CEP 813: Formative Assessment Design 3.0

Through CEP 813 I not only learned what effective assessments and feedback look like in theory and in practice, but I also learned about various tools and supports that can be used to differentiate assessments/feedback and consequently improve learning outcomes. Utilizing feedback and support from my professors and what I learned about Understanding by Design, I was able to merge theory, content, feedback and design to create the final draft of my formative assessment.

In my formative assessment design 3.0, I have elaborated on the connection between assessment and instruction, listed instructions for the teacher and student, provided a rationale for the technology tools I implemented, discussed my feedback approaches as they relate to theory and best practice, and lastly, I supported my assessment design as it relates to how students learn in theory and in context.

Here is the final draft of my formative assessment: Three Acts Math

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CEP 813: Best Work

While trying to decide what I would characterize as my “best” work in CEP 813, I really had to reflect on how to measure or evaluate my “best” work. I think most people naturally assume their highest score or highest quality work represents their best work; however, I feel that my best work in CEP 813 is best represented through my growth and accomplishments, not mastery. Through lecture and play in CEP 813, I have come to appreciate the learning process much more than the end result. Consequently, I believe that some of my best work in CEP 813 was developed throughout Module 4: Using Digital Games for Assessment. Specifically, I believe that my best work is the Minecraft assessment I built to use as a tool to measure learning in my 8th grade math class. It may not be the highest quality of work I have produced in CEP 813, but it is the work that I feel represents the most personal growth as my accomplishments relate to all facets of this course.

Our creation task was broken down into two separate activities, which resulted in two separate screencasts. For the first part of the task, I explored the Minecraft tutorial world and then created a screencast of my explorations in which I played around, interacted with the environment, and I learned “the basics” necessary to navigate around the virtual world, or so I thought. In the screencast, I communicated challenges and difficulties as I encountered them and as they related to me personally. I also discussed the potential for using Minecraft as an assessment tool in my math classroom. This was an assessment FOR learning and we were assessed on the specifics of our reflection and the technical/production elements of our screencast. For the second part of the task, I was had to create an assessment in Minecraft and reflect on how my assessment design in relation to using Minecraft as a form of electronic assessment might benefit my students. In my second screencast, I identified the math concepts I planned to use in accordance with Minecraft as a way to assess student learning, and then I proceeded to navigate around my creation in the virtual world, explaining design features as they related to the assessment task. I also elaborated on how I would use my creation to measure learning. This was an assessment AS/FOR learning. The screencast was again assessed for technical elements and the rationale behind our design as it related to theory and practice.

In lieu of feedback, we were given the criteria that we would be evaluated on prior to beginning the creation task. This was essential for many reasons: [1] it made the purpose for the task transparent, [2] it revealed the expectations of the assessment, [3] it served as a framework that I could use to inform my design decisions, and [4] it provided an outline that allowed for direct feedback in relation to the specific assessment/evaluation criteria. In addition to fully understanding the purpose for the task and the evaluation criteria, the evaluation notebook was extremely valuable as it allowed for timely and detailed feedback that I could reference at any point and the comment feature made it possible to highlight and discuss specifics with my professor as needed. The organization of the feedback allowed me to easily make connections between my creation and the professor’s feedback so I could make improvements accordingly. The feedback did much more than convey a score. The feedback was thorough and provided specific examples and supports for areas that needed improvement or that needed to be developed further. Through the personalized feedback I received I learned more about how to use Minecraft effectively and also improved my final assessment creation.

