Inquiry Based Teaching and Learning in Algebra
Graduate Credit Course
University of San Diego
Mediterranean District - DoDEA-Europe
September 1, 2014 to December 1, 2014
Facilitator: Lourdes Alonso, Secondary Math ISS
“ I never teach my pupils. I only attempt to provide the conditions in
which they learn.” –Albert Einstein
Inquiry Based Teaching and Learning in Algebra
• Using inquiry based instructional strategies students will explore
mathematics in meaningful ways, making connections to their real world.
• Use of appropriate technology will engage students in computational
thinking, algebraic reasoning and problem solving.
• Purposeful instructional planning with alignment to rigorous standards
will provide clear learning targets from which students can assess their
own progress.
• Using formative assessments to guide our instruction, differentiated
opportunities will be provided allowing each student to reach their
maximum potential.
Your District Math ISS is a resource. Through our close communication and
collaboration we can make this an innovative and learning experience. Coplanning your lessons for this course with your District ISS is encouraged.
For download:
Please download the following documents for your
efficient use throughout this module:
http://mdso.eportalnow.net Password: kent Select
Curriculum Resources > Math 6-12 > Graduate courses
 KWL Chart
 Math Journal for Inquiry Based Teaching and Learning in
Algebra
 Discussion Questions for Inquiry Based Teaching and
Learning in Algebra
 Combined Lesson Plan for 5 Es and Dufour’s
(You may want to save your journal to your desktop for convenience.)
Deadlines for submitting documents:
E-mail to your District Math ISS :
• KWL chart, Math Journal, discussion questions by
September 30, 2014.
• Lesson Plans using Combined 5 Es and Dufour’s
template are due by October 30, 2014 (first one)
and no later than December 1, 2014 (second
one).
Training objectives: Learning the 5 E framework
•
Identify prior knowledge of the 5E model of instruction through a KWL chart (What you
KNOW, What you WANT TO KNOW, What you LEARNED)
•
Engage in activities and prepared lessons explicitly aligned with the 5E model.
•
Explore each “E” using definitions, activities, and prepared lessons from school systems in
Australia and the United States.
•
Explain your thinking by answering the guiding questions and completing the Journal entries.
– Please download this document for your efficient use
•
Expand, Elaborate and Extend understanding by deconstructing and reconstructing a lesson
using the 5E Lesson Planning document provided, completing the Journal entries, and
engaging in discussion via e-mail with your District ISS and other math teachers.
•
Assess (Evaluate) your understanding of the 5E model of instruction by completing the
LEARNED portion of the KWL chart at the conclusion of the training.
KWL Chart
K (know)
W (want to know)
L (learned)
Lesson Resources
Additional Resources to be used during this training
You may want to download these for efficient use
Chart for Bloom's Revised Questioning Taxonomy
• http://www1.appstate.edu/~goodmanj/elemsci
ence/questions/Bloom-1617_Stems_for_Instruction.pdf
5E Lesson Plan in Mathematics
• http://wikieducator.org/5ELesson_Plan_in_Mat
hematics
Lesson Resources
A proposed 7E model emphasizes “transfer of
learning” and the importance of eliciting prior
understanding
https://docs.google.com/viewer?a=v&pid=sites
&srcid=c3BzLmxhbmUuZWR1fHNpc3NsZXxneDo
0ZTk1ZTZkNDRlYmUwYTFh
Overview of 5E or e5
“The e5 (or 5E)Instructional Model is not a recipe for teacher practice
but rather a framework to inform conversations and guide the
observation, critique and reflection of classroom practice. There are
many different ways that teachers can vary in their approach and their
behavior and still be highly effective in the classroom. All teachers use
their professional judgment to adapt their practice to the specific
context they work in and to the particular cohort of students they
teach. However, within this zone of discretion there are common
practices that draw on a professional knowledge base in the classroom
we can develop a great understanding of the nature of the professional
learning teachers require to improve their practice.”
http://www.education.vic.gov.au/proflearning/e5/about/default.htm
Part 1: Engaging in student centered
teaching and learning strategies
• Work through the Tootsie Roll Pop lesson
example as if you are the student.
• Post reflections to your journal as you go.
(use the downloaded math journal
attachment for guiding questions)
engage
“This stage assesses the prior knowledge of the
learner and helps them become engaged in a
new concept through the use of short activities
that promote curiosity and elicit prior
knowledge. The aim is to organize students’
thinking toward the learning outcomes of the
current activities.”
http://wikieducator.org/5E_Lesson_Plan_in_Mathematics
A lesson example of engage
Tootsie Roll Pop dilemma:
“Have you ever wondered how many Tootsie or
Jolly Rancher Pops you could pick up with one
hand? If you had a bigger hand, might you be able
to pick up even more candy? Have you ever envied
the bigger kids at Halloween? In fact, did you ever
think you might be able to predict how much
candy a person could pick up?
What are some factors which might determine how
much candy a person can pick up?”
Journal entry for engage:
• Describe how the teacher captures
students’ interest in the lesson
example.
