ID+Project+2

Design Report 2 flat =**Project title**=

=Mastering Math Mayhem = =Revisions since Report 1= Further research and analysis was conducted concerning learner needs, learner characteristics, and instructional goals. Subsequently modifications were made concerning the sequencing of learning events and the course objectives. Resources and methods to help students become more confident and engaged in their learning (Eastman, 2002; Graham & Honey, 2009) were added. Upon reflection concerning the period of instruction it was decided that the course focus would be narrowed. An instructional need for a greater emphasis on fundamental fraction terminology and rules resulted in a combination and simplification of the first two original objectives.

Original list: New list:
 * 1) Introduction to Fractions
 * 2) Factors and Simplest Form
 * 3) Multiplying Fractions
 * 4) Dividing Fractions
 * 5) Adding and Subtracting Fractions with Like Denominators
 * 6) Adding and Subtracting Fractions with Unlike Denominators
 * 7) Complex Fractions
 * 1) Introduction to Fractions and Simplifying Fractions
 * 2) Multiplying Fractions
 * 3) Dividing Fractions
 * 4) Adding and Subtracting Fractions with Like Denominators
 * 5) Adding and Subtracting Fractions with Unlike Denominators

=Goals statement= The goal of this instructional design unit will be to create a remedial, self-paced course on fractions for students registered in Algebra 1a at the University of Phoenix. The purpose of this unit is to help students master fraction concepts and operations in order to prepare them for fraction problems they will encounter in MAT 116.

The following is a list of goals for participants:
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 13px;">Become familiar with identifying parts of a fraction and simplifying fractions.
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 13px;">Review processes for fraction multiplication, division, addition and subtraction.
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 13px;">Practice fraction multiplication, division, addition and subtraction.
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 13px;">Apply fraction multiplication, division, addition and subtraction under a variety of conditions.

=Task analysis tied to the goals= <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">1.0 Background Knowledge > <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">1.1 Recognize addition, subtraction, multiplication and division signs > <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">1.2 Identify numerators, denominators and reciprocals > <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">1.3 Identify like denominators > <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">1.4 Identify unlike denominators > <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">1.5 Find least common denominator (LCD) > <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">1.6 Create equivalent fractions > <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">1.7 Simplify fractions (lowest terms or reduce) <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">2.0 Fraction Multiplication > <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">2.1 Multiply numerator by numerator and denominator by denominator > <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">2.2 Simplify answer <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">3.0 Fraction Division > <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">3.1 Find reciprocal of second fraction > <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">3.2 Multiply numerator by numerator and denominator by denominator > <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">3.3 Simplify answer <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">4.0 Fraction Addition > <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">4.1 Like Denominators >> <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">4.1.1 Add numerators and keep denominator >> <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">4.1.2 Simplify answer > <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">4.2 Unlike Denominators >> <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">4.2.1 Find LCD >> <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">4.2.2 Create equivalent fractions using LCD >> <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">4.2.3 Add numerators and keep denominator >> <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">4.2.4 Simplify answer <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">5.0 Fraction Subtraction > <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">5.1 Like Denominators >> <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">5.1.1 Subtract numerators and keep denominator >> <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">5.1.2 Simplify answer > <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">5.2 Unlike Denominators >> <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">5.2.1 Find LCD >> <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">5.2.2 Create equivalent fractions using LCD >> <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">5.2.3 Subtract numerators and keep denominator >> <span style="color: black; font-family: 'arial','sans-serif'; font-size: 13px;">5.2.4 Simplify answer =Instructional objectives= Upon completion of this review, the learner will be able to successfully apply their knowledge in order to add, subtract, multiply, and divide fraction problems under a variety of conditions.

Prior to computing problems, the learner will: Successfully recognize a problem containing fractions Accurately identify the four types of operations: add, subtract, multiply, and divide Accurately recognize the location of the numerator and denominator Accurately recognize like and unlike denominators Produce equivalent fractions using the least common denominator (LCD) Simplify a fraction to lowest terms Successfully identify the following terms: numerator, denominator, unlike denominators, like denominators, reciprocal, lowest terms, and least common denominator
 * Objective 1:** Develop background knowledge: recognize and identify terms and parts of a fraction
 * Objective will be met by achieving a score of 80% or higher.

Given a problem containing the multiplication of two fractions, the learner will: Successfully recognize the correct operation to solve the problem Multiply the numerators and denominators appropriately Demonstrate how to reduce the final answer to lowest terms
 * Objective 2:** Compute problems containing the multiplication of fractions
 * Objective will be met by achieving a score of 80% or higher.

