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Teaching Strategies:

Affective Domain

Instructional Decision Making
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Affective Domain

The Taxonomy of the Affective Domain
The Affective Domain in the Mathematics Classroom
The Role of the Curriculum

Affective refers to those actions that result from and are influenced by emotions. Consequently, the affective domain relates to emotions, attitudes, appreciations, and values. It is highly personal to learning, demonstrated by behaviors indicating attitudes of interest, attention, concern, and responsibility.

According to the National Guidelines for Educating EMS (Emergency Medical Service) Instructors, the following words describe the affective domain: defend, appreciate, value, model, tolerate, respect.

In the mathematics classroom, the affective domain is concerned with students' perception of mathematics, their feelings toward solving problems, and their attitudes about school and education in general. Personal development, self-management, and the ability to focus are key areas. Apart from cognitive outcomes, teachers stress attitude as the most common affective outcome.

The Taxonomy of the Affective Domain

Most psychologists describe five "levels of understanding" within the affective domain. These five levels define the path from passively observing a stimulus, such as watching a movie or reading a textbook ("receiving"), to becoming self-reliant and making choices on the basis of well formed beliefs ("characterization").
  • Receiving
  • Responding
  • Valuing
  • Organization
  • Characterization.
The major work in describing the affective domain was written by David R. Krathwohl in the 1950s. In his book, Taxonomy of Educational Objectives, Handbook II: Affective Domain (1956), he described the five levels mentioned above. These five levels are restated below with definitions, based on Krathwohl's book, as well as classroom examples.

Krathwohl's Taxonomy of Affective Objectives Commitment to Specific Levels Examples in the Classroom
Receiving The student has an awareness of and attends to what surrounds her and she is willing to take notice of the stimulus. She pays attention to particular stimuli, such as classroom activities, textbooks, and homework assignments. From a teaching standpoint, this level is concerned with getting, holding, and directing the student's attention.
  • Listens attentively
  • Demonstrates an understanding of the importance of learning
  • Responding The student demonstrates active participation by asking and responding to questions. At this level, the student not only attends to a stimulus, but reacts to it in some way.
  • Completes assigned homework
  • Participates in class discussions
  • Volunteers for tasks
  • Shows interest in the subject
  • Helps others (when requested)
  • Asks relevant questions
  • Contributes material for the bulletin board and school newspaper
  • Valuing The student accepts and believes a principle and demonstrates acceptance by debating the issue or making a personal stand on certain value systems. The student sees worth or value in the subject, activity, or assignment. At this level, the student responds not because he has been asked to but as a result of adhering to a particular value.
  • Shows concern for the welfare of others
  • Demonstrates a positive problem solving attitude
  • Appreciates cooperation with his classmates during discussions
  • Offers help to others (without being requested)
  • Shares material with others
  • Encourages other students in the class
  • Asks permission before using another student's materials
  • As appropriate, offers gratitude and congratulations to others
  • Organization The student actively participates and shows commitment by organizing activities such as meetings, working committees, and support groups related to a value system. The student develops an internally consistent value system that results from bringing together a set of values and resolving any conflicts between them. The student begins to develop a "philosophy of life."
  • Accepts responsibility for her own behavior
  • Acknowledges and accepts her own strengths and weaknesses
  • Formulates a life plan consistent with her abilities, interests, and beliefs
  • Formulates well-constructed rationale
  • Considers the needs of others in addition to personal needs
  • Considers the pros and cons of a situation before making a decision
  • Characterization Beliefs are integrated into the student's personality to become part and parcel of his whole value system and character. The student's behavior has reflected these values for a period of time sufficiently long enough that he can be said to have developed a characteristic "lifestyle." The student's behavior is pervasive, consistent, and predictable.
  • Demonstrates self confidence when working independently
  • Cooperates in group activities
  • Shows punctuality and self discipline

  • In the mathematics classroom, and indeed in all classrooms, instructors are role models. Sometimes, we lose sight of this inherent fact, yet we must remember that our actions model the behavior that students will emulate. When focusing on content, we model the procedures and strategies that we would like students to employ when they solve problems on their own. In the same way, we must model the attitudes and behaviors that we would like students to exhibit when interacting with others and making personal decisions.