Reflecting on my overall experience: at first, Minecraft appeared to be fairly easy to use and set up. We were given instructions that were easy to follow and video tutorials that explained how to navigate in Minecraft in addition to videos that elaborated on the affordances of using games in education. As a gamer, the “play” stage was exciting for me. However, once I began to create my own space in Minecraft, the excitement faded and the frustration set in. I realized that I didn’t really understand what I was doing while I played, and consequently, I didn’t focus on developing the skills that were necessary during the creation stages. I couldn’t figure out how to lay bricks down, and even if I did eventually figure it out, I wasn’t sure of the design in which I would lay them. Figuring out how to effectively use the virtual world of Minecraft in my math classroom was a challenge in itself. I had initially thought it would be easy to connect the three dimensional building blocks in Minecraft with a lesson on three dimensional geometry or isometric drawings, but after playing around on Minecraft and trying out a few different designs, I would reach the conclusion that the design I created for assessment would not result in authentic learning and could be more effectively completed without Minecraft. It wasn’t until I spent time reflecting on my commitment towards relentlessly creating a worthwhile task for my 8th grade math students using Minecraft that I realized the value of the virtual world and the creation task was actually in the learning process itself. That is, as I created in Minecraft, I was reminded of the importance of experimentation, play, and immediate feedback while developing new understanding. By default games provide automatic feedback, whether that is good or bad. They allow for collaborative workspaces and tangible learning opportunities, which in turn afford unique assessment opportunities that can inform instruction in ways that a traditional assessment approach could not. And, although I don’t necessarily plan to use Minecraft in my classroom, playing and designing in the virtual world, at minimum, gave me a greater appreciation for the learning process and forced me to reevaluate my teaching and assessing practices.

The assignments in CEP 813, especially the Minecraft creation task, forced me to learn outside of my comfort zone from perspectives I wouldn’t typically choose using tools that made me uncomfortable, like screencasts. This course has helped me learn to value different assessment approaches and the unique learning opportunities afforded through digital platforms. Through these experiences, I learned how to design authentic assessments through backwards design according to specific learning goals and how assessments situated in instruction can be used to inform and improve teaching and learning.

CEP 813: Self Assessment Blog Post – Sandbox for Professional Growth

Since I began the Master ‘s in Educational Technology (MAET) program at Michigan State University about two years ago, I have been using my WordPress blog as a way to submit work, reflect on my learning, and collaborate with colleagues. In CEP 813: Electronic Assessment for Teaching & Learning, I have had the opportunity to explore, examine, and learn how digital portfolios can be used as an assessment tool in educational settings. In fact, many of the benefits we learned about for using digital portfolios in classrooms mirror the benefits that WordPress offers to professionals utilizing it as a digital medium in the educational community. In this post, I will reflect on how the features of electronic portfolios, like this WordPress blog, afford opportunities for learning and professional growth.

Digital portfolios are easily used for self-assessment. Throughout the past few years, I have utilized this blog as a digital platform to organize, document, share, represent and reflect on my professional work. The digital format allows me to easily access my creations and provides a thorough documentation of my progress and performance throughout time. Being able to see where I started and where my learning experiences have taken me is rewarding and encouraging.

Unlike the paper portfolio, the digital medium makes it incredibly easy to compile, organize, tag, link, and revise work. I can easily locate work by searching tags, categories, courses, or even a specific time frame, making a digital portfolio an ideal option for multi-part work. In addition to serving as a platform for document and reflecting on personal progress and growth, digital portfolios make it easy for colleagues and other professionals to collaborate and provide/receive real-time feedback. As we have learned both indirectly and directly in CEP 813, feedback is an essential component in the growth process of any individual. We learn not only from receiving feedback, but also from reviewing our colleagues’ work and providing feedback.

Moreover, by publishing content on the web, I am not only establishing a digital profile and presence within my network of collaborators, I am also opening the door to a global network and audience, allowing for richer, more diverse feedback. By using digital portfolios, educators (and students) are able to make connections with other professionals on the web, establishing a sense of community in a digital context. This has been feature of WordPress that I have truly enjoyed since starting this blog.

Perhaps one of the most impressive affordances of using a digital portfolio for learning and professional growth is that it is both useful AND useable. Not only do digital portfolios allow users to publish text, images, files, etc., they are also accessible. Most Content Management Systems (CMSs) can be accessed on almost any networked device, such as but not limited to: cell phones, tablets, laptops, netbooks, and desktop computers. The ability to access and share information anytime, anywhere takes learning beyond the confines of the classroom walls and turns it into a life-wide experience, reconnecting learning and life. Likewise, the accessibility also extends to viewers who can see new postings in real-time, allowing them to post comments quickly and easily. This is a game-changer for giving and receiving feedback.