Given a problem containing the division of two fractions, the learner will: Successfully recognize the correct operation to solve the problem Correctly apply the reciprocal to the second fraction Multiply the numerators and denominators appropriately Demonstrate how to reduce the final answer to lowest terms
 * Objective 3:** Compute problems containing the division of fractions
 * Objective will be met by achieving a score of 80% or higher.

Given a problem containing the addition of two fractions, the learner will: Successfully recognize the correct operation to solve the problem Accurately determine if the fractions have the same denominator Successfully add fractions with the same denominator Create equivalent fractions using the least common denominator (LCD) Demonstrate the appropriate method to add fractions with different denominators Demonstrate how to reduce the final answer to lowest terms
 * Objective 4:** Compute problems containing the addition of fractions
 * Objective will be met by achieving a score of 80% or higher.

Given a problem containing the subtraction of two fractions, the learner will: Successfully recognize the correct operation to solve the problem Accurately determine if the fractions have the same denominator Successfully subtract fractions with the same denominator Create equivalent fractions using the least common denominator (LCD) Demonstrate the appropriate method to subtract fractions with different denominators Demonstrate how to reduce the final answer to lowest terms
 * Objective 5:** Compute problems containing the subtraction of fractions
 * Objective will be met by achieving a score of 80% or higher.

=Instructional sequence=



=Strategies for objectives= Sequencing: //Simple to Complex//

Concepts and problem difficulty will proceed from simple to complex. Students will be introduced to the basics of fractions before working on problems. They will need to identify the parts, operations, and terms relating to the computation of fractions. After the first objective, the multiplication of fractions will be the first operation presented because it is the easiest to learn and involves the least amount of steps. The division of fractions will be presented next as it extends on the prior skill of multiplying fractions by adding an additional step. Adding and subtracting, respectively, will be the last two objectives in the lesson since they require more steps and added procedures than the preceding two operations.

Prescriptions for objectives:

Facts- The definitions, rules, operations, and parts of the fraction will be presented in both written and visual form.

Rules- The RULEG approach will be applied by which the rule(s) will be presented followed by examples (Morrison, Ross, Kalman, & Kemp, 2011).

Procedures- First, the steps for solving a problem will be presented in detail. A worked example is one method for teaching math concepts (Morrison, et al., 2001). Next, examples with completed steps followed by examples with partially filled in steps will be presented. Learners need scaffolding in order to complete complex tasks. Examples of complete problems is one way to provide students with the help they need (Cercone, 2008). Worked examples with faded prompts are effective in learning procedural steps (Morrison, et al., 2011). Finally, the student will demonstrate mastery by completing all of the steps on their own. The student is tasked with recalling the necessary steps and applies those steps in solving a problem.

=Details on objectives= Each lesson will begin with a short prompt and description of that lesson's objectives. This prompt will be followed by an imbedded video lesson and a written lesson. Students may view one or both of these types of media. Following the instructional portion of the lesson, students will have the opportunity to practice the skill they have just learned through an interactive website that gives them automatic feedback on how they are doing. You can view each lesson at: http://masteringmathmayhem.wikispaces.com.

=Practice for objectives= Students will practice each objective at [|www.ixl.com]. This interactive site gives students automatic feedback on their progression. Students will attempt math problems and enter their answers into the textbox followed by clicking on "Submit." Below is a sample problem that students would encounter during this module: Upon completion of the problem, students will receive automatic feedback on how they did, as seen below:

If students would like to see an explanation on how to do the problem correctly, they can click on "Explanation" for more assistance. The image below is a sample explanation for the problem above: Each activity will be directly related to the objective for that particular lesson. The activities will take on the same form and the feedback will be provided in the same format for each. =Preinstructional activities= As this is a supplement to the for-credit Algebra course there will be no official pre-test, however, students in this module will be asked to go to [] to do a self-assessment of their skills. If they choose to share their scores with the instructor, the instructor can assist with setting up specific learning objectives for that student. All students will begin with an overview of the course goals and objectives. The course will be interactive with links to outside references and resources including Khan Academy and School Tube. Students will be encouraged to explore on their own with the role of the Algebra instructor acting as a guide through their learning experience (Chizmar & Walber, 1999, Conrad & Donaldson, 2004). Stigler, Givven, and Thompson (2010) noted that community college students often struggle with mathematic procedures, so this course will be organized in a manner which includes context and procedures for solving problems. A wiki will be used to host all the discussion postings. Students can also use the online resources to take advantage of the opportunity to create study groups (Ko & Rossen, 2004).

