Essay Grade

GCU College of Education
LESSON PLAN TEMPLATE
Section 1: Lesson Preparation
Teacher Candidate
Name:
Grade Level:
Date:
Unit/Subject:
Instructional Plan Title:
Lesson Summary and
Focus:
In 2-3 sentences, summarize the lesson, identifying the central focus
based on the content and skills you are teaching.
Classroom and Student
Factors/Grouping:
Describe the important classroom factors (demographics and
environment) and student factors (IEPs, 504s, ELLs, students with
behavior concerns, gifted learners), and the effect of those factors on
planning, teaching, and assessing students to facilitate learning for all
students. This should be limited to 2-3 sentences and the information
should inform the differentiation components of the lesson.
National/State Learning
Standards:
Review national and state standards to become familiar with the standards
you will be working with in the classroom environment.
Your goal in this section is to identify the standards that are the focus of
the lesson being presented. Standards must address learning initiatives
from one or more content areas, as well as align with the lesson’s learning
targets/objectives and assessments.
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LESSON PLAN TEMPLATE
Include the standards with the performance indicators and the standard
language in its entirety.
Specific Learning
Target(s)/Objectives:
Learning objectives are designed to identify what the teacher intends to
measure in learning. These must be aligned with the standards. When
creating objectives, a learner must consider the following:
•
Who is the audience
•
What action verb will be measured during instruction/assessment
•
What tools or conditions are being used to meet the learning
What is being assessed in the lesson must align directly to the objective
created. This should not be a summary of the lesson, but a measurable
statement demonstrating what the student will be assessed on at the
completion of the lesson. For instance, “understand” is not measureable,
but “describe” and “identify” are.
For example:
Given an unlabeled map outlining the 50 states, students will accurately
label all state names.
Academic Language
In this section, include a bulleted list of the general academic vocabulary
and content-specific vocabulary you need to teach. In a few sentences,
describe how you will teach students those terms in the lesson.
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LESSON PLAN TEMPLATE
Resources, Materials,
Equipment, and
Technology:
List all resources, materials, equipment, and technology you and the
students will use during the lesson. As required by your instructor, add or
attach copies of ALL printed and online materials at the end of this
template. Include links needed for online resources.
Section 2: Instructional Planning
Anticipatory Set
Your goal in this section is to open the lesson by activating students’ prior knowledge, linking
previous learning with what they will be learning in this lesson and gaining student interest for the
lesson. Consider various learning preferences (movement, music, visuals) as a tool to engage
interest and motivate learners for the lesson.
In a bulleted list, describe the materials and activities you will use to open the lesson. Bold any
materials you will need to prepare for the lesson.
For example:
•
I will use a visual of the planet Earth and ask students to describe what Earth looks
like.
•
I will record their ideas on the white board and ask more questions about the amount of
water they think is on planet Earth and where the water is located.
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LESSON PLAN TEMPLATE
Multiple Means of Representation
Learners perceive and comprehend information differently. Your goal in this section is to explain
how you would present content in various ways to meet the needs of different learners. For
example, you may present the material using guided notes, graphic organizers, video or other
visual media, annotation tools, anchor charts, hands-on manipulatives, adaptive technologies,
etc.
In a bulleted list, describe the materials you will use to differentiate instruction and how you will
use these materials throughout the lesson to support learning. Bold any materials you will need
to prepare for the lesson.
For example:
•
I will use a Venn diagram graphic organizer to teach students how to compare and
contrast the two main characters in the read-aloud story.
•
I will model one example on the white board before allowing students to work on the
Venn diagram graphic organizer with their elbow partner.
Explain how you will differentiate materials for each of the following groups:
•
English language learners (ELL):
•
Students with special needs:
•
Students with gifted abilities:
•
Early finishers (those students who finish early and may need additional
resources/support):
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LESSON PLAN TEMPLATE
Multiple Means of Engagement
Your goal for this section is to outline how you will engage students in interacting with the content
and academic language. How will students explore, practice, and apply the content? For
example, you may engage students through collaborative group work, Kagan cooperative
learning structures, hands-on activities, structured discussions, reading and writing activities,
experiments, problem solving, etc.
