitive demand tasks

59. Best Practices for English
Learners
Provide high cognitive demand tasks
Scaffold the language by amplifying and enriching
the language to access the content

60. Best Practices for English
Learners
Provide high cognitive demand tasks
Scaffold the language by amplifying and enriching
the language to access the content
Expect students to “do” the mathematics

61. Best Practices for English
Learners
Provide high cognitive demand tasks
Scaffold the language by amplifying and enriching
the language to access the content
Expect students to “do” the mathematics
Access prior knowledge and build on prior
knowledge

62. Best Practices for English
Learners
Provide high cognitive demand tasks
Scaffold the language by amplifying and enriching
the language to access the content
Expect students to “do” the mathematics
Access prior knowledge and build on prior
knowledge
Understand flexibility in ways students respond

63. Encourage and expect mathematical talk
Best Practices for English
Learners

64. Encourage and expect mathematical talk
Ask students probing questions to clarify and draw
out their thinking
Best Practices for English
Learners

65. Encourage and expect mathematical talk
Ask students probing questions to clarify and draw
out their thinking
Have students share and justify their reasoning and
process they used to solve the problem
Best Practices for English
Learners

66. Encourage and expect mathematical talk
Ask students probing questions to clarify and draw
out their thinking
Have students share and justify their reasoning and
process they used to solve the problem
Provide opportunities for students to work individually,
pair share, and in small and whole groups
Best Practices for English
Learners

67. Use language as a resource for learning not only
as a tool for communicating but also as a tool for
thinking and reasoning mathematically
Best Practices for English
Learners

68. Use language as a resource for learning not only
as a tool for communicating but also as a tool for
thinking and reasoning mathematically
Provide diverse avenues of action and expression
Best Practices for English
Learners

69. Use language as a resource for learning not only
as a tool for communicating but also as a tool for
thinking and reasoning mathematically
Provide diverse avenues of action and expression
Be aware of multiple meanings of words
Best Practices for English
Learners

70. Use language as a resource for learning not only
as a tool for communicating but also as a tool for
thinking and reasoning mathematically
Provide diverse avenues of action and expression
Be aware of multiple meanings of words
Have students Think, Ink, Pair, Share
Best Practices for English
Learners

71. Use language as a resource for learning not only
as a tool for communicating but also as a tool for
thinking and reasoning mathematically
Provide diverse avenues of action and expression
Be aware of multiple meanings of words
Have students Think, Ink, Pair, Share
Increase discourse in the classroom
Best Practices for English
Learners

72. We want to provide access to ALL students. We also
want ALL students to make sense of rigorous, high
quality, and high cognitive demand mathematics tasks.
We want them to approach the zone of proximal
development, not the zone of minimal effort. We want
equity AND excellence.

73. We want to provide access to ALL students. We also
want ALL students to make sense of rigorous, high
quality, and high cognitive demand mathematics tasks.
We want them to approach the zone of proximal
development, not the zone of minimal effort. We want
equity AND excellence.
“Equity without excellence is meaningless. Excellence
without equity is unjust. We must always ask
ourselves, what can we do to incorporate both?”

74. The mission of TODOS: Mathematics for ALL
is to advocate for equity and high quality
mathematics education for all students—in
particular, Latina/o students.

75. TODOS Membership
JOIN TODOS for only $25 for a one-year
membership, $70 for three years!
Read Social Justice Position Statement
TODOS Website
http://www.todos-math.org

76. Resources
Framework for ELPD Standards
http://www.ccsso.org/Documents/2012/ELPD%20Framework%20
Booklet-Final%20for%20web.pdf
Judit Moschkovich
http://ell.stanford.edu/papers/practice
K-12 SMP in CCSS PLM
https://www.mydigitalchalkboard.org/portal/default/Content/Viewer
/Content?action=2&scId=306591&sciId=11608
Beyond Good Teaching
https://www.nctm.org/store/Products/Beyond-Good-Teaching--
Advancing-Mathematics-Education-for-ELLs/

77. Thank You!
Susie W. Håkansson, Ph.D.
Immediate Past-President
TODOS: Mathematics for ALL
shakans@g.ucla.edu
http://www.todos-math.org

78. Question & Answer Session
Dr. Susie W. Håkansson
Email: shakans@g.ucla.edu
Follow on Twitter @SusieHakansson
Follow Todos on Twitter @todosmath
Visit www.todos-math.org

79. DreamBox Learning® K–8 Math
Transformative Learning Experiences available in English & Spanish

80. DreamBox Lessons & Virtual Manipulatives
Intelligently adapt & individualize to:
• Students’ own intuitive strategies
• Kinds of mistakes
• Efficiency of strategy
• Scaffolding needed
• Response time
“I’ve tried teaching this topic
with pencil, paper, and
plastic manipulatives for
twenty years and students
have never really gotten it. I
can immediately see that
DreamBox has invented
new, digital manipulatives
and games that are far
more powerful for student
learning.”
– Urban District Math
Leader, CA

81. AssignFocus™
Differentiated assignments for every student through your
Insight Dashboard
To accelerate learning, offer remediation, and adjust classroom instruction

82. Prepare for
the Next
Unit
Homework
Assignment Review for
Assessment
Empowered Teaching with Data.
Inspired Learning with Technology.

83. iNACOL is right around the corner…
Catch us at @DreamBox_Learn
Learn more and see how it works:
www.DreamBox.com/request-a-demo
Efficacy: Independent Validation from SRI
and from CEPR at Harvard University

84. We value your feedback!
Let us know how we’re doing:
www.surveymonkey.com/r/GC6ZCM7

85. Thank you to our speaker!
Dr. Susie W. Håkansson
Mathematics Education Consultant
and Immediate Past-President,
TODOS: Mathematics for ALL

86. edWeb would like to thank
www.dreambox.com
for sponsoring this webinar!

87. If you logged in live with your email address:
Your certificate will be emailed to you the next business day.
If you joined by phone or if you’re watching this as a recording:
Take the CE quiz located in the Webinar Archives.
To get your CE Certificate:
Thanks for Attending This Webinar!
Presented by edWeb.net
___________________________________________________________________________
Name
All requirements for this in-service program have been completed.
Number of clock hours completed: 1
CERTIFICATE OF COMPLETION
You’ll receive a certificate for this webinar within 24 hours!
edWeb.net is a free professional social and learning network.
edWeb.TV is a premium subscription service from edWeb.
To take the CE quiz:
Join the community at www.edweb.net/blended
You’ll find a CE quiz in the Webinar Archives

88. Join the free community!
Blended Learning: Extending Classes Online
 Invitations to upcoming webinars
 Access to recordings of past webinars
 Online discussion forums
 A CE certificate for each quiz you take
www.edweb.net/blended
You’ll receive the following benefits:
Thank you all for attending!