<span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Researchers have reported that students can experience a decline in mathematics performance due to feelings of shame or guilt associated with math anxiety (Ma, 1999). These negative feelings have been shown to indirectly affect students' math performance (Hembree, 1990; Ma, 1999; Richardson & Suinn, 1972). <span style="font-family: Arial,Helvetica,sans-serif;">//Mastering Math Mayhem// will include ways to help alleviate math anxiety by making students aware of the symptoms, offering suggestions for handling negative feelings and providing an opportunity for students to discuss their experiences openly. Students will be asked to read the information at [] and [] then post on the wiki any thoughts, suggestions, or questions they have. The prompt will ask “Did you read about a technique that might help if you begin to have symptoms of math anxiety? Can you think of other techniques you have previously used that might help your fellow students? Are there other issues that were not addressed? Be honest, your postings and questions can also help others.”

The students will then be asked to visit [], [] and []. They can also listen to the Math Guy in his interview with NPR entitled //To Make Algebra Fun, Rethink The Problem// [] or go to //Math Can be Fun// at [] and try some of the episodes. Then they will be asked to post their thoughts based on the prompt “Can you see how math can benefit you today and in the future? Can you think of some ways you use math on a regular basis?” It will be noted that these postings are not just for the benefit of the individual student, but to help their classmates.

=Groupings and media= This course is a voluntary review and support mechanism for students, and it is possible that not all students in the Algebra 1a course will choose to participate. It will be done online and individually with minimal instructor support (Knowles, 1970). There will be an opportunity to add observations and post questions in a forum and receive asynchronous feedback from the instructor or other learners. The media will be designed in order to best grab student attention (Gagné, 1985) and help keep them motivated to learn through an open and self-paced approach to incorporate a variety of online learning environments (<span style="font-family: Arial,Helvetica,sans-serif;">Al-Omari, 2009). Interactions such as online videos, tutorials and practice tests will be integrated into the course material.

=Sample assessments=

Pre-assessments: []

Web resources for interactive practice problems (with scaffolding) and videos:

Fraction review/ introduction to fractions- [] [] [] []

Introduction to Fractions: media type="custom" key="12448540"

Equivalent fractions: media type="custom" key="12448434"

Least Common Denominator and Fraction Comparisons: media type="custom" key="12448474"

Multiplying fractions: media type="custom" key="12448486"

Dividing fractions: media type="custom" key="12448502"

Adding fractions: media type="custom" key="12448514"

Subtracting fractions: media type="custom" key="12448522"

Post-assessment- The following sample problems are in addition to the ones provided in the websites listed above. These problems can be used as a final assessment to ascertain the student's mastery of the objectives, therefore scaffolding is not offered for these problems.

Create a fraction and label its parts. What are the four operations that can be used with fractions? Create a fraction problem with like denominators. Create a fraction problem with unlike denominators. Write two fractions equivalent to 1/8. Write the reciprocal of 5/7. Simplify 12/27 to lowest terms. Find the least common denominator of 2/3 and 5/12. Write equivalent fractions for 2/3 and 5/12 using the LCD.

Multiply the following fractions: 4/7 * 1/4 2/9 * 5/8 2/5 * 3/5 3/7 * 3/11

Divide the following fractions: 4/5 / 3/4 5/6 / 3/7 1/3 / 2/1 6/9 / 3/8

Add the following fractions: 3/8 + 1/8 2/5 + 1/5 1/6 + 1/4 3/5 + 2/9

Subtract the following fractions: 8/11 - 3/11 5/8 - 2/8 3/5 - 1/3 4/7 - 3/6

=Relevant current references= <span style="font-family: Arial,Helvetica,sans-serif;">Al-Omari, A. (2009). Investigating online learning environments in a web-based math course in Jordan. //International Journal of Education and Development using ICT//, //5//(3). Retrieved from @http://ijedict.dec.uwi.edu/viewarticle.php?id=700.

<span style="background-color: #ffffff; color: #231f20; font-family: Arial,Helvetica,sans-serif;">Cercone, K. (2008). Characteristics of adult learners with implications for online learning design. //AACE Journal, 16//(2), 137-159.

<span style="font-family: Arial,Helvetica,sans-serif;">Chazan, D. (2002). Algebra for all students? <span class="articleAltTitle" style="font-family: Arial,Helvetica,sans-serif;">: The algebra policy debate. //The Journal of Mathematical Behavior, 15//(4), <span style="font-family: Arial,Helvetica,sans-serif;"> 455–477.

<span style="font-family: Arial,Helvetica,sans-serif;">Chizmar, J.F. & Walber, M.S. (1999). Web-based learning environments guided by principles of good teaching practice. //Journal of Economic Education//, //30//(3), 248-259. Retrieved from http://www.jstor.org/stable/1183061

<span style="font-family: Arial,Helvetica,sans-serif;">Conrad, R-M. & Donaldson, J. A. (2004). //Engaging the online learner: Activities and resources for creative instruction.// San Francisco, CA: Jossey-Bass.