In a bulleted list, describe the activities you will engage students in to allow them to explore,
practice, and apply the content and academic language. Bold any activities you will use in the
lesson. Also, include formative questioning strategies and higher order thinking questions you
might pose.
For example:
•
I will use a matching card activity where students will need to find a partner with a card
that has an answer that matches their number sentence.
•
I will model one example of solving a number sentence on the white board before having
students search for the matching card.
•
I will then have the partner who has the number sentence explain to their partner how
they got the answer.
Explain how you will differentiate activities for each of the following groups:
•
English language learners (ELL):
•
Students with special needs:
•
Students with gifted abilities:
•
Early finishers (those students who finish early and may need additional
resources/support):
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LESSON PLAN TEMPLATE
Multiple Means of Expression
Learners differ in the ways they navigate a learning environment and express what they know.
Your goal in this section is to explain the various ways in which your students will demonstrate
what they have learned. Explain how you will provide alternative means for response, selection,
and composition to accommodate all learners. Will you tier any of these products? Will you offer
students choices to demonstrate mastery? This section is essentially differentiated assessment.
In a bulleted list, explain the options you will provide for your students to express their knowledge
about the topic. For example, students may demonstrate their knowledge in more summative
ways through a short answer or multiple-choice test, multimedia presentation, video, speech to
text, website, written sentence, paragraph, essay, poster, portfolio, hands-on project, experiment,
reflection, blog post, or skit. Bold the names of any summative assessments.
Students may also demonstrate their knowledge in ways that are more formative. For example,
students may take part in thumbs up-thumbs middle-thumbs down, a short essay or drawing, an
entrance slip or exit ticket, mini-whiteboard answers, fist to five, electronic quiz games, running
records, four corners, or hand raising. Underline the names of any formative assessments.
For example:
Students will complete a one-paragraph reflection on the in-class simulation they experienced.
They will be expected to write the reflection using complete sentences, proper capitalization and
punctuation, and utilize an example from the simulation to demonstrate their understanding.
Students will also take part in formative assessments throughout the lesson, such as thumbs upthumbs middle-thumbs down and pair-share discussions, where you will determine if you need to
re-teach or re-direct learning.
Explain if you will differentiate assessments for each of the following groups:
•
English language learners (ELL):
•
Students with special needs:
•
Students with gifted abilities:
•
Early finishers (those students who finish early and may need additional
resources/support):
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LESSON PLAN TEMPLATE
Extension Activity and/or Homework
Identify and describe any extension activities or homework tasks as appropriate. Explain how the
extension activity or homework assignment supports the learning targets/objectives. As required
by your instructor, attach any copies of homework at the end of this template.
Rationale/Reflection
After writing your complete lesson plan, explain three instructional strategies you included in your
lesson and why. How do these strategies promote collaboration, communication, critical thinking,
and creativity? Bold the name of the strategy.
For example:
.
• Think-Pair-Share promotes engagement, communication, and collaboration because all
students get a chance to share their ideas or answers. This is beneficial to students
because they get to put their ideas into words, and hear and discuss the perspectives of
others.
