More Rigorous

Mathematics for All-Are We There Yet? If Not, How Do We Get There- Through Equity and Pedagogy

Beatrice Moore LuchinNUMBERS Mathematics Professional

Developmentabluchin@sbcglobal.net

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 ..

• 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

Auditory Tactile Kinesthetic Visual

Independent seat work

Partner work

Small group 3-5

Whole class

modeling and developing correct

mathematical thinking and

reasoning abilities

17

Use < , > or = to make the expression true.

45_____39Adjust “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

2 42 tens 4 ones2o 4

A total of 24

21

Discussion: what is the appropriate “teacher talk” to explain the algorithm for this situation?

48x 7

Academic Language

distinguishes feature indicatesdiagram conclusion outcomebest describes most likely primarilyenabled affect/effect determineevidence relationshipindicated by reasonable affectedvalid conclusion analyzemost accurately

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 KEYWhat 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?

• Ensure mathematics curriculum is based on challenging content

• Ensure that the mathematics curriculum is vertically and horizontally articulated

Recommendation 3: Alignment of ALL materials and activities to the

TEKS

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.

Additional notes:

Term Definition How it is determined

Example

Situation where it is the appropriate measure of central tendency

Mean

Median

Mode

PositiveAddCombineUpIncreaseProfitGain

Negative Subtract Decompose Down DecreaseLoss Opposite of

base

2-d figures

3-d figures

exponents

logarithms

number systems

science

homophonic partner

sports

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 QuestioningFour Corners Think Pair Share Discussion Exit/Admit SlipsGraphic Organizers Peer/Self Assessments Visual RepresentationsKinesthetic Assessments Individual WhiteboardsLearning/Response Logs

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:

Involving all Stakeholders

parents

students

teachers

administrators

Involving all Stakeholders

EVERYBODY needs a

chance and a champion

And that champion is you!