Nathan Albertin, Jenny Harris

Becky Putt, Susie Sherlow

EDU 551 Mastery Strategies 1. Graduated Difficulty

2. New American Lecture

3. Direct Instruction

4. Teams, Games and Tournaments Mastery Strategies:

What are they? Students function at different levels of proficiency and comprehension in our classrooms. Some students may not be ready for the most challenging problems, while others become bored with problems and concepts that they have already mastered. This means that when teachers rely on one-size-fits-all teaching and problem-solving approaches, students at both the higher and lower levels of proficiency will likely become frustrated and may disengage from the learning at hand. Graduated Difficulty:

Strategy Overview New American Lecture:

Strategy Overview Strategy Overview Direct Instruction: Please answer at least one of the following questions in our discussion room! Discussion

Question Strategy Overview Why are these

strategies

so successful? They focus on increasing student abilities in the area of remembering and summarizing. They provide a clear and effective sequence, useful and timely feedback, and provide a very clear and measurable objective. They allow several opportunities for students to experience success. What skills does

Mastery Learning

involve? Mastery Learning relates best

to explanation, application

and perspective when making

connections to the 6 facets. Mastery learning provides a focus on skills involving read and study (i.e. taking notes), vocabulary and reading and interpreting, as well as analyzing and summarizing. In a Graduated Difficulty lesson, the teacher creates three levels of problems, all representing the same concept or skill but at distinct levels of challenge. The first level requires students to demonstrate basic knowledge, understanding, and proficiency associated with the concept or skill. The second level includes an extension or challenge that requires students to apply their knowledge, understanding, and proficiency beyond the basic level. The third level calls for the application of higher levels of reasoning within or even beyond the context of the concept or skill. Graduated Difficulty:

How to Use the Strategy 1. Select a concept or skill you want your students to master.

2. Develop three problems or problem sets that represent three levels of difficulty.

3. Explain the process and the value of accomplishment associated with the varying levels of difficulty. Make sure students understand that three levels of difficulty are provided so they can analyze their own skill and comprehension levels, make choices, succeed, advance to higher levels, and get the most out their learning experience.

4. As students analyze the different problems, encourage students who are capable to select the more challenging levels, and assure all students that it’s okay to begin with the easier problems and to switch levels during the activity. Provide an answer key (or rubric) so students can check their work.

Students who successfully complete the level-three problems can serve as coaches for other students, or they can design even more challenging problems of their own and then solve them.

After all the students complete their work, invite students to present their solutions to the class.

At the conclusion of the Graduated Difficulty activity, help students establish personal goals for improvement. Provide additional tasks or problems so students can build their knowledge, understanding, and proficiency. The additional practice can come in the form of in-class work or homework.

Graduated Difficulty:

The strategy in action Topic: Three Levels of Solving Quadratic Equations

Quadratic Formula: If ax^2+bx+c=0,then x=(-b ± √(b^2-4ac))/2a .

I. Perfect Squares or Real Numbers

Solve quadratic equations with real or perfect square roots using the Quadratic Formula.

x^2-10x+25=0

x^2+2x+1=0

4x^2+4x-3=0

x^2-8x+7=0 II. Irrational Roots

Solve by using the quadratic equation. Leave irrational roots in simplest radical form. (Hint: You may have to write problems in standard form first.)

1. 3x^2+5x+1=0

2. 2x^2-8x+3=0

3. x^2+4x=3

4. -2x^2-6x=-3 III. Imaginary Roots

Solve each equation using the quadratic formula. Leave imaginary roots in simplest radical form.

x^2-4/5 x+5/25=0

x^2-2x-5=0

-2x^2-x-0.3=0

4x^2+20x=-23

3x^2+10x=4x Strategy Benefits • Increased opportunities for all learners to succeed

• Higher levels of student engagement and focus

• Boosts in student confidence with more students attempting higher-level tasks

• Development of task-analysis and self-assessment skills as students work to find the best match for themselves

• Establishment of a collaborative environment in which teachers work with students as they reflect on and discuss their work, their decisions, and their goals What makes the strategy especially appealing to students is the choice. Choice is a strong intrinsic motivator, and it allows the teacher to challenge students in a supportive environment. An additional benefit is the development of students’ goal-setting skills, which has been shown to increase their achievement levels. How can we make the information we present in the classroom more engaging and more memorable?