In addition to being useable, content management systems offer various tools and supports making them very useful. For example, the review comments feature that allows users to view, accept, or decline public feedback on posts prior to them being viewable to the public is very useful for shy users or users who lack confidence. This way they can still receive feedback without fearing what others may think when they see it. Actually, I prefer this tool so I can manage spam and unrelated posts, but from an instructors perspective, it is a great support to ensure students are not giving or receiving inappropriate feedback. Another useful tool is automatic email notifications whenever there is activity on your site or on the site of those you follow. This way users can manage their online presence and decide how active they want to be with other bloggers they follow.

While my digital portfolio could use some fine tuning and organization, I genuinely appreciate having a medium that allows me to record my thoughts and share my work. There are so many features and supports that digital portfolios offer that often go unnoticed. Before, I don’t think I truly appreciated the global audience and connections I have made with other professionals through this WordPress blog because I didn’t understand the importance of community and feedback. Currently, I value and appreciate the connections and dialogue much more than I had and from a new perspective, too now that I know how to use the feedback given. Before this course, I wasn’t entirely sure how to use a digital portfolio as an assessment tool, but as we bring this course to a close, I have a much better understanding of how utilize digital portfolios in my content area as well as how to assess student learning and provide effective feedback.

CEP 813: CMS Assessment Design with Haiku Learning

Assessments should be used as a way to gauge where students are in their learning and the feedback from the assessments should inform both instruction and learning. However, I think that more often than not educators are forced to give assessments that generally don’t align with their instructional style and fail to provide insightful feedback. Sometimes I feel like assessments are used just to provide some sort of data to parents…to communicate a grade in a way that parents understand, even if it doesn’t serve a purpose for improving teaching and learning. For me, I didn’t understand math until I was in college and was taught to reflect on my learning rather than erase mistakes. Based on my personal experiences, for my online math assessment design, I included both traditional assessment measures and nontraditional assessment measures such as, reflective think-aloud, investigations that require problem solving, reasoning, and proof, and collaborative workspaces.

Through both my screencast and this post I am going to tell you about the assessment I created for 8th grade math students enrolled in a fully online math class using Haiku Learning.

CMS: Haiku Learning

Log-in Link to Haiku Learning Math 8 Course, or you can self enroll using this link and by entering 527L3. Keep in mind, this fully online 8th grade math course is something that I am still designing and working on. It is a perpetual work in progress.

Subject Matter: 8th Grade Math: Pythagorean Theorem Unit (Geometry)

Assessment Location: Unit 6: Pythagorean Theorem; Lesson 1: Assess.

Age/Grade level: 8th Grade

Role of intended student: 8th Grade Math Student

Type of course: Fully Online

CMS SCREENCAST LINK

CMS ASSESSMENT DESIGN/CREATION RATIONALE:

There are several reasons why I chose to use Haiku Learning for my CMS assessment design. First, haiku learning is both effective and efficient: the design is clean, user-friendly, and easy to manage from an instructor and student’s perspective. Haiku Learning also has gradebook and multiple assessment features built into the site making it not only a great platform to teach learn and assess but also to communicate progress and proficiency accurately and in a timely manner to both parents and students.

Additionally, Haiku learning is extremely efficient from an instructors perspective as content is easily embedded and uploaded, as you can see in the videos and the multiple-choice assessment on the site. Moreover, for both teachers and students, there is an equation editor available any time you choose to type, which is key for math students especially in an online environment. Lastly, the calendar, announcements, discussion forum and Dropbox are just a few great features designed in the CMS’s infrastructure that make assigning, collecting and assessing a well-organized process.

For this particular task, the assessments I created are designed to measure whether learners have reached the desired learning outcomes at the end of the first lesson of the Pythagorean theorem unit. Since assessment should inform both teaching and learning, I will show you how the lesson design, activities, and tasks align with the assessment tasks, goals, and standards.

As shown in the screencast, the lesson and assessments are aligned with Common Core State Standards for 8th Grade Geometry and the Common Core State Standards for Mathematical Practice. Additionally, I explain how the assessment tools I have created will be used to measure proficiency regarding the basics of the Pythagorean theorem: what it is; why it makes sense; and how to use it.

The Pythagorean theorem is one of the main topics covered in an 8th grade mathematics geometry unit, which is also a standard students will be expected to further develop in both high school geometry and trigonometry. Furthermore, the Pythagorean Theorem is commonly present on standardized assessments such as the M-Step and ACT, and in the ever changing world of standardized assessments, the Pythagorean Theorem and its applications have withstood the test of time, making it a key standard for secondary math learners.