<span style="font-family: Arial,Helvetica,sans-serif;">Dray, B., Lowenthal, P., Miszkiewicz, M., Ruiz-Primo, M.A., & Marczynski, K. (2011). Developing an instrument to assess student readiness for online learning: a validation study. //Distance Education//, 32:1, 29-47.

<span style="font-family: Arial,Helvetica,sans-serif;">Eastman, D. (2002). Adult learners and Internet-based distance education. //New Directions for Adult and Continuing Education,// //1998//(78), 33-41. doi: 10.1002/ace.7804

Gagné, R. (1985). //The Conditions of Learning and the Theory of Instruction//, (4th ed.), New York: Holt, Rinehart, and Winston.

<span style="font-family: Arial,Helvetica,sans-serif;">Garrison, D. R., Cleveland-Innes, M., & Fung, T. (2004). Student role adjustment in online communities of inquiry: Model and instrument validation. //Journal of Asynchronous Learning// //Networks// 8(2): 61–74.

<span style="font-family: Arial,Helvetica,sans-serif;">Graham, A. & Honey, S. (2009). Algebra - I just don't get it. // Mathematics Teaching // <span class="medium-font" style="font-family: Arial,Helvetica,sans-serif;">, //212//, 38-41 <span style="font-family: Arial,Helvetica,sans-serif;">//. //

<span class="medium-font" style="font-family: Arial,Helvetica,sans-serif;">Hannafin, M. J. & Hll, J. R. (2007). Epistemology and the design of learning environments <span style="font-family: Arial,Helvetica,sans-serif;">//.// In R. A. Reiser & J. V. Dempsey (Eds.), //Trends and issues in instructional design and technology// (pp. 53-61), Upper Saddle River, New Jersey: Pearson Education Inc.

<span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety. //Journal for Research in Mathematics Education, 21//, 33-46.

<span style="font-family: Arial,Helvetica,sans-serif;">Knowles, M. (1970). //The modem practice of adult education,// New York: Association Press.

<span style="font-family: Arial,Helvetica,sans-serif;">Ko, S. & Rossen, S. (2004). //Teaching online: A practical guide//. Boston, MA: Houghton Mifflin.

<span style="color: black; font-family: 'Arial','sans-serif'; font-size: 13px;">Ma, X. (1999). A meta-analysis of the relationship between anxiety toward mathematics and achievement in mathematics. //Journal for Research in Mathematics Education, 30//(5), 520-540.

<span style="font-family: Arial,Helvetica,sans-serif;">Miami-Dade County Public Schools. (2009). //Literature review virtual schools//. Retrieved from []

<span style="font-family: Arial,Helvetica,sans-serif;">Moor, J., & Zazkis, R. (2000). Learning mathematics in a virtual classroom: Reflection on experiment. <span class="journaltitle" style="font-family: Arial,Helvetica,sans-serif;">//Journal for Computers in Mathematics and Science Teaching// <span style="font-family: Arial,Helvetica,sans-serif;">, 19(2) 89–115.

<span style="background-color: #ffffff; font-family: Arial,Helvetica,sans-serif;">Morrison, G. R., Ross, S. M., Kalman, H. K., & Kemp, J. E. (2011). //Designing Effective Instruction//, 6th ed. Hoboken, NJ: Wiley.

<span style="font-family: Arial,Helvetica,sans-serif;">Oliver, K. M., Kellogg, S., & Patel, R. (2010). An investigation into reported differences between online math instruction and other subject areas in a virtual school. //Journal of Computers in Mathematics and Science Teaching, 29//(4), 417-453. <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 13px;">Richardson, F. C. & Suinn, R. M. (1972). The mathematics anxiety rating scale: Psychometric data//. Journal of Counseling Psychology, 19//(6), 551-554.

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<span style="font-family: Arial,Helvetica,sans-serif;">Schaeffer, C.E., & Konetes, G.D. (2010). Impact of learner engagement on attrition rates and student success in online learning. //International Journal of Instructional Technology & Distance Learning, 7//(5), 3-9.

<span style="font-family: Arial,Helvetica,sans-serif;">Stigler, J.W., Givven, K. B. & Thompson, B. J. (2010). What community college developmental mathematics students understand about mathematics. //MathAMATYC Educator, 1//(3), 4-16. Retrieved from http://www.carnegiefoundation.org/sites/default/files/elibrary/MathAMATYC_Stigler.pdf

<span style="font-family: Arial,Helvetica,sans-serif;">Wang, A. Y., & Newlin, M. H. (2002). Predictors of performance in the virtual classroom. //The Journal// //Online,// //29//(10).