New American Lecture provides teachers with a strategic way of delivering content and providing direct instruction in the classroom. In a typical New American Lecture, the teacher provides students with five kinds of support: 1.The students are prepared for the lecture with an engaging hook that bridges background knowledge to the new content. 2.The teacher presents brief chunks of content which students record on a visual organizer that lays out the structure of the lecture content. 3. Memory devices and active participation

techniques are used to make the content more memorable. 4. The teacher pauses after each chunk and poses a review question. 5.The teacher provides time for students to process content and/or practice skills with synthesis and reflection activities during and after the lecture. Phases of the Lecture: The Strategy in Action Mrs. Sherlow teaches Algebra. She will use New American Lecture to teach her students about three common transformations: translations, reflections, and dilations.

Phase One: Prepare Students for Learning

Begin the lesson by asking students if they’ve seen any of the Transformers movies. “What do you know about Transformers? Why are they called Transformers?” After students offer their ideas, explain that Transformers help illustrate a critical concept in mathematics: transformation. Provide students with a simple definition of transformation and then helps students brainstorm some real-world examples, including

• Changing an assigned seat in the classroom

• Changing lanes while driving

• Changing the size of a photograph or computer graphic

• Changing direction while dancing

With each new example, ask students to think about two questions: 1) What does each type of change look like? 2) What does each change feel like? Then, to focus students’ attention on the specific content of the lecture, ask students to describe the actual or apparent change in their physical position or size if they

• Took one step backward (translation)

• Looked in a full-length mirror (reflection)

• Viewed a 3" × 5" picture of themselves (dilation) Phase Two: Present the Content

Distribute a visual organizer designed around the three transformations. For each transformation, students have to take notes that define the transformation, then show it visually, represent it algebraically, and cite at least one real-world example.

Example of a student’s partially completed organizer: Phase Three: Pause Every 5 Minutes

Each type of transformation represents one chunk of the lecture, and each should take roughly 5 minutes to present. After each 5-minute segment, stop lecturing, give students an extra minute or two to complete their notes, and then pose a question to help students think more deeply about transformations and how to apply them. To engage all learners and to help students develop greater perspective and understanding of the content, rotate the styles of the questions that are posed.

After the first chunk on translations, ask a mastery question designed to help students practice and review what they learned: In terms of a function f(x), can you algebraically define g(x), a horizontal translation of eight units?

After the second chunk on reflections, pose an understanding question focused on comparative analysis: Compare and contrast translations and reflections. What is similar and different about them algebraically, graphically, and numerically?

After the third chunk on dilation, pose an interpersonal question focused on real-world applications of the three transformations: Many careers, especially those involving design, use transformations as part of the planning and creative process. Think of a career activity that might use these three types of transformations (architect, artist, graphic designer, etc.). Describe or illustrate how all three types of transformations might be part of the career activity. Phase Four: Practice/Process

For the final phase of the New American Lecture, help students develop mastery over the skill of graphing and describing transformations. A practice activity could include the following:

1. Using the function f(x)=|x|,

a. Graph, label, and describe the transformation y = f (x + 3).

b. Graph, label, and describe the transformation y = f (− x).

c. Graph, label, and describe the transformation y = 2 f (x).

After students have completed the activities, present students with a task that requires them to explain how transformations work numerically and to use their explanations to make mathematical predictions:

For each type of transformation, explain how knowing the value of the constant, in each transformation’s algebraic form, enables you to predict the pattern of change that will be seen in a corresponding set of numerical data. Use a sketch to support your explanation. Direct instruction has a four phase process for obtaining mastery of a skill. This strategy works because research

shows that teachers who spend more time demonstrating and explaining are more

effective than those who don’t. This skill also works for general education students as well as special education students. Four Phase Process Modeling: Teacher first models the skill aloud while also

demonstrating the skill to help students understand. Directed Practice: Students attempt the skill with the teacher’s help. The teacher asks questions and guides them through the process. The students then write down the procedure. Guided Practice: Students ask their own questions while working on the skill. The teacher steps back and becomes a facilitator and observer. Independent Practice: Students continue to

work on the skill on their own and at their own pace. Direct Instruction Lesson Plan Choose a skill you want students to master.

