Portfolio ProjectEDUC 765: Trends and Issues in Instructional Design

By: Sara Provost

Submitted June 26, 2015

PROJECT PROPOSAL

Project Title

Place Value Instruction

Sponsoring OrganizationTrillium Creek Primary School, West Linn / Wilsonville School District

How do we create learning communities for the greatest thinkers and most thoughtful people... for the world? This question is at the forefront of the mission of the West Linn / Wilsonville School District. The district envisions a school learning community which demonstrates personal and academic excellence, provides a personalized education to improve student performance, establishes community partnerships and expands the classroom beyond the school, creates a circle of support for each student, educates the whole person (intellectually, emotionally, physically, and ethically), and integrates technology into daily learning.

Project DescriptionStudent understanding of place value is a foundational mathematical skill. In primary grades, students must develop a solid understanding of place value in order to be successful in making sense of our number system, adding and subtracting multi-digit numbers, counting, understanding money, and numerous other math skills. To meet Common Core State Standards, students must be able to utilize their understanding of place value to solve math problems involving multi-digit numbers. Without a solid understanding, students experience difficulty with computing accurately and using mental math strategies. If this foundational skill of place value is not developed, math becomes more procedural rather than conceptual. The performance gap that is present with students having a solid understanding of place value demonstrates the need to put into place an intervention. This intervention will include training for teachers in learning the prerequisite skills necessary for students to develop a solid understanding of place value, as well as helping teachers develop strategies for teaching place value and assessing place value knowledge.

AimIncrease teachers’ knowledge and understanding of place value concepts, as well as improve instructional and assessment practices related to place value.

Target AudienceThe primary audience will consist of both male and female teachers of students in kindergarten through fifth grade. Teachers have a wide range of experience in the

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classroom. For some teachers, this is their first year teaching and for others they have over 30 years of experience in the classroom. All teachers consistently participate in district wide professional development.

Other audiences may include school specialists, such as our school administrator, school counselor, and instructional coordinator.

Delivery OptionsDue to the lack of time available, the majority of the instruction will take place on-line. One introductory face-to-face session between the instructor and audience will take place at the start of the training.

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FRONT-END ANALYSIS: INSTRUCTIONAL NEED

Instructional NeedPlace value is a foundational mathematical skill that necessitates that all students develop a solid understanding. By developing a solid understanding of place value, students are able to develop math skills conceptually rather than procedurally. Based on the survey I conducted, only 47% of the teachers indicated that between 75% and 99% of their students have a strong understanding of place value. The remaining teachers indicated that less than 50% of their students have a solid understanding of place value. No teachers indicated that 100% of their students have a solid understanding of place value. With this large gap in performance by students in their understanding of place value, it is essential to equip teachers with the necessary knowledge, skills, and strategies to effectively teach students to master this math concept. Essentially, teachers strive to have 100% of students develop this solid understanding.

The needs assessment survey that was conducted also indicated that the majority of teachers felt “moderately knowledgeable” in regards to identifying prerequisite skills for place value, providing instruction to students struggling with the concept of place value, providing whole group instruction about place value, extending students’ understanding of place value, and assessing student knowledge of place value. Teachers are in need of further education in these areas in order to gain the knowledge and skills necessary to teach students and help them to make learning gains.

The majority of teachers who participated in the survey also indicated that they would find value in additional training in strategies for teaching place value, prerequisite skills for place value (such as unitizing, subitizing, cardinality, and the composition and decomposition of numbers), conducting place value assessments, and identifying student misconceptions of place value. Without knowledge of these prerequisite skills, as well as a means for assessing and teaching these skills, teachers will continue to have difficulty meeting the learning needs of students.

Lack of knowledge about assessing place value also impacts a teacher’s ability to instruct students as they are unaware of the learning gains made by students. Only 60% of respondents indicated that they have conducted a formal place value assessment. Some teachers were unsure of whether they have or not. This low percentage demonstrates the need for teachers to receive more training in this area.

Overall, based on the results of this survey, the school and administration recognize the importance of providing and participating in professional development to achieve growth in teachers in order to contribute to the mathematical learning of the students served at the school.

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FRONT-END ANALYSIS: LEARNER CHARACTERISTICS

Learner Analysis

Primary Audience (training will be mandatory for these instructors): Primary level classroom teachers: grades K-2 Intermediate level classroom teachers: grades 3-5 Instructional coordinator Learning specialist

Secondary Audience (training will be voluntary for these instructors): School counselor Music and wellness teachers Principal Instructional assistants

General Learner Characteristics Age: 22-64 Work Experience: 1-15+ years Gender: 86% female, 14% male (primary audience: 87% female, 13% male) Language: 93% speak English as a first language, 7% speak another language as

their first language and are fluent in English

Entry CharacteristicsPrerequisite skills and knowledge:

Most teachers are somewhat familiar with the terms, “subitizing,” “unitizing,” “cardinality,” “decompose,” and “compose,” but they may not be able define them or know strategies for teaching these skills.