• What kind of questions should the
students ask themselves after the
engagement?
explore
“Expose the students to a variety of experiences at
this stage. These experiences may involve
observations of events or objects, manipulations of
materials, work with simulations, examinations of
representations, viewing a short video, or reading.
These experiences provide a common basis for all
students that the teacher can use to assist them in
identifying and developing concepts and skills.”
http://wikieducator.org/5E_Lesson_Plan_in_Mathe
matics
An example of explore
• The goal of this project is to investigate if there is a relationship
between the size of a person’s hand and how many Tootsie/Jolly
Rancher Pops that person can pick up.
Data collection & summary:
Each person should measure his or her hand span according to the
rules the class agreed upon. Record your group’s data below. Be
sure to include units on hand span.
Hand span:__________
# of Tootsie Pops: __________
Gender: ________
How might the class determine if a relationship exists? Which is the
independent variable and which is the dependent variable for this
experiment?
An example of explore, continued
Given the scatterplot of the data, model a line of
best fit for this relationship.
Do the values of the intercept and slope make sense
in this exploration?
How many Tootsie Pops would a person with a 22cm
hand span be able to pick up? What about a
person with a 27cm hand span? Are these
estimates or actual values? Which is more
reliable?
Journal entry for explore:
• Describe what hands-on/minds-on activities
students will be doing in this lesson example.
• List “big idea” conceptual questions the teacher
will use to encourage and/or focus students’
exploration. Give two examples.
• In the lesson example, explain how DoDEA
process standards are being incorporated into the
lesson.
explain
“Here students are provided with opportunity to
explain their understanding of their experiences
from the explore phase. The questions and
discussion lead students to patterns,
regularities, and/or similarities and prompt
them to describe concepts or skills in their own
words.”
http://wikieducator.org/5E_Lesson_Plan_in_Ma
thematics
An example of explain
The students are to explain this relationship in
their own words.
Sample graphs and algebraic models can be
posted around the room in a gallery walk. A
discussion should ensue where students defend
and compare their work.
http://wikieducator.org/5E_Lesson_Plan_in_Mathematics
Journal entry for explain:
• Student explanations should precede introduction of
terms or explanations by the teacher. What questions
or techniques will the teacher use to help students
connect their exploration to the concept under
examination? (again use the lesson example)
• List higher order thinking questions which teachers will
use to solicit student explanations and help them to
justify their explanations. Two questions please. See
the resource chart for “Blooms revised questioning
taxonomy”.
expand/extend/elaborate
The next phase challenges students to extend
their understandings or skills and/or to practice
them. Through new experiences at this time,
students develop deeper understanding, an
extended conceptual framework, and improved
skills. Some of the tasks, such as reading an
article, may be done as homework and
discussed during the following class period.
http://wikieducator.org/5E_Lesson_Plan_in_Mathematics
An example of
expand/extend/elaborate
Repeat the investigation with Starburst Candies.
Is using a linear approximation the best model for this data?
What are the significant differences between the data for the Tootsie/Jolly
Rancher Pops and the Starburst Candies? Why might these differences
exist?
If the data was separated by gender, would the models have greater or lesser
predictive value?
If following relationships were added to the model, how would they influence
the model:
(HandSpan = 16, # = 14) and (HandSpan = 27, # = 32)?
(HandSpan = 21, # = 17) and (HandSpan = 22.5, # = 23)?
http://wikieducator.org/5E_Lesson_Plan_in_Mathematics
Journal entry for
expand/extend/elaborate
• Describe how students will develop a more
sophisticated understanding of the concept
using expand, extend, and elaborate. Read
the article “a proposed 7E model” under the
Resources tab for further information if
needed.
evaluate
“The final phase of the instructional model
encourages students to assess their
understanding and abilities and provides
opportunity for the teacher to evaluate student
progress toward achieving the learning
objectives for the activity. The tasks may involve
writing summaries, applying concepts and skills
to novel situations, constructing a concept map,
or taking a quiz.”
http://wikieducator.org/5E_Lesson_Plan_in_Mathematics
An example of evaluate
Answer the following questions in your math journal:
When a scatter plot is examined, what are some indicators that the
relationship is linear?
If “hand span” had been measured in different units, would there be
changes to the slope and y-intercept?
Some people believe that larger the number people that participate in
the study, the better the results. Do you believe this is always
true…why or why not?
http://wikieducator.org/5E_Lesson_Plan_in_Mathematics
Journal entry for evaluate:
• How will students demonstrate that they have
achieved the lesson objective?
• How could evaluation be embedded
throughout the lesson as well as at the end of
the lesson. Give an example.
Final Journal Question
• How does this instructional model differ from
the way you were taught? Name at least
three ways.
KWL chart
• Complete the W portion of the KWL chart
indicating what you WANT TO KNOW.
• As you continue this training, please keep in
mind those questions you still have about this
model of instruction.
