Incorporating Technology

Teaching Math to Secondary Students with LD

Culturally Responsive Teaching

Ashley ShahidullahCEP 802A

October 7, 2011

Technology

Technology

National Library of Virtual Manipulatives

http://nlvm.usu.edu/en/nav/vlibrary.html

Quia-Who Want s to be a Millionairehttp://www.quia.com/rr/10206.html

Promethean Planethttp://www.prometheanplanet.com/en/

Teaching Math to Secondary Students

with LD

Many School districts require: ALL students pass at least one

algebra course or high school assessments that include algebra and geometry skills to receive a high school diploma

In Michigan, this is required as part of the Michigan Merit Exam

Michigan Merit Curriculum

• Algebra I, Algebra II, Geometry, and one additional math course during senior year

• 4 years of ELA• Biology, Physics or Chemistry, and one

additional Science credit• Civics, Economics, U.S. History and

Geography and World History and Geography

• Online learning experience• 2 years of foreign language

Emphasize the need to prepare ALL students for algebra beginning in Kindergarten and progressing through each grade

Yet almost half of special educators are not aware of the NCTM standards (Maccini & Gagnon, 2000)

NCTM Standards

NCTM Standards

5 basic goals Learning to value mathematics Becoming confident in their ability to do

math Becoming mathematical problem solvers Learning to communicate

mathematically Learning to reason mathematically

NCTM Standards

http://standards.nctm.org/

1. Teaching prerequisite skills, definitions, and strategies

2. Providing direct instruction in problem representation and solution

3. Providing direct instruction in self-monitoring procedures

4. Using organizers5. Incorporating manipulatives6. Teaching conceptual knowledge7. Providing effective instruction

7 critical components of successful interventions for teaching algebra to secondary students with LD (Maccini et al., 1999)

Strategies (Steele, 2002) Present advance organizers

Review prerequisite skills or concepts no matter how long ago they were taught

Model procedures enough times for clarity

Use step-by-step procedures

Provide sufficient guided and independent practice

Teach the skill of generalization specifically and directly

Use real life and meaningful examples

Strategies continued

Focus on essential ideas for connections and foundations

Use mnemonic strategies

Teach self-questioning and self-monitoring

Teach and practice the use of visual aids

Teach gradually from the concrete to the abstract

Use cooperative learning groups

Teach Prerequisite Skills

Before introducing a new concept, use quizzes or reviews to determine if students have the necessary prerequisite skills

Mnemonic strategies are effective with older students with mild disabilities

S earch the word problem – read it carefully, write down facts and known information

T ranslate the words into an equation in picture form – choose a variable, identify the operation , and represent the problem through manipulatives or picture form

AR

nswer the problem.

eview the solution (i.e., reread the problem, check the reasonableness of the answer

Strategy Questions S earch the word problem (a) Read the problem carefully (b) Ask yourself questions: “What do I know? What do I need to find? (c) Write down the facts

T ranslate the words into an equation in picture form

A nswer the problem

R eview the Solution (a) Reread the problem (b) Ask yourself questions: “Does the answer make sense? Why? (c) Check the answer 

 

I know I have two temperatures :

I can cancel –8 and +8, which leaves me with +9 tiles remaining, therefore, (-8 ° F+ (+17 ° F) = +9 ° F

I checked my answer (+9 remains when I cancel –8 and +8 and I keep my units of 9 ° F)

Problem: On a certain morning in College Park, Maryland, the low temperature was -8 °F, and the temperature increased by 17 °F by the

afternoon. What was the temperature in the afternoon that day?                                 

Direct Instruction in Problem Representation and Problem Solution

Need to teach problem representation (visually representing the problem) and problem solution (applying appropriate procedures to derive solution)

Use a cue card or structured worksheet that includes: “Draw a picture of the problem” “Does the answer make sense? Why?”

Organizers

Using visual organizers helps ALL students analyze and solve problems: Structured worksheets Prompt cards Graphic organizers

Teaching Algebraic Reasoning To students with disabilities as young as

Kindergarten may seem like an unrealistic goal.

If we consider algebraic reasoning as the study of patterns within mathematicswe can certainly approach this type of reasoning at many levels (VanDeWalle, 2001).

Simple repeating patterns: run, ran, run 2, 4, 6, 8, circle, square, circle

Many modifications and strategies can be integrated into effective instruction for students with LD. The strategies discussed in this PowerPoint clearly benefit the population of secondary students with LD however, because good teaching for students with LD is good teaching for everyone, the modifications are also well worth the time and effort required to implement them for the whole class. (Steele, 2002)

Video

See how high school teachers use the National Council of Teachers of Mathematics standards and group learning to reach a broad range of students. In this video, teachers demonstrate the fine art of guiding students through reasoning and problem solving. Students comment on the new way of learning, often expressing frustration as well as the sense of accomplishment they feel when working through problems with peers.

Click on link below – scroll to number 3, “Group Test” video and click on the VOD tab at the right.

http://www.learner.org/vod/vod_window.html?pid=923

Connections In excerpts from eight classrooms, students make connections within mathematics, to other disciplines, and to situations in the real world

Click on link below – scroll to bottom of page – find “Connections” video and click on the VOD tab at the right.

http://www.learner.org/vod/vod_window.html?pid=934

Discussion Questions

What is the purpose of a group test? What different roles could a teacher play in this kind of test setting?