    Model the behaviors and values that you would like your students to emulate, such as:
    • Honesty
    • Punctuality
    • Fairness
    • Competence
    • Sensitivity
    • Preparedness
    • Dependability
    • Helpfulness
    • Self-reliance.
    Remember that students constantly observe and scrutinize your actions, and immediately correct behaviors that do not model appropriate values. Consider affective objectives when assessing student work. Establish classroom procedures that support affective objectives; that is, through classroom rules, encourage students to be honest, punctual, fair, and so forth, and provide opportunities for them to develop as independent thinkers and self-reliant problem solvers.

    Effective teachers promote inquisitiveness and perseverance, and they do not make statements such as "This is an easy problem." Successful teachers establish good relationships with students by acting more friendly than formal, and they share personal anecdotes about their own problem-solving that reveal their strengths and weaknesses. Effective teachers hold students accountable for performance and base assessment on strategies and communication of conjectures, not simply on finding the correct answer.

    Read what Mike Melville has to say about developing student confidence:

    Read transcript from teacher Mike Melville
    The grouping starts at the beginning of the unit. I pass out cards, and in this class there are eight groups, so I use the numbers Ace to 8... Read More

    As seen in the video for Workshop 6, Part II, Mike Melville creates an atmosphere in which students feel safe to share their feelings, an environment in which students are able to develop emotionally. All students in his class are required to share their thoughts with group partners and to present their ideas to the entire class. Although students may feel intimidated by these activities at the beginning of the year, by the end of the year, they develop confidence in their abilities to discuss mathematics, to present their ideas to others, to disagree when appropriate, and to ask questions when they do not understand.

    The National Council of Teachers of Mathematics (NCTM) asserts in Principles and Standards for School Mathematics (PSSM):
    Learning mathematics is stimulating, rewarding, and at times difficult. Mathematics students, particularly in the middle grades and high school, can do their part by engaging seriously with the material and striving to make mathematical connections that will support their learning. If students are committed to communicating their understandings clearly to their teachers, then teachers are better able to plan instruction and respond to students' difficulties. Productive communication requires that students record and revise their thinking and learn to ask good questions as part of learning mathematics. (PSSM, p. 374)
    While this is likely true, it may at times be difficult to convince students to make connections, ask questions, and communicate their understandings. A classroom in which students are free to share their thoughts and express their ideas - like the classroom that Mike Melville has established - will go a long way in ensuring that all students learn.

    Read what Jane Schielack has to say about the classroom environment:

    Read transcript from teacher educator Jane Schielack
    It was clear that the environment in [Melville's] classroom was very conducive to students feeling safe about sharing their questions with each other... Read More

    Read what Mike Melville has to say about encouraging participation from all students:

    Read transcript from teacher Mike Melville
    I have some students who are very, very interpersonal and so they keep the groups going... Read More

    Reflection:
    What policies, rules, and regulations have you enacted to help your students proceed through the five levels of the affective domain? In other words, what do you do to help your students progress from being passive recipients of knowledge ("receiving") to being self-confident thinkers with admirable values ("characterization")?

    record your thoughts in your journal



    The Affective Domain in the Mathematics Classroom

    Imagine a classroom, a school, or a school district where all students have access to high-quality, engaging mathematics instruction ... Students confidently engage in complex mathematical tasks chosen carefully by teachers. They draw on knowledge from a wide variety of mathematical topics, sometimes approaching the same problem from different mathematical perspectives or representing the mathematics in different ways until they find methods that enable them to make progress. Teachers help students make, refine, and explore conjectures on the basis of evidence and use a variety of reasoning and proof techniques to confirm or disprove those conjectures. Students are flexible and resourceful problem solvers. Alone or in groups, and with access to technology, they work productively and reflectively, with the skilled guidance of their teachers. Orally and in writing, students communicate their ideas and results effectively. They value mathematics and engage actively in learning it. (PSSM, p. 3).
    The above passage advocates a mathematical education that contains rich mathematics, complex tasks, and the use of technology. Yet NCTM does not promote that those three components are enough to successfully teach all students. The phrases highlighted above in bold (emphasis added by this author) show that NCTM pays attention to the affective domain - that is, the council recognizes that how students perceive mathematics is at least as important as the topics they study.

