The purpose of this instructional unit and lesson plans are to demonstrate how open educational resources (OER) may be integrated into instructional practices to teach a mathematics methods course for pre-service teachers. UNIT:
This unit details three course meetings (durations 3 hours) and the instruction that occurs during the sessions. Each of the lesson plans are subdivided into weekly meetings. The lessons describe the particular content that is covered during each session and as noted in the green textboxes on the right side of the page the integration of open educational resources are highlighted to demonstrate the inclusion of an array of resources into the teaching and learning process. The content described in the textboxes is written as a narrative to describe the changes that have been implemented to the instructional design to promote the use of OER. PURPOSE:
The integration of OER in public education is a needed resource. Due to limited time and resources incorporating OER resources will promote quality education opportunities. As additional OER become available the need to understand the potential for such resources and locate them becomes essential. OER resources are licensed and under Creative Commons certain editing conditions may be allowed. For example, if the author permits, the work may be shared, copied, and distributed. Other conditions may include attributing the original author with credit for their original work. Also, under the Creative Commons license there may be noncommercial conditions that inhibits one from using the authors work for commercial purposes. Another benefit of using Creative Commons is that others may gain from the revised product; the Share Alike condition allows the author to distribute the revised work under the same or similar license agreements. To view a list of the Creative Commons licenses visit http://creativecommons.org/choose/
MATHEMATICS INTRODUCTION & OER
Open Education Resources (OER) integrated during session:
• Understanding OER in K-12 education
• Intro to data collection and using data
• discussing the importance of self-concept as related to engaging with math and being successful
• Student teachers will analyze their own experiences as the first step in providing deep and rich mathematics instruction for their students
(1) Introduce myself to the block through my personal numbers. Display a PowerPoint with various numbers that describe me and describe the significance of several numbers.
? 28 miles from my childhood home
? 52- number of weeks I’ve lived outside of CA
? 34%-- percent of my life I’ve been married
? 4 number of siblings
? 5’6” height
? 2 number of sons
? 20: number of states I’ve visited: Washington, Oregon, Nevada, Florida, Mississippi, Texas, Louisiana, Utah, Wyoming, New Mexico, Arizona, Alabama, New York, Pennsylvania, New Jersey, Massachusetts, Colorado, Virginia, Maryland, Hawaii
(2) Permit time for students to jot down at least three personal numbers. Share numbers with a partner.
(3) Distribute folded construction paper and allow them to illustrate one of their favorite numbers on the front cover and provide a description.
(4) Whole class share
(5) Process it
? Great beginning of year bulletin board
? See the power of numbers to capture human experience, regardless of the language you speak, or the number of years you've been in school.
? How can this be modified for different learners or different grade levels?
B. Prior experiences with mathematics
(1) Sticky note activity – write what you remember from learning/doing math in elementary school.
(2) Place the notes on the board along a continuum from positive to negative. (1-10) to create a bar graph
(3) Ask students to show where they are at on the continuum by holding up that many fingers and find someone who have a number that is significantly different. (Hence if I’m a 1 I’ll look for a 9 or 10). Pair share—each person shares for 1 minute and explains the reason for their personal rating.
C. Statistics with concrete graphing
(1) Ask students to line up from 1-10 (just in a straight line according to what their rating was)
• Find: Median (count up from one end, down from the other). How would mean be calculated? Can you easily see the mode? (no)
• Create a bar graph ("stack" people with same numerical rating so that last person in line is on zero on the y axis). Now look at mode: How many modes? What is it? Is the distribution skewed or normal?
• Create a pie graph: Circle up with them still in numerical order. Stand in center and throw yarn to the beginning of the ones (cut), the beginning of the twos (cut), the beginning of the threes (cut)…so that you hold one end of each yarn, and the "first" person of each number holds an end.
D. Continue discussion of experiences
Group students in like groups: ask students to line up again and pull students from ends and center to create mixed groups. Cooperative group roles: recorder, taskmaster, gatekeeper, praise giver
Small group talk about four specific questions: When you think back to your elementary school experience….
(1) What was the mathematics content?
(2) What did the teacher do?
(3) What tasks did the students do?
(4) How did the teacher assess your learning?
E. Whole group discussion of these using two column notes for whole class discussion:
• Have one butcher paper for each question item divided in half. One half is for our experiences the other for current ideas about best practice
• After teams have had time to discuss ask the teams to record their responses for 1-2 questions.
• Discuss these as a whole class adding other ideas and discussing what is now considered to be best practice
F. Process activities
• What did you learn about graphing? What did you note about these graphing activities? (Possible thoughts: concrete graphs…concrete materials will be a major focus of the course; statistics helped us summarize and draw conclusions; successful lessons engage students; visual representations aid learning…)
• What did you learn about grouping?
• What did you learn about discussion?
• About listening?
G. Reading Materials
Build to chapter points focusing on good mathematics education, National Council of Teachers of Mathematics, etc. and introduce what they will be reading for our next meeting.
Check out our blackboard site and show students how to edit personal information
J. Closure outcome statements I learned, I think, I wonder… give students about 5 minutes to write down something they learned, something the class got them thinking about or a question they have or want to talk about more. Then toss a ball or stuffed animal around the room to share statements.
Open Education Resources used during session
Theory: Multiple Intelligence Literature: Greedy Triangle
Focal questions & topics
Review the Personal Math Narrative Assignment.
(1) What do I need to consider when planning mathematics activities that will:
a. Promote mathematical competence
b. Be supportive of all of my children’s needs, levels (Gardner MI)
c. Be developmentally appropriate
d. Actively create a community of math learners in my classroom
(2) Instructional planning: what questions do I need to ask myself when planning for instruction?
(3) What is the spiral curriculum and what are pros and cons?