Specifically, for this task, I created three different assessments. For the first assessment, I used the built in assessment creation tool in Haiku Learning. This tool, the equation editor, automatic feedback, and direct link to the gradebook made Haiku learning an easy choice for this assessment. The last two assessments utilize the discussion board tool built in Haiku learning. Again, the discussion board tool has a built in equation editor and also allows students to upload pictures and documents to their posts. Perhaps the most impressive tool, though, is the built in rubric creation tool that links rubrics directly to assessments, discussion forums, and the gradebook, making Haiku learning the best choice for all three different types of assessments I created. In addition to those unique features, the discussion board assessment tool allows for collaboration and stimulates conversation.

These three different assessment tasks are designed to give all learners the opportunity to show they have mastered the skills in the first lesson. By differentiating the instruction and assessments, I believe I will be able to more accurately gauge what students truly know in addition to identifying misconceptions. That is, the multiple choice assessment allows me to check their computation and retention, while the metacognitive problem writing and reflective proof re creation assessments allow me to assess transfer, or each learners ability to apply their learning to new scenarios, in addition to each learners ability to consolidate and connect new learning with old. For example, in the Starbursts Re-Creation Proof assessment, I ask learners to consider using half of a Cheez-It on one side of their right triangle. By posing that question, I will be able to see if learners have made the connection between irrational numbers and the Pythagorean Theorem. Additionally, by having students write and solve their own problems dealing with the Pythagorean Theorem, I can ensure that students understand both the math content and vocabulary associated with the Pythagorean Theorem and how to apply that to new real world contexts.

Taken together, these assessments will accurately and effectively measure whether or not learners understand what the Pythagorean Theorem is, when to use the Pythagorean Theorem, and how to use the Pythagorean Theorem.

REFLECTION ON ASSESSMENT DESIGN AND IMPROVED LEARNING OUTCOMES:

Moreover, after reflecting on this weeks task of using a Content Management System to create an assessment, I feel as though the assessments I have designed align with my instructional design, which I hope stimulates learners’ curiosity, engages them in differentiated tasks, and intrinsically motivates them. By creating a collaborative workspace, students are able to ask questions and participate in interactions between one another.

I’ve also included traditional quizzes and non-traditional performance tasks. In addition to traditional assessments, which students may try to cheat on but I feel are still necessary, the performance tasks allow students to demonstrate what they know and evaluate their own learning through reflection. I tried to balance the types of assessments so that they scaffold learning but also inform teaching and learning in different capacities. For example, the results from a multiple-choice test provide much different information on learners’ understanding than the evidence revealed through reflective posts or performance tasks. I don’t think that one form of assessment provides an accurate measure of students understanding, so I included various forms that allow me to gauge where my students are at and how they are progressing using different approaches. Through this process, students will receive feedback regularly from their peers and me.

  • What went into your choices as you focused on certain aspects of your assessments?   While designing my online math assessments I decided I would take what I have learned thus far in the MAET program about online learning, how we learn and instructional design and combine those factors with the format and design of many of my MAET classes, which are also fully online. In addition to the design, I tried to focus on efficient, yet differentiated presentations of lesson content and assessments that aligned accordingly. This task has proved to be harder than I initially thought it would be. I tried to focus on including both traditional and nontraditional assessment methods that allow learners to demonstrate what they know. So, in addition to multiple-choice-like assessments, I made it a priority to implement performance based assessments, reflective assessments, and collaborative assessments. Regardless of the assessment type, I also focused on providing feedback within and throughout the lessons and assessments. For example, responding to reflective posts or setting up quizzes so learners receive automatic feedback based on their correct/incorrect answers.
  • How will your assessment of your students be a tool to grow your students’ learning? The assessments shown in the screencast are designed to inform teaching and learning. Through immediate feedback on lesson quizzes students are able to identify their strengths and weaknesses. Similarly, that data provides insight to me as their instructor on which areas I need to go back and re-teach. Moreover, the assessments I implemented in each lesson are designed to stimulate collaboration and reflection. This allows me to assess learners understanding on an individual level and within a community. For example, in the third assessment, students are recreating a proof using Cheez-It snacks and posting their findings to the class discussion. They are also writing their own real world problems and providing insightful feedback to their classmates. Through differentiated assessments learners are receiving feedback from multiple sources and are making adjustments in their learning as they progress, which ultimately leads to personal growth. In fact, learners will not only grow by completing the assessment tasks, they will also grow by reading and providing feedback to their classmates and reflecting on the process. Through this process, by providing multiple different methods of assessment in each lesson, I hope that learners are appropriately challenged and stimulated and if they aren’t that the data collected from the various assessments informs my instruction and allows me to make changes.
  • How will students be involved in the assessment and evaluation process? The way students are involved in the assessment and evaluation process differs based on the assessment design. For example, in reflective assessments, students will receive personal one-on-one feedback from me, sort of like the feedback we receive in our portfolio for CEP 813. Based on my feedback and questions, learners are able to modify and edit their posts and assignments. Moreover, in collaborative assessments, students are involved not only by providing feedback to their peers, but also by responding to the feedback they receive from their peers and me. In additional to reflective and written assessments, students are involved in their lesson assessment quizzes based on how they respond to their immediate feedback and score. They should accommodate their study habits based on their performance scores so they can make improvements by the time they reach the unit summative assessment.