    As the affective domain is concerned with student attitudes and beliefs, one goal for teachers should be to make students believe that mathematics is useful, interesting, and tangible. In addition, teachers should promote self confidence by helping all students experience success in the classroom.

    Reflection:
    Consider the adjectives used to describe mathematics students in the passage above: confident, flexible, resourceful, productive, reflective, active. Of course, there are also the implied adjectives: persistent, determined, open minded, resolute, cooperative. List at least three things that you do to create confident students, persistent problem-solvers, and active learners.

    record your thoughts in your journal


    The Role of the Curriculum

    The curriculum is the single most important factor in whether students will find mathematics both exciting and necessary. As PSSM states:
    A school mathematics curriculum is a strong determinant of what students have an opportunity to learn and what they do learn. In a coherent curriculum, mathematical ideas are linked to and build on one another so that students' understanding and knowledge deepens and their ability to apply mathematics expands. (PSSM, p. 14.)
    In addition to providing the content of what they learn, a solid curriculum also provides motivation for learning. As stated in a recent issue of the journal Educational Leadership:
    A teacher's personality, voice, and style of instruction are not key factors in producing boredom. Instead, boredom is primarily an effect of curriculum. Curriculum design based on four natural human interests - the drive toward mastery, the drive to understand, the drive toward self-expression, and the need to relate - will not only reduce student boredom, but will yield boredom's opposite: abiding interest in the content that students need to learn. ("Boredom and Its Opposite." Educational Leadership, September 2003: pp. 24-29.)
    Students express their desire to make sense of the world by raising questions, pointing out errors, insisting on explanations, and sharing their opinions. Conversely, when these behaviors are not present, it's likely that students are uninterested. The following student-interest rubric can be used to evaluate your classroom, to assess your curriculum, and to gauge your effectiveness in the affective domain.

    Student-Interest Rubric for Curriculum Design

    Think of a unit you teach and consider the following questions in terms of the unit's strengths and weaknesses in each area.
    MASTERY
    • Is the goal of the unit defined in terms of a product or performance?
    • Have students been involved in analyzing the competencies and qualities of the product or performance?
    • Have the constituent skills been clearly modeled?
    • How well has on-the-spot feedback and refinement been built into the work?
    INTERPERSONAL
    • How closely connected to the real world are the content and products of the unit?
    • How well-designed is the use of audiences, clients, and customers as a way to stimulate reflection and improvement?
    • How carefully modeled are strategies for collecting real-world information and communicating with authentic audiences?
    • How vital a role do real-world samples of products and performances play in the unit?
    UNDERSTANDING
    • Is the unit organized around provocative questions?
    • Are the sources used in the unit sufficiently challenging and based on powerful ideas?
    • Does the unit teach students strategies for evaluating ideas and evidence?
    • Are students able to critique and correct their own and others' products and ideas?
    SELF-EXPRESSION
    • How strong a role does choice play in the unit?
    • How regularly are strategies for creative thinking modeled?
    • Is a rich set of samples available for student study?
    • Are discussions of student work used to drive student progress?
    Source: "Boredom and Its Opposite." Educational Leadership, September 2003: pp. 24-29.

    Data suggests that students generally believe that mathematics is important yet difficult, that it is based on a set of rules, and that it is skill-oriented. Researchers note that while teachers do not share these same beliefs, a poorly designed curriculum may contribute to students' negative attitudes toward the discipline. As a consequence, students' narrow views on mathematics may weaken their ability to solve non-routine problems, especially if they believe problems should always be completed quickly.

    To supplant these beliefs, teachers must invigorate the curriculum with activities that promote student engagement and that require thought and deliberation at an appropriate cognitive level. For students to grasp that mathematics is necessary and attainable, they must participate in mathematical simulations that foster conceptual understanding, realize that the material they are learning is necessary, and experience real world examples that make the mathematics tangible.

