Transcript More Rigorous Mathematics for Are We There Yet? If Not, How Do We Get There- Through Equity and Pedagogy Beatrice Moore Luchin NUMBERS Mathematics Professional Development [email protected].

More Rigorous
Mathematics for
Are We There Yet? If
Not, How Do We Get
There- Through
Equity and Pedagogy
Beatrice Moore Luchin
NUMBERS Mathematics Professional
Development
[email protected]
Equity
and
Equality
ARE NOT
synonymous
In education, the
term equity refers to
the principle of
fairness.
While it is often used interchangeably with
the related principle of equality, equity
encompasses a wide variety of educational
models, programs, and strategies that may
be considered fair, but not necessarily equal.
It is has been said that “equity is the
process; equality is the outcome,”
given that equity—what is fair and
just—may not, in the process of
educating students, reflect strict
equality—what is applied, allocated,
or distributed equally.
Inequities ..
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Staffing
Programmatic
Instructional
Assessment
Linguistics
Pedagogy
• Pedagogy is the art (and science) of
teaching.
• Effective teachers use an array of teaching strategies
because there is no single, universal approach that suits all
situations.
• Different strategies used in different combinations with
different groupings of students will improve learning
outcomes.
• Some strategies are better suited to teaching certain skills
and fields of knowledge than are others.
• Some strategies are better suited to certain student
backgrounds, learning styles and abilities.
• Effective pedagogy, incorporating an array of teaching
strategies that support intellectual engagement,
connectedness to the wider world, supportive
classroom environments, and recognition of
difference, should be implemented across all key
learning and subject areas.
• Effective pedagogical practice promotes the wellbeing
of students, teachers and the school community - it
improves students' and teachers' confidence and
contributes to their sense of purpose for being at
school; it builds community confidence in the quality of
learning and teaching in the school.
The new mathematics TEKS requires more
emphasis on problem solving, integration of
algebraic thinking, and multiple
representations than ever before.
Equity and pedagogy in daily instructional
practices and high levels of student
engagement are critical to getting there, and
getting there quickly!
Recommendation 1: Focus on
planning
Challenges for the PLCs
People use this term to describe every
imaginable combination of individuals with an
interest in education—a grade-level teaching
team, a high school department, a grade level
meeting, and so on.
In fact, the term has been used so ubiquitously
that it is in danger of losing all meaning.
Big Idea of the PLC -Ensuring That
Students Learn
As the school moves forward, every professional
in the building must engage with colleagues in
the ongoing exploration of three crucial
questions that drive the work of those within a
professional learning community:
• What do we want each student to learn?
• How will we know when each student has learned
it?
• How will we respond when a student experiences
difficulty in learning?
In addition to being systematic and schoolwide,
the professional learning community's
response to students who experience difficulty
is
•Timely. The school quickly identifies students who need
additional time and support.
•Based on intervention rather than remediation. The plan
provides students with help as soon as they experience difficulty
rather than relying on summer school, retention, and remedial
courses.
•Directive. Instead of inviting students to seek additional help,
the systematic plan requires students to devote extra time and
receive additional assistance until they have mastered the
necessary concepts.
• Common Misconceptions
• Common Error patterns
• Overgeneralizations
Discussion:
How could you use this during PLC to support better
planning?
Grouping
practice
Independent
seat work
Partner work
Small group
3-5
Whole class
Auditory
Tactile
Kinesthetic
Visual
modeling and developing
correct mathematical
thinking and reasoning
abilities
Use < , > or = to make the
expression true.
45_____39
Adjust “teacher talk” from “Which is greater?” to “How does
45 compare to 39? Is it greater than, less than or are they
equal?”
Changing how you talk about it changes how I analyze it, read
it, and think about it.
78 _____91
17
2
4
2 tens 4 ones
2o
4
A total of 24
Discussion: what is the appropriate
“teacher talk” to explain the
algorithm for this situation?