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Math Tools and Strategies for Differentiating Instruction and
Increasing Student Engagement
Presented by:
Daniel R. Moirao, Ed.D (TrDan)
Pam L. Warrick, PhD (TrPam)
ASCD | 2010 Annual Conference | San Antonio, TX | Monday March 8, 2010
Table of Contents
Math Tools and Strategies for Differentiating Instruction and Increasing Engagement ……………… 1
The Human Element of Mathematics ………………………………………………………………………………………… 2
What Is Mathematical Literacy? ………………………………………………………………………………………………… 3
Teaching With Style ………………………………………………………………………………………………………………….. 8
Five Ways to Use Math Tools …………………………………………………………………………………………………… 9
Math Notes ……………………………………………………………………………………………………………………………… 10
The Canoe Problem ………………………………………………………………………………………………………………… 13
Mastery | Fist Lists and Spiders …………………………………………………………………………………………… 14
Understanding | Always-Sometimes-Never (ASN) ………………………………………………………………. 16
Understanding | Three-Way-Tie …………………………………………………………………………………………… 18
Self-Expressive | M + M: Math and Metaphors…………………………………………………………………….. 20
Self-Expressive | Group and Label ………………………………………………………………………………………. 22
Interpersonal | Who’s Right? ……………………………………………………………………………………………….. 26
Math Tools and Strategies for Differentiating Instruction and Increasing Engagement
Our Thoughtful questions:
•
Why do some students succeed in mathematics while others do not? Is it a matter of skill
or will?
•
How can we use research-based teaching tools and strategies to address the styles of
all learners so they succeed in mathematics?
Our workshop is based on the following assumptions:
•
What teachers do and the instructional decisions they make have a significant impact on
what students learn and how they learn to think.
•
Different students approach mathematics using different learning styles and need
different things from their teachers to achieve in mathematics.
•
Style-based mathematics instruction is more than a way to invite a greater number of
students into the teaching and learning process; it is, plain and simple, good math—
balanced, rigorous, and diverse.
In this workshop, you will learn:
•
The characteristics of the four basic mathematical learning styles (Mastery,
Understanding, Self-Expressive, and Interpersonal) and how to assess both your own
mathematical teaching style and your students’ mathematical learning styles.
•
How to use a variety of mathematical teaching tools and strategies to differentiate
instruction and increase student engagement.
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Page 1
The Human Element of Mathematics
Describe a personal incident in your life using as many mathematical terms as
you can (in the box below). Then meet with a neighbor to share and compare
your stories. Keep count of how many mathematical terms are used.
Mathematical Story
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Page 2
What Is Mathematical Literacy?
Mastery of procedural and
conceptual knowledge.
A language to communicate ideas and
solve real-world problems.
_______________________
_______________________
Understanding of logical reasoning to
explain and prove a solution.
Application of strategies to formulate and
solve problems.
_______________________
_______________________
What percentage of your classroom practice would you estimate you spend in each of these
areas? (Write your percentage on the line in each box above).
How does your classroom practice compare with the NAEP data?
NAEP data shows that proficiency in these four areas has developed unevenly.
In many classrooms, students are able to mimic rules and procedures
demonstrated by their teacher: however, students often acquire these skills with
little depth of understanding or the ability to use them to solve complex problems
(Kowley & Wearing 2000).
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Page 3
Mastery Learners
In general, Mastery learners want to work and do well in school. When they withdraw from
learning, many of their problems can be addressed cognitively according to four basic
principles:
ƒ
Mastery students are motivated by clarity, competence, and success. Motivation starts
with clear expectations. Set explicit and measurable goals for both academic achievement
and behavior. The better Mastery students know the criteria for evaluating their
performance, the more they will work to meet them.
ƒ
The skills necessary for success hold whether the skill is fairly straightforward (e.g., studying
for a test on factoring) or it’s a more abstract and complex skill, such as making inferences,
establishing a thesis for an essay, or developing a plan for solving a word problem. The
more explicitly the teacher models the skill, the stronger Mastery students will perform.
ƒ
Mastery students need lots of practice on key skills and central concepts. It is not
necessary to reduce the thinking, reading, writing, or problem-solving in their work; it is
only necessary to provide more practice and better feedback on their performance.
ƒ
When it comes to learning complex content, Mastery students need organizational tools.
They frequently fool us because they are so good at following directions, but their
tendency to focus on details makes it difficult for them to see and use the higher-level
concepts necessary to understand abstract content. The use of visual organizers, as well
as effective modeling and practice of study skills, can provide an effective boost to
Mastery learners.
Possible Solutions for Mathematics
ƒ
Focus work in mathematics around a math log where students do fewer, but more
complex problem-solving assignments. Insist that students illustrate and prove the
reasoning they use.