All teachers know the meaning of “place value.” All teachers have access to and are able to utilize the internet. All teachers are familiar with how to use computers to engage in on-line

trainings.Attitudinal and motivational characteristics:

All teachers recognize the importance of students having a solid understanding of place value.

All teachers have a positive attitude about learning strategies for place value and methods for assessing place value.

Most teachers are motivated to engage in on-line trainings.Prior experience:

All teachers have previous experience with place value and have varying levels of familiarity with the prerequisite skills.

All teachers have completed on-line trainings in the past.

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Contextual Analysis

Orienting Context The learners’ goals include: learning prerequisite skills for place value as well as

strategies for teaching students these skills, identifying student misconceptions of place value, and learning assessment practices for place value.

Based on the needs assessment, learners are motivated to learn this information and find the content to be useful and valuable.

Learners believe they are being held accountable to the instruction provided based on the requirement to submit student scores on place value assessments.

Potential misconceptions include: assuming place value is procedural, younger students are not developmentally ready to learn place value, and a students’ ability to name the ones, tens, and hundreds places in a number means they have a solid understanding of place value.

Instructional Context Schedule: The initial orientation to the training will take place on a “Professional

Development Early Release” day. The remainder of the training will take place on-line.

Lighting: The training will take place in a classroom with south facing windows so the trees from the wetlands can block the sun from entering the room and interfering with the projector onto the screen (the blinds do not block out enough sun light).

Noise: The training will take place in an upstairs classroom to avoid the noise produced from students participating in after school clubs.

Temperature: The temperature is monitored electronically and the computer system automatically adjusts. If need be, our building engineer can override the computer and adjust the temperature as needed.

Seating: Tables and chairs in the classroom are all mobile. The table and chairs can be moved to accommodate small group work, partner work, and enable all participants to see the presentation on the screen.

Accommodations: Restaurants, grocery stores, and entertainment are within three miles of the location. On-site there are refrigerators and microwaves for participants to use to store and reheat any food items. Although not necessary for these participants, there are not any hotels within a close proximity and would require driving approximately 10 minutes to the closest lodging.

Equipment: All necessary equipment is available free of charge including laptop computers for all participants, a document camera, speakers, projector, projector screen, wireless internet, math manipulatives, and an Apple TV to wirelessly connect presenter’s laptop.

Transportation: The classroom and the building are easily accessible. All participants work in the building so they will not need transportation provided for them. In case of an inability to use stairs, an elevator can be used to access the second floor of the building.

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Transfer Context Place value is a mathematical skill that students at every grade level utilize. As a

result, all teachers will be able to transfer the knowledge and skills they develop through this training directly to their students.

At the primary grades, teachers will be able to use the information gained from this training on a daily basis in their classrooms with their students. Teachers in the intermediate grades will also be able to use the skills gained on a frequent basis, but many of their students have already developed a solid understanding of place value. They can use this information for students who struggle with the concept or to help extend student learning.

Teachers that participate in this training will have ongoing support from myself (since I am on the staff) as well as our instructional coordinator who specializes in professional development for teachers. The on-line training resources will be available for teachers to revisit as they need it. Teachers will have access to all the tools and resources used in the training to use in their own classrooms with students.

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INSTRUCTIONAL IMPACT BASED UPON LEARNER CHARACTERISTICS

Application of Learning TheoriesFirst and foremost, the learning objectives and expectations for the learners will be clearly defined at the start of the training. The first training session will include an overview of the entire training experience to ensure the learners that the content is relevant and practical for their classrooms.

One learning theory that will be applied in the training is a constructivist approach, which will allow the learners to build on their current knowledge and experiences. By reinforcing with the learners what they already know about place value, the training can then build on their experiences and knowledge to extend their learning. Both assimilation and accommodation will allow the learners to process new learning with their schema. Hopefully by reflecting on previous experiences, learners will be motivated to learn the new material presented. They will also have opportunities to apply their new learning in their classrooms by trying out various teaching strategies and conducting assessments. Furthermore, the opportunities to try out their learning in their classrooms can help to deter any skepticism about the training that they may hold.

In addition, due to individuals all having various ways in which they best learn, Howard Gardner’s multiple intelligences theory will be applied in the training. The individualized instruction will allow students to work at their own pace. Due to the learners being various ages and having varying amounts of experience with teaching place value, a self-directed pace will work best with this group of learners. Moreover, a variety of instructional practices will be used to meet the needs of the learners’ multiple intelligences (such as visual, auditory, kinesthetic, etc.) that will maintain the attention of the learner and meet their individual needs. The learners will have opportunities to work in small groups, partnerships, and individually. This will benefit all learners who prefer different learning styles.