Part 2: Exploring the role of teacher
as a facilitator of learning
Part 2: Exploring the role of teacher
as a facilitator of learning
Part 2: Exploring the role of teacher
as a facilitator of learning
engage
The teacher fosters positive relations with and between students and
develops shared expectations for learning and interacting. They
stimulate interest and curiosity, promote questioning and connect
learning to real world experiences.
The teacher structures tasks, elicits students’ prior knowledge and
supports them to make connections to past learning experiences. They
present a purpose for learning, determining challenging learning goals
and making assessment and performance requirements clear.
The teacher assists students to consider and identify processes that
will support the achievement of the learning goals.
• http://www.education.vic.gov.au/proflearning/e5/model/engage/d
efault.htm
Discussion Question 1:
Please answer your discussion questions in the document “
Discussion Questions for Inquiry Based Teaching and
Learning, Part 2”.
People are usually more convinced by reasons they
discovered themselves than by those found by
others – Blaise Pascal
What does the above statement mean to you in
relationship to this model of instruction?
explore
• The teacher presents challenging tasks to support students to
generate and investigate questions, gather relevant information and
develop ideas. They provide tools and procedures for students to
organize information and ideas.
• The teacher identifies students’ conceptions and challenges
misconceptions. They assist students to expand their perspectives
and reflect on their learning.
• The teacher is mindful of the learning requirements of the task,
attentive to student responses and intervenes accordingly.
• http://www.education.vic.gov.au/proflearning/e5/model/explore/d
efault.htm
Discussion Question 2
Explain the purpose and benefits of questioning
in the exploratory phase of instruction. (discuss
teacher to student, student to teacher, and
student to student generated questions)
explain
• The teacher provides opportunities for students to demonstrate their
current level of understanding through verbal and non-verbal means.
They explicitly teach relevant knowledge, concepts and skills. This
content is represented in multiple ways.
• The teacher provides strategies to enable students to connect and
organize new and existing knowledge. They assist students to
represent their ideas, using language and images to engage them in
reading, writing, speaking, listening and viewing.
• The teacher explicitly teaches the language of the discipline. They
progressively assess students’ understanding and structure
opportunities for students to practice new skills.
• http://www.education.vic.gov.au/proflearning/e5/model/explain/defa
ult.htm
Discussion Questions 3
What verbal and non-verbal methods might a
student use to explain their thinking about a
mathematical concept?
What strategies might a teacher use to facilitate
learning through discussion during this phase of
instruction?
expand/extend/elaborate
• The teacher engages students in dialogue, continuously extending
and refining students’ understanding. They support students to
identify and define relationships between concepts and to generate
principles or rules.
• The teacher selects contexts from familiar to unfamiliar, which
progressively build the students’ ability to transfer and generalize
their learning.
• The teacher supports students to create and test hypotheses and to
make and justify decisions. They monitor student understanding,
providing explicit feedback, and adjusting instruction accordingly.
• http://www.education.vic.gov.au/proflearning/e5/model/elaborate/
default.htm
Discussion Question 4
How, when and where is differentiation
embedded in this model of instruction?
evaluate
• The teacher supports students to continuously refine and
improve their work using assessment criteria in preparation
for a performance of understanding. They integrate evidence
from each phase, formally recording students’ progress
against learning goals.
• The teacher provides feedback and assists students to
evaluate their progress and achievements. They support
students to reflect on their learning processes and the impact
of effort on achievement.
• The teacher guides students to identify future learning goals.
• http://www.education.vic.gov.au/proflearning/e5/model/eva
luate/default.htm
Discussion Question 5
Explain the role of both formative and
summative assessment in this instructional
model.
So, what is missing?
But where do I
start? What
content guides the
5 Es?
What about if some students
need more scaffolding or there
are some who already know
the material?
Dufour’s model
• What do we want students to learn?
• How will we know when they’ve learned it?
• How will we respond when some students don’t
learn it?
• How will we respond when some students
already know it?
Combined Lesson Plan Template
incorporating 5 Es and Dufour’s Model
It all starts with the
standards!
Standards need to be
chunked into daily
objectives with specific
learning targets so that
the students know
exactly what they are
responsible for.
Part 3: Expand, Extend, and Elaborate
understanding of the 5E instructional model
Now…put it to action!
• Submit your completed lesson plans using the combined
template (5E and Dufour’s) to your district secondary
mathematics ISS.
Continuous improvement…even the best can get better!
EVALUATE
• Complete the L portion of your KWL chart by indicating what
you have LEARNED about the 5E model of instruction
specifically and inquiry based learning in general.
• Evaluate how the lessons planned using the 5 Es went.
Provide a short reflection on what worked, what didn’t, and
what could be done to improve the lesson the next time.
Congratulations on completing this module! If you experienced
success, please share with your district ISS and colleagues.
Teachers are their own best resource and you can inspire and
encourage others!
Think of a positive memorable
moment where you or a student of
yours experienced an AHA
moment…what was going on?
“…Students learn mathematics best by actively doing mathematics
within a clear and meaningful context.”
"It is easy to forget something that you are told, but almost impossible
to forget something that you have discovered on your own."
-The Consortium for Foundation Mathematics, Mathematics in Action