Review of Content Management Systems Through the Lens of Assessment

This week in CEP 813 we examined and compared the affordances of free Content Management Systems (CMSs) through the lens of assessing student learning. I chose to compare Weebly for Education, COURSEsites by Blackboard, and Haiku Learning. The results of my critical review of the three sites listed can be found in this spreadsheet.

Based upon my analysis of these three CMSs, I have chosen to use Haiku Learning to create my CMS assessment. The main reason I chose Haiku Learning is because it not only had all of the redeeming qualities and capabilities I was looking for in the assessment framework, but it also was very user friendly- from an instructor and student perspective. All three sites appeared to offer unique and differentiated options for assessing students-formative and summative, but I was most impressed with the design and usability of Haiku Learning. For example, Haiku Learning offers the following options that could easily be used to assess student learning: 1) discussion forums, 2) dropbox submission, 3) surveys, 4) rubrics, 5) learning portfolios, and 6) peer and self assessment tools. However, I did find that COURSEsites by Blackboard offered perhaps more specific options for collaborative group work, like assigning roles and jobs, but it was much more difficult to navigate and set up than both Weebly for Education and Haiku Learning, which made the features not worth it to me. I felt like Haiku Learning‘s traditional and non-traditional assessment tools worked harmoniously within the framework design and flowed well with content, opposed to Weebly for Education and COURSEsites by Blackboard where I spent a lot of time clicking around in different places to utilize and create different assessment types, but again, that is a design issue not an issue of whether or not the features exist. I am just a huge believe in USEFUL and USEABLE tools, and the challenging design framework in both Weebly for Education and COURSEsites by Blackboard made some of the features and tools less USEABLE.

Since assessment should inform teaching and learning and in many ways drive our instruction, I was pleased to see the various options for feedback in relation to the assessment type. Some sort of gradebook feature is available on each of the CMSs I reviewed, keeping both parents and students informed and up to date. Additionally, through various multimedia tools and options on each of the sites, students are able to express themselves creatively and receive direct feedback via comments from their instructors and peers. For example, in math class, I like to utilize GeoGebra as a teaching, learning and assessing tool. Unless I used a link to a new page for each GeoGebra activity, I would need to be able to embed Java applets into my site. Having learned to navigate Weebly for Education quite well over the past few years and through my explorations with Haiku Learning the past few weeks in both this course and CEP 820: Teaching Students Online, I know I am able to embed Java applets into both of these sites; however, I was not able to figure out how to embed Java applets into COURSEsites by Blackboard. I don’t want to say it isn’t possible, though, because I am still learning to navigate the site and it’s tools. To view a GeoGebra lesson I created on Weebly with a Java applet embedded in the site page, check out my webpage on quadrilaterals and technology. Feel free to play around with the Java applet 🙂

Another great feature I was surprised to find is that all three sites offered an equation editor. As a math teacher, that was a feature I looked for right away. Having created online assessments using a shifty equation editor in Schoolnet for over three years now, I have become all too familiar with writing an equation in Microsoft Word, taking a screenshot of the equation, uploading the PNG file to the assessment question, and then repeating for additional assessment questions as needed. This daunting process is something I would definitely want to avoid while developing an online math course because we use equations so often in math class. As far as I can tell, the equation editors in each of the three sites appear to be up to par and don’t require coding like the equation editor in Schoolnet does.