ƒ
Emphasize the role of diagramming in interpreting and solving problems in mathematics.
ƒ
Use samples of high, medium, and low student problem-solving, and explanations of
reasoning to provide a touchstone to help Mastery learners assess their progress.
ƒ
Model reasoning and explaining processes frequently.
ƒ
Make sure that a high percentage of student work involves word problems.
ƒ
Provide visual organizers at the beginning of units to show the central concepts and
kinds of problems that will be addressed.
ƒ
Use manipulatives, but remember that for Mastery learners two of the best tools are
money and graph paper.
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Page 4
Understanding Learners
In general, Understanding learners like to be engaged in critical thinking and academic
learning. When they withdraw from learning, many of their problems can be addressed
cognitively according to four basic principles:
ƒ
Increase the intellectual content of the curriculum and the complexity of the thinking
tasks assigned.
ƒ
Provide clear reasons for routine work and a system that permits Understanding
learners to measure and assess their own progress in these areas.
ƒ
Where the curriculum calls for exploration of personal experiences or cooperative
group work, model explicitly how this work is done but also permit discussion of why it
is important.
ƒ
Emphasize the role of reflection in deep learning. Model and practice with students how
to become aware of the thinking and attention processes they are using in solving
problems or collecting information.
Possible Solutions for Mathematics
• Focus work in mathematics on solving a small number of complex problems rather than a
larger number of simpler exercises.
• Explicitly model for students how to observe and take notes on their problem-solving
processes while they are doing math.
• Explicitly model and practice how to use notes taken during the problem-solving process to
build specific explanations.
• Provide a visual organizer at the beginning of a unit to show not just the central concepts
and kinds of problems that will be addressed, but the intriguing questions that will be
explored as well (e.g., “When is a fraction superior to a percentage and vice versa?”).
• Make sure Understanding students can compute easily and well, but emphasize the use of
mental math rather than either routine algorithms or calculators.
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Page 5
Self-Expressive Learners
In general, Self-Expressive learners need opportunities for choice, to express their creativity,
and to pursue project work that stimulates their imaginations. Whenever learning becomes
rote or they have few or no opportunities to pursue their interests, Self-Expressive students
may lose their motivation. When they withdraw from learning, many of their problems can be
addressed cognitively according to four basic principles:
ƒ
Increase the imaginative stimulation in the content by focusing on large and engaging
ideas, investigating curious and mysterious objects, going on field trips, telling stories,
and working on imaginative projects.
ƒ
Provide more sustained time for reading, writing, problem-solving, and research.
ƒ
Ensure that there are frequent opportunities for coaching and conversation.
ƒ
Explicitly model and practice all routine and organizational skills.
Possible Solutions for Mathematics
• Focus mathematics learning on problem-solving (first), writing and illustrating mathematical
ideas (second), and computational precision (third).
• Regularly emphasize the relationship between art and mathematics.
• Wherever possible, replace worksheets on computation with practice in mental
computation where students solve problems in their heads and then discuss and
compare strategies.
• Explicitly model and practice computational algorithms and the use of formulas only after
students have taken considerable time to explore mathematical ideas.
• Explicitly teach students how to use their natural tendency to form images in their mind’s
eye to create diagrams for the problems they are solving.
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Page 6
Interpersonal Learners
In general, Interpersonal learners want to “experience” learning, and forge social connections
during the process. As learning becomes increasingly abstract and seems to have little to do
with human feelings and personal experiences, these learners often lose motivation. When they
withdraw from learning, many of their problems can be addressed cognitively according to four
basic principles:
ƒ
Connect content and tasks as closely as possible to students’ experiences and realworld contexts, especially those connected to the students’ own communities.
ƒ
Increase preparation for, and implementation of, learning partners (student pairs) and
cooperative learning groups.
ƒ
Build more opportunities for discussion and the sharing of personal opinions and values
into the learning process.
ƒ
Use explicit modeling, practice, feedback, and organizational strategies to develop
students’ capacities for handling abstract concepts and complex tasks.
