Inquiry Based Teaching and Learning in AlgebraGraduate Credit CourseUniversity 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.  Co-planning 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 ChartK (know)

W (want to know) L (learned)

   

   

   

   

   

Lesson ResourcesAdditional Resources to be used during this trainingYou may want to download these for efficient use

Chart for Bloom's Revised Questioning Taxonomy • http://www1.appstate.edu/~

goodmanj/elemscience/questions/Bloom-16-17_Stems_for_Instruction.pdf

5E Lesson Plan in Mathematics• http://

wikieducator.org/5ELesson_Plan_in_Mathematics

Lesson Resources

A proposed 7E model emphasizes “transfer of learning” and the importance of eliciting prior understandinghttps://docs.google.com/viewer?a=v&pid=sites&srcid=c3BzLmxhbmUuZWR1fHNpc3NsZXxneDo0ZTk1ZTZkNDRlYmUwYTFh

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_Mathematics

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, continuedGiven 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_Mathematics

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 evaluateAnswer 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

 

engageThe 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/default.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/default.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/default.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/evaluate/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 Elaborateunderstanding 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