Lastly, as this course is focused on instructing adults, the Knowles’ andragogy adult learning theory will be applied. As stated earlier, the needs assessment showed that the content of the course is timely and relevant for the participants. They will have the opportunity to apply what they learn in relevant environments, namely their own classrooms with their own students. It will allow learners to be self-directed, providing ample opportunities for the participants to reflect on their learning and tailor learning opportunities to fit the needs of their classrooms. Moreover, the learners will be given clear expectations at the start of the course to ensure there is a full understanding of the course objectives and the expectations for meeting the course goals.

Application of Motivational TheoriesThe results of my needs assessment demonstrated that the majority of the learners are motivated to gain more information that will help them to learn more about place value skills, assessment, and strategies for teaching this concept. Since the information is

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personally meaningful, learners will most likely have a sense of intrinsic motivation to engage in the course and apply the new information that they gain. Since the information is relevant to their current job positions and the information will be applicable to their students, learners will most likely foster a sense of intrinsic motivation. Learners will also get continual feedback on their discussion posts, assignments, and activities completed.

Extrinsic motivation will also be applied in that students will receive points earned to go toward a cumulative total with each assignment completed, although no letter grades will be given at the completion of the course. Learners will receive a certification of completion at the end of the course. This certificate can be uploaded as an artifact of learning and professional development on the school district’s website, which is in turn used as a part of the annual teacher review process.

Impact of a Diverse Audience on InstructionSince all students do not learn the same, it will be essential to use a variety of learning strategies to best meet the diverse needs of the participants. All learners gain information in different ways and it will be essential to provide multiple formats for students to learn, including in small groups, in partnerships, individually, on-line, in-person, and with a variety of materials to use to aid in learning. The participants’ varying ages and amount of experience with place value will necessitate that a variety of learning strategies are used so their diverse learning needs are met.

Modifications can and will be made for participants who need alternatives to the current training methods. Materials will be made available in Spanish if needed. In addition, tutoring and additional assistance will be made available to any learner needing additional support.

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GOAL ANALYSIS

Goal Analysis

Step 1 - Write down the goals.

Original goals:

Increase teachers’ knowledge and understanding of place value concepts, as well as improve instructional and assessment practices related to place value.

Step 2 - Write down everything someone would have to say or do for you to agree that the someone has achieved the goal.

Identify student misconceptions of place value.Assess students’ understanding of place value by utilizing a formal place value assessment tool like the “23’s Task” and can demonstrate this skill.Identify the prerequisite mathematical skills a learner needs to understand place value.Define the terms unitizing, subitizing, cardinality, decompose, compose, hierarchical inclusion, and place value.Accurately assess a student’s understanding of cardinality and demonstrate this skill.Accurately assess a student’s understanding of subitizing and demonstrate this skill.Accurately assess a student’s understanding of unitizing and demonstrate this skill.Accurately assess a student’s understanding of composing and decomposing numbers and demonstrate this skill.Accurately assess a student’s understanding of hierarchical inclusion and demonstrate this skill.Accurately administer assessments for prerequisite skills for place value and demonstrate this skill.Demonstrate how to implement strategies for instructing students in each of the prerequisite skills for place value.Determine instructional strategies to use after conducting a formal place value assessment.Identify student misconceptions in student work and determine a strategy to use to help correct this misconception.Know and can demonstrate multiple strategies for teaching place value concepts to students.

Step 3 - Sort the items listed in step 2.

Sorted items and grouped them into three categories: Place Value Instructional Strategies and Assessment, Student Misconceptions of Place Value, and Prerequisite Skills for Place Value.

Place Value Instructional Strategies and Assessment

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Assess students’ understanding of place value by utilizing a formal place value assessment tool like the “23’s Task” and can demonstrate this skill.

Determine instructional strategies to use after conducting a formal place value assessment.

Know and can demonstrate multiple strategies for teaching place value concepts to students.

Measure of Success:Teachers learn assessment techniques for place value, determine instruction based on the assessment, and utilize a variety of instructional strategies to teach place value concepts.

Combined place value instructional strategies and assessment:Teachers demonstrate understanding of assessing place value using a formal assessment tool, create instructional strategies based on the assessment, and use a variety of strategies to teach place value concepts.

Student Misconceptions of Place Value Identify student misconceptions of place value. Identify student misconceptions in student work and determine a strategy to use to

help correct this misconception.

Measure of Success: Teachers understand misconceptions related to place value understanding and develop strategies for remediating the misconceptions of their students.

Combined student misconceptions items into one statement:Teachers will be able to identify students’ misconceptions of place value and determine instructional strategies to help correct the misconceptions.