Moving forward, the plan is to create a collaborative formative assessment activity using Haiku Learning and GeoGebra that allows learners to explore the Pythagorean Theorem. My Math 8 students will work together in a collaborative group space, using GeoGebra to explore and develop an informal proof of the Pythagorean Theorem. Through this activity I will be able to monitor and direct learning by providing feedback and stimulating discussion conversation, allowing my learners to eventually demonstrate their understanding of the Pythagorean Theorem.  In the assessment, students will go on to become “Problem Writers” posting a real-world question involving the Pythagorean Theorem for their peers to read. Then, they will go on to review and respond to at least three questions posted by their classmates.  This will foster collaboration between the students while also assessing students’ understanding of the Pythagorean Theorem (the question they write) and it’s application (their ability to solve their classmates real-world questions).

CEP 813: Infographic

Here is a link to my Infographic: Exploring a Mobile, Networked Curriculum in Secondary Math Classrooms

We live in a highly mobile, globally connected society making mobile devices a handy medium of gaining knowledge: with two-thirds of K-12 learners in the US already using smart phones and of 75% of the US workforce already mobile, 65% of those workers declaring their mobile devices to be their “most critical work device” (U.S. Department of Education Office of Educational Technology, 2010). The increasing prevalence of technology in both academic and corporate settings necessitates that students become comfortable using technology to facilitate learning and productivity. Thus, the challenge for our education system is to leverage technology to create relevant learning experiences that mirror students’ daily lives and the reality of their futures. Learning can no longer be confined to the years we spend in school or the hours we spend in the classroom: It must be lifelong, life-wide, and available on demand. It is evident that mobile devices are an integral part of learning strategies in workplaces, educational settings, and casual environments.  To address the diverse demands of 21st century education and prepare children for life in a global economy, I believe mobile learning must be harnessed as an integral part of learning strategies in workplaces, educational settings, and casual environments.

Mobile learning devices offer consolidated access to high- quality learning materials, including a myriad of tools within the supporting infrastructure built into the device (seamlessly integrated applications, calendar, internet capabilities, social media, multimedia, calculator, e-mail, notes, reminders, & management of technology), allowing users to do more with less. A key tenet of personalized learning is the ability of individuals to choose the right tools for the right tasks and mobile devices equip learners to do just that.

With that said, this week I decided to create an infographic using Piktochart to show how mobile learning devices can be used in accordance with a networked curriculum to stimulate engaging learning experiences that align with 21st century education.

CEP 813 – Module 1 – Annotated Assessment/Evaluation Exemplar

In Module 1: Foundations of Assessment and Evaluation, we were asked to take a critical look at the design of a typical classroom assessment we have used in our teaching profession. The assessment I am analyzing was designed as a summative assessment for an 8th grade math unit on the Pythagorean Theorem. The formatting/sizing of the questions may look funky because I built the test on Schoolnet, an online assessment and reporting system we use in my school district, so it is a digital assessment that I downloaded into a PDF version so you all could see.

Underneath the assessment shown below, you will find my critical analysis of the assessment.

Critical Analysis of Assessment Design:

a) How would I describe the design of this assessment? The assessment was designed as a summative (end of chapter test) for an 8th grade math unit on the Pythagorean Theorem. The assessment includes multiple choice, gridded (type in the number), and open response questions. The assessment is also designed to have at least a two question spread for each of the six skills (3 standards) I assessed.

b) What is the purpose of the assessment? Since it is a summative assessment, it is designed to be evaluative rather than diagnose. That is, the purpose of this assessment is to determine levels of understanding and achievement for each learner and convey that information to them in a transparent way, evaluate the effectiveness of my instruction and assessment design for the unit and make changes accordingly, measure each learners’ progress/improvement on each learning goal (skill in terms of growth and proficiency levels, and make decisions regarding students that need re-teaching and re-assessment before moving onto the next unit. Specifically, the purpose of this assessment is to convey the growth and mastery level of each skill for each student in a transparent way and report/record the achievement levels. The specific learning goals/standards are shown in part (c).

c) How does this assessment align, if at all, with the curriculum standards that guide my professional practice?  The assessment aligns with the Common Core State Standards for 8th Grade Mathematics. There are three standards that align with the unit, which are broken down further into six skills that can be seen in the document shown beneath the standards.

