B. UNIT / LESSON PLANNING

SECTION B - UNIT / LESSON PLANNING

CAPTION

This section shows my ability to construct unit and lesson plans, which are primarily differentiated by general and specific objectives respectively. A unit plan provides a holistic perspective of the topics that must delivered, while lesson plans which are contained within each unit are more specific. That is, a unit plan is analagous to a city tour from the sky, while a lesson plan is a similar tour from ground level. Accompanying the unit plan is the learning hierarchy, which is a map that projects the suggested pathway through which concepts in that unit should be taught. In the first component of this section, a unit plan and learning hierarchy are constructed.

The second component consists of four parts which revolve about the theme of lesson plans. The first entry provides a linkage between stated unit and lesson objectives, while the second yields lesson plans with different teaching strategies. Next, the idea of instructional scaffolding is discussed, while the concept of task analysis is explicated in the last entry. This component is significant as it delves into various processes which may provide more student-centered, well articulated and efficient curriculum delivery.

B-1: Learning hierarchy

B-2-a: Sample of instructional objectives for a lesson related to unit goals and objectives.

Lesson 2 – Problem solving with Venn Diagrams

Instructional Objectives: At the end of the lesson, students will be able to:

1. Define the term cardinality of a set. (Cognitive, Knowledge)

2. Deduce the cardinality rule for combined sets. (Cognitive, Algorithmic Thinking, Comprehension)

3. Solve problems, given two set Venn Diagrams. (Cognitive, Problem Solving, Application)

4. Draw Venn Diagrams for worded problems involving two combined sets. (Cognitive, Problem Solving, Synthesis), (Psychomotor)

5. Solve worded problems involving two sets, using Venn Diagrams. (Cognitive, Problem Solving, Application)

6. Develop an appreciation that real-life problems may be solved using Venn Diagrams. (Affective)

Associated Unit Objectives, matched to numbered instructional objectives

1. Analyze information relating to sets and subsets. (1, 2)

2. Illustrate information regarding two sets on a Venn Diagram. (4)

3. Solve problems involving Venn Diagrams. (3, 5)

4. Appreciate the applicability of sets in real life. (6)

Section B – Part 2 (c): Instructional Scaffolding

Part (i): Introduction to Instructional Scaffolding

The idea of scaffolding was inspired by the Social Constructivism theory of Vygotsky, which suggested that learning may be enhanced by social interaction among peers and teachers. Bruner (1996) intimates that learners who veer through a new skill accomplish more with support. Using instructional scaffolding, educators instruct students during the early stages of learning, then gradually remove supports as the student gains competence. Instructional scaffolding is beneficial, since formative feedback is provided through the initial phases of learning. Thus, misperceptions related to content and understanding are immediately localized and addressed, before the student moves to more advanced stages of a task. Scaffolding has the added benefit of creating momentum in learning. Since the sources of error are now localized by the teacher, more time can be spent by the student on discovery. However, it may be quite challenging for a teacher to grant all students such individualized attention within a classroom environment. Thus, much thought and preparation must be directed by the teacher before implementing this instructional strategy.

Part (ii): Component parts of Instructional Scaffolding

According to Hogan and Pressley (1997), there are critical components to the process of instructional scaffolding. These include modelling, explanation, student participation, clarification of student understanding, and inviting students to contribute hints. To implement scaffolding, it is therefore suggested to first model and perform a skill while asking and answering questions aloud, then encourage students for their responses while guiding them with immediate feedback. As students gain competence, the input of the teacher is gradually released, while students contribute more into the problem solving process. Eventually, the student should work independently to answer any questions that are posed.

Part (iv) – Explanation of process depicted on Scaffolding Diagram

The unit plan that has been attached to this section is for a Form two class studying sets and relations.

Learning Objective:

Students are able to organize information involving two combined sets on a relevant Venn Diagram.

Context of the Problem:

Two sets are listed in set notation. They must be combined, and their relationships shown on a Venn Diagram. Thereafter, the regions of the diagram must be enumerated to yield relevant cardinalities.