Possible Solutions for Mathematics
• Continually provide opportunities for students to solve complex math problems
through conversation and collaboration in small groups and learning partnerships.
• Provide opportunities for students to teach their new mathematical ideas to others.
• Model and practice a variety of ways of representing mathematical ideas and procedures
visually and verbally.
• Use “prove-it” sessions to practice mental computation, and then explain the how and the
why of the strategies students used to perform these mental computations.
• Use home-based and community-based mathematics projects to explore how mathematics
can be used as a real-life learning tool.
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Page 7
Teaching With Style
Teaching with style is..
Implementing a variety of instructional teaching tools, strategies, and activities to differentiate
instruction in order to support and challenge each student’s learning profile.
Four Styles of Teaching
S
T
T
R
E
U
P
S
S
T
P
I
R
M
O
A
B
G
E
E
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Page 8
Five Ways to Use Math Tools
1
2
3
4
5
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Page 9
Math Notes
Purpose: Math Notes helps students build notemaking skills as they examine key components
of word problems from multiple angles and work to develop thoughtful solutions.
Steps:
1. Model the notemaking process with an example and a blank Math Notes organizer.
Make sure students “hear” your thinking while you break the problem down into:
•
The Facts
Identify the facts of the problem and determine what is
important, what isn’t important, and what is missing.
•
The Question
Determine the main question that needs to be answered as
well as any hidden questions that are important to solving
the problem.
•
The Diagram
Sketch a visual representation of the problem.
•
The Steps
Decide what steps need to be taken to solve the problem.
2. Have students practice solving problems on their own—they should collect their Math
Notes work in a problem-solving notebook.
3. Move students to independent use of Math Notes. When they encounter new problems,
have students review their notebooks and look for effective problem-solving models to
guide them.
For more about this tool, see pages 212-213 in The Strategic Teacher: Selecting
the Right Research-Based Strategy for Every Lesson.
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Page 10
Example:
Source: Silver, H.F., Strong, R.W., & Perini, M.J. (2007). The Strategic Teacher: Selecting the Right
Research-Based Strategy for Every Lesson. (p.213)
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Page 11
Math Notes Organizer
The Facts
The Steps
What are the facts?
What steps can we take to solve the
problem?
What is missing?
The Question
The Diagram
What question needs to be answered?
How can we represent the problem
visually?
Are there any hidden questions that
need to be answered?
The Solution
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Page 12
The Canoe Problem
Nineteen campers are hiking through Acadia National Park when they come to a river. The river
is moving too rapidly for the campers to swim across. The campers have one canoe, which fits
three people. On each trip across the river, one of the three canoe riders must be an adult.
There is only one adult among the nineteen campers. How many trips across the river will be
needed to get all of the children to the other side of the river?
___________________________________________________________________________
Source: Silver, H.F., Thomas, E., & Perini, M.J. (2003) Math Learning Style Inventory. (p.2)
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Page 13
Mastery | Fist Lists and Spiders
For more about this tool, see pages 29-32 in Math Tools, Grades 3-12: 64 Ways to
Differentiate Instruction and Increase Student Engagement.
Purpose: Fist Lists and Spiders help students build and master critical vocabulary by mapping
out the connections between mathematical ideas. When creating a Fist list or Spider, students
identify and then visually connect important ideas, words, attributes, characteristics, or
procedures that are strongly related to the mathematical concept at hand.
Steps:
1. Identify a mathematical concept or critical term for students to consider.
2. Provide students with a Hand or Spider Organizer, or allow students to create their own.
3. Have students write the mathematical concept or term being discussed in the center.
4. Allow students time to think about the focus of their maps and to generate ideas. Have
students write down their five or eight best ideas, one in each digit of their Fist List or on
each leg of their Spider.
5. Have students share and discuss their maps with a partner or within a small group.
6. Encourage students to share their Fist Lists or Spiders with the entire class and explain
the connections that they made between their key ideas and the central mathematical
concept or term.