Prerequisite Skills for Place Value Identify the prerequisite mathematical skills a learner needs to understand place

value. Define the terms unitizing, subitizing, cardinality, decompose, compose, and

hierarchical inclusion. Accurately assess a student’s understanding of cardinality and demonstrate this

skill. Accurately assess a student’s understanding of subitizing and demonstrate this skill. Accurately assess a student’s understanding of unitizing and demonstrate this skill. Accurately assess a student’s understanding of composing and decomposing

numbers and demonstrate this skill. Accurately assess a student’s understanding of hierarchical inclusion and

demonstrate this skill. Accurately administer assessments for prerequisite skills for place value and

demonstrate this skill. Demonstrate how to implement strategies for instructing students in each of the

prerequisite skills for place value.

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Measure of Success: Teachers gain knowledge of prerequisite skills, are able to assess student knowledge of the prerequisite skills, and provide instruction to students based on these prerequisite skills.

Combined prerequisite skills items into one statement:Teachers are able to identify, define, and accurately assess the prerequisite skills students need to understand place value, as well as demonstrate strategies for instructing students in each of these prerequisite skills.

Step 4 - Write a complete sentence to describe each of the items on your final list.

Teachers are able to identify, define, and accurately assess the prerequisite skills students need to understand place value, as well as demonstrate strategies for instructing students in each of these prerequisite skills.

Teachers will show an understanding of assessing place value using a formal assessment tool, create instructional strategies based on the assessment, and use a variety of strategies to teach place value concepts.

Teachers will be able to identify students’ misconceptions of place value and determine instructional strategies to help correct the misconceptions.

INSTRUCTIONAL OBJECTIVES

Project (Instructional) Goal

Teachers will identify and accurately assess students’ prerequisite skills for place value as well as students’ misconceptions of place value, and determine instructional strategies to correct the misconceptions and ensure students develop a full understanding of place value. Teachers will demonstrate understanding of formal place value assessments and use the results of the assessments to determine instructional strategies to teach place value concepts.

Terminal Objectives and Enabling Objectives

Teachers will apply their knowledge of prerequisite skills for place value to accurately assess student knowledge and determine appropriate instructional strategies to meet individual student needs. – Cognitive Domain

o Using your notes as a guide, define each of the five prerequisite skills for place value with 100% accuracy. – Cognitive Domain

o Using your notes as a guide, give one example of each of the five prerequisite skills for place value with 100% accuracy. – Cognitive Domain

o Given examples of problems demonstrating five different prerequisite skills for place value, distinguish between these skills with 100% accuracy. – Cognitive Domain

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o Given example problems using five different prerequisite skills for place value, illustrate one strategy of instruction for each prerequisite skill with accuracy on 4 out of the 5 skills. – Cognitive Domain

o Given three examples of student work, evaluate the students’ understanding of the perquisite skills with 90% accuracy. – Cognitive Domain

Teachers will evaluate student work to assess students’ misconceptions of place value and determine instructional strategies to correct the misconceptions.

o Given three examples of student work, identify the students’ misconceptions of place value with 100% accuracy. – Cognitive Domain

o Based on three examples of student work, create instructional strategies to correct the student misconceptions, enumerating at least one strategy to use with each of the three examples. – Cognitive Domain

Teachers will assess student knowledge of place value using a formal place value assessment tool and use the results of the assessments to design instructional strategies to teach place value concepts. – Cognitive Domain

o Using the “23s Task,” assess five students on their knowledge of place value with 100% accuracy. – Cognitive Domain

o Based on the results of the “23s Task” for 5 students, generate instructional strategies to meet students’ needs, enumerating at least one strategy to use with each of the five students. – Cognitive Domain

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REFERENCES

Adult Learners. (n.d.). Rochester Institute of Technology: Teaching and Learning Services.

Retrieved from

http://www.rit.edu/academicaffairs/tls/course-design/instructional-design/adult-

learners

Carey, L., Carey, J.O., & Walter, D. (n.d.). The Systematic Design of Instruction. Retrieved from

http://www.hastudio.us/5_CV/thesystematicdesignofinstruction.pdf

Guild, P.B. (n.d.). Diversity, Learning Style and Culture. Retrieved from

http://education.jhu.edu/PD/newhorizons/strategies/topics/Learning

%20Styles/diversity.html

Kirk, K. (n.d.) Student Motivations and Attitudes: The Role of the Affective Domain in

Geoscience Learning. Retrieved from

http://serc.carleton.edu/NAGTWorkshops/affective/motivation.html

Morrison, G., Ross, S., Kalman, H., & Kemp, J. (2013). Designing Effective Instruction (7th

ed.). Hoboken, NJ: J. Wiley & Sons

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