48
x7
21
Academic Language
distinguishes feature
diagram
conclusion
best describes most likely
enabled
affect/effect
evidence
relationship
indicated by
reasonable
valid conclusion
analyze
most accurately
indicates
outcome
primarily
determine
affected
Recommendation 2: Integrate
Mathematical Process Standards
1A apply mathematics to problems arising in everyday life, society, and the workplace;
1B use a problem-solving model that incorporates analyzing given information,
formulating a plan or strategy, determining a solution, justifying the solution, and
evaluating the problem-solving process and the reasonableness of the solution;
1C select tools, including real objects, manipulatives, paper and pencil, and technology
as appropriate, and techniques, including mental math, estimation, and number sense
as appropriate, to solve problems;
1D communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate;
1E create and use representations to organize, record, and communicate mathematical
ideas;
1F analyze mathematical relationships to connect and communicate mathematical
ideas;
1G display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
Recommendation 2: Integrate
Mathematical Process Standards
1A apply mathematics to problems arising in everyday life, society, and the workplace;
1B use a problem-solving model that incorporates analyzing given information,
formulating a plan or strategy, determining a solution, justifying the solution, and
evaluating the problem-solving process and the reasonableness of the solution;
1C select tools, including real objects, manipulatives, paper and pencil, and technology
as appropriate, and techniques, including mental math, estimation, and number sense
as appropriate, to solve problems;
1D communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate;
1E create and use representations to organize, record, and communicate mathematical
ideas;
1F analyze mathematical relationships to connect and communicate mathematical
ideas;
1G display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
Vertical Articulation
is KEY
What is your campus and
district problem solving
plan?
Is everyone using it with
integrity and fidelity?
Is it posted?
Do students know the
plan?
Are connections made across disciplines?
Recommendation 3: Alignment of
ALL materials and activities to the
TEKS
• Ensure mathematics
curriculum is based on
challenging content
• Ensure that the
mathematics curriculum
is vertically and
horizontally articulated
Campus/district review teams or rubric
Recommendation 4: Focus on Literacy
Integrating writing into your mathematics
classroom can be easy for you and beneficial for
your students.
Communicating about mathematics helps
strengthen student learning, which can build
deeper understanding. It provides students an
opportunity to organize their thoughts related to
the math topic, which helps clarify their thinking.
Include symbols as well as words
≅
‖
∏
°
bases faces
vertices edges
surface
1-dimensional
2-dimensional 3-dimensional
Mathematics is a Technical Subject
It requires Technical Reading which is more
difficult than general reading because of
specialized vocabulary,
the way information is organized, and
the diagrams and charts included with
the reading.
Term
Definition
Mean
Median
Mode
Additional notes:
How it is
determined
Example
Situation
where it is
the
appropriate
measure of
central
tendency
Positive
Add
Combine
Up
Increase
Profit
Gain
Negative
Subtract
Decompose
Down
Decrease
Loss
Opposite of
3-d
figures
2-d
figures
science
exponents
base
logarithms
homophonic
partner
sports
number
systems
Recommendation 5:
Best practices are an inherent part
of a curriculum that exemplifies the
connection and relevance identified
in educational research.
They interject rigor into the
curriculum by developing thinking
and problem-solving skills through
integration and active learning.
Recommendation 6:
When incorporated into classroom practice, the
formative assessment process provides information
needed to adjust teaching and learning while they
are still happening.
The process serves as practice for the student and a
check for understanding during the learning
process.
The formative assessment process guides
teachers in making decisions about future
instruction.
Observations
Four Corners
Discussion
Graphic Organizers
Visual Representations
Kinesthetic Assessments
Individual Whiteboards
Learning/Response Logs
Questioning
Think Pair Share
Exit/Admit Slips
Peer/Self Assessments
Recommendation 7: Increased
Student Engagement
Create a Culture of Explanation Instead of a
Culture of the Right Answer
Find the area of the region shown
below.
Support
metacognition
Recommendation 8: Questioning
Strategies
Lower Level
• What is photosynthesis?
• What is the name of the main character in the story?
• 9×3=→?
Higher Level
• How is the formula for photosynthesis similar to respiration?
• Who is your favorite character in the story? Why?
• How could you simplify this equation: 9x + 27y = 153?
Convergent vs Divergent
Examples of convergent questions:
•How many of the pilgrims who sailed on the Mayflower
survived the first winter?
•Which is smaller, 5/16 or 3/8?
•Is saltwater denser than freshwater?
Examples of divergent questions:
•What do you predict will happen?
•What can you tell me about shadows?
•What sacrifices made by settlers traveling west by covered
wagon would be most difficult for you?
•What different strategies can we use to solve the problem?
Academic Language
Recommendation 9: Content Support
Grade 3
Recommendation 10:
students
parents
administrators
EVERYBODY
needs a
chance and a
champion
And that champion is you!