Identify the steps of the skill and convert them into questions.

Choose examples of various stages of practice.

Set up a schedule to practice the skill.

Assess the skill using a synthesis task. (something that has students demonstrate their understanding of the skill.) Strategy In Action Skill: Basic Addition (one digit) with counters.

Modeling: Teacher models skill with counters. Does 3-4 examples and explaining what he/she is doing. “ Look at the problem (2+4). Say the problem 2 + 4. Look at the first number (2). Count out two counters. Then look at the second number (4). Count out four counters. Count all the counters together. Touching each counter and saying the numbers out loud (1,2,3,4,5,6). Say the answer (6). Say the number sentence 2+4=6. Write six on your paper.

Continue with other three examples.

Directed Practice: Teacher and students do problems together. Teacher asks questions such as “What comes next?” “Why do you need to count out the counters?” “How do you know you did it correctly?” Write out the procedure with the students. It gives them a visual reminder of the process. Have them visualize doing the skill.

1. Look at the problem.

2. Say the problem.

3. Count out counters for each number.

4. Count all counters together.

5. Say problem with answer.

6. Write down answer. Guided Practice: Continue to practice the skill with problems already made up. Give students the practice problems. Walk around and monitor student progress. Ask students to explain what they are doing and why.

Independent Practice: Give students problems to complete on their own. Have a worksheet ready to pass out. Teams, Games and Tournaments

(TGT) This strategy focuses on cooperation and competition.

Students of all ability levels work together in study teams to review content. Why TGT works * It incorporates the best of cooperation and competition.

* Meets all requirement of an effective learning strategy.

* Builds student learning through repetition and variation.

* Provides good assessment data for teachers.

* Uses a motivation-based scoring model.

* Uses a variety of questions. TGT Steps Prepare a variety of questions/answers about a topic. Give students a study sheet.

Separate students into teams of 3-5 members.

Give teams time to review the content and prepare.

Assign one member of each study team to compete against another member from a different team. (assign according to level – high vs. high). * Explain tournament roles and rules

* Everyone fills out answer sheets

* Players answer verbally

* Challenger can challenge answers

* Checker verifies answer Collect scores and validate results

while students reflect on process.

Post the results. Strategy In Action Topic is the Civil War

Type questions/answer cards and study sheets. Ask questions like who was president of the confederacy? How many states in the union? In what years was the war fought? What does the phrase “hallow ground” mean in Lincoln’s Gettysburg Address?

Divide the class into 4 groups. Give them a day or two to study the review sheet and discuss.

Then create a competition list from the study groups. Pair up students of the same ability level to compete against each other. Explain the rules and roles you have created to the students.

Begin the game. Choose which player to go first. The person to the right of the player is the checker. The person to the left is the challenger.

Player takes the top card from the deck and reads aloud. Everyone writes down their answers on the answer sheet. After everyone has an answer, the player asks the challenger if they want to challenge it while the checker find the answer on the answer sheet. ( Who shot President Lincoln?, John Wilkes Booth) If there’s no challenge, checker reads the answer aloud. If player answer correctly, then they keep the card. If not, read the correct answer and put card back in deck. ( John Wilkes Booth)

If there IS a challenge, challenger answers question before checker reads answer. If challenger answers correctly then they keep card, if not challenger must give a card to the player. If no one is correct then card goes back in the deck. (John Wilkes Booth) Game moves clockwise around the table until cards are gone or no time is left.

Students count their cards.

Scores are totaled based on the scoring sheet.

Players return to study teams and teams scores are determined by adding up all the scores of team members. Question 1:

Pick one of the strategies and give an example of how you could incorporate into your classroom. Question 2:

Which strategy do you believe

is the most realistic for your classroom? Question 3:

How do the

mastery strategies

appeal to our students'

different learning styles? Question 4:

Out of the four strategies, which do you find the most beneficial for your classroom and why?

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# Mastery Strategies

EDU 551
Nathan Albertin, Jenny Harris, Susie Sherlow, Becky Putt

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