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Page 14
Fist List
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Page 15
Understanding | Always-Sometimes-Never (ASN)
For more about this tool, see pages 66-69 in Math Tools, Grades 3-12: 64 Ways to
Differentiate Instruction and Increase Student Engagement.
Purpose: Always-Sometimes-Never (ASN) is a reasoning activity that focuses students thinking
around the important, and often subtle, facts and details associated with mathematical
concepts. Students are asked to consider statements containing mathematical information and
determine if what is stated is always, sometimes, or never true.
Steps:
1. Provide students with a list of statements about a recently discussed or familiar
mathematical concept or topic.
2. Allow students enough time to read and consider all of the statements carefully.
3. Have students think about each of the statements and decide whether each is always
true, sometimes true, or never true.
4. Make sure that students explain the reasoning behind their choices.
Examples:
Arithmetic: Addition and Subtraction
1.
2.
3.
4.
The sum of two 3-digit numbers is a 3-digit number (sometimes)
The sum of two even numbers is an odd number (never)
The difference of two odd numbers is an even number. (always).
The sum of additive inverses is zero. (always)
Statistics: Mean, Median, Mode
1.
2.
3.
4.
A list of numbers has a mean. (always)
A list of numbers has a median. (always)
A list of numbers has a mode. (sometimes)
The mean of a set of numbers is one of the numbers of that set. (sometimes)
Trigonometry: Graph Analysis
1. The graph of a trigonometric function is periodic. (always)
2. Doubling the amplitutude of a trigonometric function doubles the period of the function.
(never)
3. The graph of a cosecant function has an infinite number of asymptotes. (always)
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Page 16
Always-Sometimes-Never Worksheet on Polygons
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Page 17
Understanding | Three-Way-Tie
For more about this tool, see pages 108-111 in Math Tools, Grades 3-12: 64 Ways to
Differentiate Instruction and Increase Student Engagement.
Purpose: A deep understanding of mathematical content means more than knowing what the
key concepts are: it also means understanding how these concepts are related, how they fit
together to form a bigger picture. Three-Way Tie gives students the opportunity to focus their
attention on these hidden relationships. Students identify the relationship between pairs of
critical concepts or terms and then distill their understanding of the relationship into a single
sentence.
Steps:
1. Identify an important mathematical concept.
2. Graphically “triangulate” the concept with two related terms or concepts. Alternatively,
you can have students generate the three terms themselves by selecting the three most
important ideas in a reading or unit.
3. Along each side of the triangle, the student writes a sentence that clearly relates the two
terms.
4. Have students use their three sentences to develop a brief summary of the concept.
5. Allow students time to share and explain what they wrote on their organizers.
Example:
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Page 18
Name_________________________ Date ____________
triangle
Summary
hypotenuse
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tangent
Page 19
Self-Expressive | M + M: Math and Metaphors
For more about this tool, see pages 129-131 in Math Tools, Grades 3-12: 64 Ways to
Differentiate Instruction and Increase Student Engagement.
Purpose: M + M engages divergent and creative forms of thinking by linking metaphorical
thinking and mathematics. Students compare two seemingly unrelated concepts. By finding new
and unusual parallels, students deepen their understanding of both the mathematical content
and the content they are using to compare against it. The M + M technique taps into the wellknown power of metaphors to increase conceptual understanding and academic performance
(Cole & McLeod, 1999; Chen, 1999).
Steps:
1. Introduce (or review) the process of metaphorical thinking with your students by
comparing two dissimilar concepts or objects. (Often, this is done in the form of a simile:
How are parentheses in a mathematics problem like an eggshell?).
2. Review a mathematical concept with students.
3. Allow students to choose a non-mathematical concept or object to serve as a
metaphorical counterpart to the mathematical concept, or provide students with a range
of choices. Encourage students to explain their metaphors/similes.
4. An alternative to the basic M + M technique is to fill a box or bag up with “stuff”—random
items collected from the home or classroom. Students are given a mathematics concept
and then pull an item from the bag or box.