To what degree should a test be novel so that it evaluates how students would use current knowledge to solve a new problem?

How would you assess these students' understanding of the mathematics based on their group discussions?

How would you gather information about the knowledge and skills of students who do not appear to be participating in group work? How would you structure the group assignment so that each group member has an opportunity and is expected to make a contribution?

How would you score a group test? Would different members of the group receive different grades? How would you determine the differences between the grades?

Discussion QuestionsHow does Mr. Cabana empower students by having them use multiple representations?

How does Mr. Cabana empower students by having them use multiple representations?

How would you have intervened in similar or different ways compared to Mr. Cabana? Explain.

Is there a set of definitions, formulas, or procedures that students must memorize in one of your courses? If so, why is it important to memorize this information? Is there any information that students have memorized but don't fully understand? How would you increase their understanding?

Culturally Responsive Teaching

We live and work…

In a culturally diverse world In a culturally diverse country In a culturally diverse community

How do we teach children in our culturally sensitive environment?

Culturally Responsive Teaching: “An approach that empowers students intellectually, socially, emotionally, and politically by using cultural referents to impart knowledge, skills, and attitude.” Gloria Ladson-Billinas

Critical Obstacles to Culturally Responsive Teaching

Negative teacher attitudes

Expectations for students of color and confusing diversity for disability

In Education

The more variance there is between students’ culture, racial, ethnic, or intellectual abilities, the greater the chances their school achievement will be compromised by low or negative teacher expectations.

Children of color, poverty, and disability are subjected to greater unfair teacher attitudes, expectations, and actions.

Disparity in education

Many teachers believe that because students with learning disabilities often look and act “normal”, they should be “normal” students.

Comfort (1992) explains that:Teachers may not know how to plan for

children who do not fit the mold, so they become scared and resentful of these students and their parents. Teachers may sense that they will not be able to provide the child with an appropriate learning environment, that their teaching may be criticized, and that they will be accountable for a child who they could not serve…

“Several researchers (Anyon, 1997; Gay, 2001; Good & Brophy, 1994; Grossman, 1995; Oakes, 1985) have found strong correlations among the educational quality students receive, their race, class, and ethnicity, and teacher’ social attitudes toward and expectations of them.” (Gay, 2002)

Black in America

“a disproportionate number of students from culturally diverse groups have been inaccurately labeled disabled.” Attitudes, values, and behaviors that cause

students from nonmainstream racial, ethnic, and cultural groups to be diagnosed and assigned to special education-stem from misunderstood in incongruencies between home and school cultural standards

What would happen if we disposed of special education LABELS and simply looked at students as conventional and unconventional learners?

Gay, 2003

African Americans interject motion, movement, and emotional energy into their thinking, communication, social relations, and variability in the formats of their self-presentations

May be misdiagnosed as hyperactivity, attention deficit, irritability, attention-seeking, disruption, and being quarrelsome

The reluctance of some Latino students to engage in individual competitive learning activities may be perceived as a lack of motivation and aspiration instead of a possible indication of their cultural socialization toward cooperative group and mutual aid actions in task performance

Gay, 2003

Asian-American children who do not engage readily in conversations and activities with teachers and other students may be considered as exhibiting the social disability traits of being unfriendly, withdrawn, reclusive, insecure, and self-conscious

Gay, 2003

Native American students who frequently learn by observation and reserving task demonstration until mastery is assured may be diagnosed as lacking motivation and interest in learning, and not having adequate strategies for attacking academic problems, which are characteristics attributed to learning disability

Gay, 2003

What does this mean for us?

Instructional Reform

Critical cultural consciousness Culturally responsive classroom

climates Learning communities Multicultural curriculum content Culturally congruent instructional

strategies

Critical Cultural Consciousness Teachers must become critically conscious

of their own cultural socialization and how it affects their attitudes and behaviors toward the cultures of other ethnic groups.

Cultural values, communication styles, learning styles, contributions, social problems, and levels of ethnic identity development and affiliation are important to know and have direct implications for teaching and learning.

Classroom Climate

The physical layout of the classroom, psychoemotional tone, and quality of interactions among and between students and teachers have a significant impact on learning.

Most students of color perform much better in emotionally warm, caring, and supportive classroom climates (Gay, 2001)

Communities of Learners

Much cooperation and collaboration is involved in every learning situation.

People from different cultures, social groups, and backgrounds need to learn how to work together to deal with common concerns.

When you were assigned to cooperative groups in school, how were differences handled? How did students respond to each other? How did the teacher respond?

Multicultural Curriculum and Culturally Congruent Instruction

Students learn better when content is familiar, has high interest appeal, is challenging, and is presented in ways that are linked directly to their prior knowledge and ways of knowing.

How do we get here when teachers have limited input regarding curriculum decisions?

“As the soil, however rich it may be, cannot be productive without cultivation, so the mind without culture can never produce fruit.” -Unknown

References

Steele, M. M., 2002. Strategies for helping students who have learning disabilities in mathematics. Teaching in the Middle School, 8 (3), p. 140-143.

Gagnon, J.C. & Maccini (2001). Preparing students with disabilities for algebra. Teaching Exceptional Children, p. 8-16.

Gay, G. (2002). Culturally responsive teaching in special education for ethnically diverse students: setting the stage. Qualitative Studies in Education, 15 (6), p. 613-629

For next week…

• Draft of lesson plan• Article• Observation folder with 6 total observations