    Using Mathematical Simulations

    Simulations, such as the Skeeters activity Orlando Pajon used in the video for Workshop 6 Part II, help to foster positive feelings toward mathematics. In general, students enjoy simulations because:
    1. They are tactile and fun.
    2. They typically represent a situation in the real world.
    3. They are tangible and usually more comprehensible than abstract ideas.
    4. They promote student success because most students will require a similar amount of time to explore. This differs from solving simple, routine problems, which some students do quickly while others struggle.
    With each shake of the box containing Skeeters, students were able to see and understand the results. They were able to notice that each time, approximately half of the Skeeters were showing a mark, indicating that the population would grow by one half at each stage. Because of the tactile nature of the simulation, students were able to form the mathematical connections between the actual numbers and the exponential model that described the situation. This is in concert with NCTM's belief that students must recognize the mathematical connections between the ideas they learn. A curriculum which fosters these connections is imperative.

    According to PSSM:
    Students will be served well by school mathematics programs that enhance their natural desire to understand what they are asked to learn. From a young age, children are interested in mathematical ideas. Through their experiences in everyday life, they gradually develop a rather complex set of informal ideas about numbers, patterns, shapes, quantities, data, and size, and many of these ideas are correct and robust. (PSSM, p. 20.)
    Read what Orlando Pajon has to say about a teacher's role during simulations:

    Read transcript from teacher Orlando Pajon
    One of the most important components of this curriculum is that the teacher serves as a facilitator of the learning... Read More

    Hear what Orlando Pajon has to say about student explorations in the affective domain:

    Listen to audio clip of teacher
    Orlando Pajon
    First of all they are required to work in teams, which means that before they give an answer to a topic, they have to share their individual views about that question... Read More


    Explain Why the Material Is Necessary

    No mathematics classroom is free of the question "When are we ever going to use this?" Students ask this question all the time, and unless we are able to provide acceptable answers, students may believe that mathematics has no use in their lives.

    At the same time, answering "Why do we need this?" can be difficult. When teaching the rules of exponents, for instance, it's not always easy to explain why students must know the rules regarding a product of powers. And the justifications - "Because it'll be on the test" or "Because you'll need it for other math classes" - generally don't satisfy inquisitive teenagers.

    Questions about the necessity of a topic, however, can often be diffused at the outset. Prior to a unit or lesson, an explanation of why the material students are about to learn is important should set the stage. You may also encourage and challenge students to investigate the topic for themselves and to bring potential applications and uses to the class. If the material is mostly needed for advanced study or to improve their understanding of the structure and language of mathematics, offer this explanation before students question the need for the topic. This way, you may avert classroom-management and motivation issues.

    Present Real-World Examples

    The students in Mike Melville's class experienced an activity that had fewer real-world applications than Orlando Pajon's population simulation. Students in Melville's class considered the size of Alice when she ate cake (and her size doubled) or drank beverage (and her size reduced by half). Yet the fact that it was tangible - that students could understand how Alice's height changed, and that they could imagine her growing and shrinking as she consumed - made the mathematics of the activity concrete. Most importantly, the situation allowed students to see how exponents influence the value of a number.

    Hear what Mike Melville has to say about helping students understand abstract concepts:

    Listen to audio clip of teacher
    Mike Melville
    I think for most students mathematics is abstract and the way it's been approached by them in their past has been from an abstract basis... Read More

    Research suggests that many of the instructional strategies that promote mathematical achievement also promote growth in the affective domain. Teachers should incorporate group work and assign tasks more compatible with the development of higher-order thinking skills. In their work, students should experience the wonder of discovery in mathematics, and teachers need to present more problem-solving and fewer skill-based assignments in the classroom. To help alleviate problem-solving anxiety and to expand student attitudes about the length of time required to complete a task, teachers should assign problems that require and foster research skills and that may have more than one possible solution.

    In short, to foster positive student attitudes regarding mathematics, the activities and assignments in which they engage ought to challenge them; require them to struggle, persist, and succeed; and show them the beauty of mathematics that math educators already see.

    Reflection:
    Explain how the activities, tasks, and problems in your curriculum relate to the affective domain.

    record your thoughts in your journal


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