The scaffold shown will assist students since the material to be covered is partitioned into manageable steps. As a reinforcement, cooperative learning is utilized. Students are tasked with the placement of elements into a Venn Diagram, then counting the number of elements within each region. To begin the task, a transparent Venn Diagram is drawn and students are asked to determine the elements that are common to both sets, which will be placed in the region of intersection. As a preliminary scaffold, students that cannot solve this task will be given assistance by their peers, while the teacher will act as the secondary scaffold. The students will then navigate through four more tasks, with primary and secondary scaffolds offered at each level, until the problem is completely solved. The manageable tiers are delineated in the flow chart attached.

References

Bruner, J. S. 1996. The Culture of Education, Cambridge, MA: Harvard University Press.

Hogan, K. & Pressley, M. (Eds.), 1997. Scaffolding student learning: Instructional approaches and issues. Cambridge, MA: Brookline.

Section B – Part 2 (d): Task Analysis

Part (i): Introduction to Task Analysis

Task analysis refers to strategies that simplify instructional tasks by partitioning them into teachable or manageable steps (Carter & Kemp, 2006), and is vastly applied for a variety of reasons. Firstly, formative assessments may not yield adequate information regarding student learning, whereas task analyses may provide detailed performance assessments regarding specific skills and curriculum sequences (Moyer & Dardig, 1978). The task analysis is therefore an invaluable strategy for tracking student progress, providing both curriculum-related information and reference points for instruction.

There are several ways in which task analyses may be recorded. In one approach, an instructor may ask an expert to write the task analysis (Schuster & Griffen, 1990). Another strategy involves observing a competent learner and recording the steps of the task (Moyer & Dardig, 1978). Another point of note concerns the sequence of steps in a task analysis. Some tasks occur in a rigid sequence, such as substituting and calculating the value of a mathematical function. There are other tasks which may be completed in a variety of ways, such as when computing the roots of a quadratic equation. However, even though there may be relative flexibility in a task analysis, there are usually critical subtasks which must always be observed. Such is the case for the calculation of the discriminant when using the quadratic formula, say.

Part (ii): Components of Task Analysis

Szidon & Franzone (2009) explicate the steps that are involved in a task analysis algorithm. The first component involves the identification of a target skill, which should neither be too simple nor complex, and should ideally take a finite number of discrete steps. For instance, drawing a horizontal line is a discrete skill and too simple, while sketching a cubic polynomial and a circle to locate their points of intersection may be too complex a task. An appropriate target may be to determine the radius and centre of a circle, sketching it on a Cartesian plane. For the second part of the process, the teacher should identify the learner’s prerequisite skills, and this suggests that previously mastered material should be excluded from the task analysis. Next, the teacher deconstructs and sequences the task into manageable steps. A check is then done with the assistance of a colleague or student, to test the task analysis ad verbatim. If the analysis is appropriate, then a relevant teaching strategy is chosen. Finally, the lesson is implemented and the progress of students monitored, to see if learning objectives are being met.

Part (iii): Task Analysis Sheet

Unit: Sets and Relations

Topic: Venn Diagrams

Target Task: Organize information on a Venn Diagram, given two sets A and B.

Pre-Knowledge: Set Notation, Universal Set, Complement, Venn Diagram, Intersection, Union, Subset.

Question:

U = {letters of the word COMPLIMENT}

A = {letters of the word CENT}

B = {letters of the word MINT}

(i) Illustrate the members of these sets on a Venn Diagram.

(ii) Hence, illustrate the numbers of elements in each region on a Venn Diagram.

[nb: Task analysis sheet shown on the right]

Part (iv): Explanation of process that is depicted on the task analysis chart

In the analysis chart shown, the target skill involves the construction of a Venn Diagram with cardinalities. The prerequisite skills are clearly stated, and assumes that the student has a basic knowledge of set notation, Venn Diagrams and so forth. The task is broken down into five manageable steps; the first four assists in the construction of a Venn Diagram that shows elements. The fifth step facilitates the goal of the task, which is the enumeration of regions in the diagram.

References

Carter, M., & Kemp, C. R. (1996). Strategies for task analysis in special education. Educational Psychology, 16 (2), 155-170.

Moyer, J. R., & Dardig, J. C. (1978). Practical task analysis for educators. Teaching Exceptional Children, 11, 16-18.

Szidon, K., & Franzone, E. (2009). Task Analysis. Madison, WI: National Professional Development Center on Autism Spectrum Disorders, Waisman Center, University of Wisconsin.

Schuster, J. W. & Griffen, A. K. (1990). Using time delay with task analysis. Teaching Exceptional Children, 22, 49-53.