(4) How can I relate math to other curriculum? (today’s example is literature- read the Greedy Triangle)
(5) Different kinds of lesson plans: direct instruction, investigative, and exploratory
(6) What is the difference between formative and summative assessment?
(7) Phases of assessment: planning, gathering evidence, interpreting evidence, applying the results
(8) Using an analytical rubric to assess student work
• SIOP video
• Table of ?s to consider when planning for instruction
• p. 46; Table 3-1
• Example of content standards review assignment.
• Class chart with data on gas mileage, etc.
• Write warm up on board or overhead.
• Handout with student work from book (p. 85-86)
• Create display of student personal number puzzles.
• Hand out Gardner and MI teaching strategies Print out a copy for each student add link to Blackboard. http://www.learnnc.org/lp/editions/mathmultintell/1?style=print
• Take the MI test to learn about yourself in relation to the MI theory http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks1/ict/multiple_int/what.cfm
• A digital map of Southern California with Bolsa Chica and Fullerton highlighted. Make sure that there is a scale- (the map is saved as a PowerPoint slide on Blackboard).
I. Warm up and creating contexts for mathematics lessons and instruction
a. Our class has decided to take a trip to Bolsa Chica Preserve to do some research on waterfowl. We are going to carpool from school and want to be economical and fair. The roundtrip distance from California State University Fullerton is about 45 miles. Using our data decide who you think should drive, how many gallons of gas we will consume and how much each person should pitch in for gas money. Provide reasoning for your responses. You may work together or individually.
b. Difference between contexts for using math and concepts, procedures and materials.
c. Come up with an idea for creating a context for using the class data we collected regarding gas mileage of our vehicles and commuting distances.
II. Planning for instruction
a. Planning for meaningful and rich mathematics experiences takes a lot of time and advanced thought. Chapter 3 focused on the kinds of questions we need to be asking ourselves as we plan for instruction. I would like us to view the following lessons excerpt and consider the questions put to us in Chapter Three:
i. With your group take a 3-5 minutes to look back at Ch. 3 and come up with a list of at least 5 questions you want to consider as you plan for instruction for your students.
ii. Pass out the table I made with questions to consider when planning for instruction and review this. Are there items or questions you thought of that are not addressed here? If so add these at the bottom.
iii. View SIOP video Chapter 9 44:40-52:28. Use the table to record your ideas about each question as we view the video.
iv. Discuss as a class.
v. View the place value video (15 minutes). Again record your ideas on each question and discuss in small groups.
Content Standards Review Assignment
b. Review my example with the students. Ask them to think about what we have discussed during the planning section and apply that to their activities and plans
d. Allow students about 45 minutes of class time to work on this assignment.
a. What are purposes of assessment? (summative and formative) Why do we assess?
b. What kinds of assessment are there and what are their purposes?
c. Discuss these questions as a class and list answers. Some ideas include: observation, interview, paper and pencil task, letter to myself,
d. Use the work samples from Reys book and the analytic scoring scale. Be prepared to justify your ratings. Compare your ratings to those in our text p. 84
e. Highlight the OER resources that were used during the session. As a ticket out the door ask students: Think about the OER used today, what other resources would have been appropriate to use today?
f. Blog Entry: What other ways can you use the OER that we used today during class (Curriki, OER Commons)?
ASSESSING MATHEMATICS PROFICIENCIES
Topics: assessing student math proficiency, mental math estimation, professional literature, Task 2 assignment, assessment creating rubrics online using Rubistar, technology in the classroom evaluation websites.
(1) PowerPoint opening. Review the topics for today. There is a significant amount of content to cover and a limited amount of time. Need to stay focused and on task for the next 3 hours. Today we will be using a timer to track activities and manage time.
(2) Review of the readings for today. Use PowerPoint to show the questions. How will you assess math proficiencies? Draw from the readings.
(3) Mental Math- I have a slide that contains a series of questions about mental math. When should you use mental math and when should you practice mental math skills with students?
(4) Jigsaw Activity- students have the handouts for this activity. Explain the Think/Pair/Share model and complete the activity. Set the timer for this activity.
(5) Share out any comments about the mental math activity. I noticed in your math histories that many of you practiced mental math with your family members. Father’s in particular were the primary person responsible for mental math practice.
(6) Professional Literature about math Distribute the math journals- time to read through and discuss. Show the website too. The website is a free resource that students may access to reinforce mathematics education.
(7) Assignment Task 2- show the details and the example available in Bb. This will be completed in TaskStream, a template for this assignment is being created at this time and you will have it available as soon as possible. Note the requirements for this assignment. It is a good idea to complete this assignment in a word document, then to copy and paste to TaskStream---just in case it freezes, you will have another copy and not have the original text lost.
(8) Log in to Task Stream and show the lesson plans that are examples – I made.
(1) Log in to Rubistar and show how this works. Explain the basics of a rubric and how to use it in the classroom. The rubrics connect to the objectives for the lesson. Show the resources available online at Curriki that reinforce rubric use in K-12.
Ivers PowerPoint—review the basics of this show and tell them that it is available on Bb.
Work with a partner and complete the Website Evaluation—pass out the template, just fill it in with a pen. No need to type. Use Kathy Schrock template to create the website evaluation.
Discuss the need to evaluate sites to check for content, appropriate uses, adaptability and resources.
Webquests: What is a webquest? Where to locate one? The benefits of webquests.
Reflection: Add a blog entry to the class blog: What other OER were covered during today’s session? What is the difference between OER and Open Source resources? Have you started to notice the application of OER in education and how you can adapt materials to your future teaching careers? http://oermath.blogspot.com
Ticket out the door. This is a strategy that you can use to review what you covered with your students, or what they learned about math. This can be something as simple as flashcards or more complex. Use the free flashcards that reinforce math concepts to model this process.