CCSS.Math.Content.8.G.B: Understand and apply the Pythagorean Theorem.

  • MATH.CONTENT.8.G.B.6: Explain a proof of the Pythagorean Theorem and its converse.
  • Skills for standard:
  • MATH.CONTENT.8.G.B.7: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
  • MATH.CONTENT.8.G.B.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

d) What information will this assessment give me about each student? This summative assessment will tell me each students scale score for each skill assessed this unit. That is, I will know the level of understanding each student has in relation to each skill I assessed. I will also look for growth shown throughout the unit. Between smaller assessments covering each individual skill (concept quizzes) and formative assessments in class, the students and I have been tracking their progression throughout the unit. The summative assessment should reveal growth for each student from where they were at the start of the unit, where they were as we progressed in the unit, and where they were when they finished the unit.

e) How do I intend to use the information provided by this assessment? I use the information on summative assessments to tell me which students need to stay after for re-teaching sessions and a re-assessment. Students only re-assess on skills they aren’t proficient in, so they aren’t necessarily retaking the entire assessment. The nice thing about having concept quizzes and formative assessments throughout the unit is that most of the misconceptions and/or gaps in understanding have been addressed before we get to the summative assessment. Like I said previously, the summative assessment is evaluative rather than diagnostic. I typically have a good idea on what students know and how they are going to do before they take the summative assessment. I think the students would agree and say they also have a pretty good idea of how they will perform on the summative assessment. I use the findings from the summative assessment to report progress and achievement to students/parents in a transparent way. Further, I use the data collected on summative assessments to analyze, modify, and improve the assessment. Sometimes the data reveals that I may have a confusing or just plain bad question that needs to be thrown out or rewritten, so I use those findings to evaluate the effectiveness of my assessment, too.

f) What assumptions have I made about whether this assessment will, in fact, give me the information I need about the students who do it? I have assumed that this assessment will reveal accurate results regarding each student’s level of proficiency in each of the six skills. I have assumed that my questions are transparent, accurate, effective, and do not need to be modified. I have assumed that the scale scores I have established are accurate, fair, and represent growth and achievement levels accurately for each learner & each skill. I have assumed that students who practiced the skills and made improvements based on the feedback they received throughout the unit will continue to improve and will show levels of mastery for each skill being assessed. Contrastingly, students who have continuously not completed practice sets, concept quizzes, or participated in formative assessments in class assessments will lack growth in most areas and will not show levels of proficiency for most, if not all, of the skills being assessed. I have assumed that this assessment design will accurately assess all of the skills we have covered this unit. Lastly, I have assumed that the assessment can be easily broken down into the different skills being assessed to show where students need improvement and where they are proficient.

g) What skills have I assumed students have that will enable them to complete this assignment? I have assumed that students can read and work technology, since the assessment is online. I have also assumed that they understand how to use the online assessment and the embedded tools. In relation to the content, I have assumed that, when given formulas, students can perform mathematical operations to either simplify or solve equations depending on the scenario… although I am not sure I would say I assumed that information since this is the summative assessment and I typically have a pretty good understanding of what students can and cannot do mathematically at this point.

h) For whom would this assessment prove difficult? Why?  This assessment will be difficult for students who struggle with application of mathematical concepts and theorems in real world and mathematical scenarios. Moreover, students that struggle with relating mathematical formulas to word scenarios will struggle as several questions require deconstructing text and applying multistep mathematical computations. Students who struggle with graphing will also struggle with the skills that requiring graphing distances in the coordinate plane. Further, students who have not practiced the skills throughout the unit or worked towards improvement based on the feedback they received throughout the unit will also struggle on the summative assessment.

i) Based on my readings this week, are there ways that I can imagine re-designing this assessment so that it’s better in some way? Explain your rationale and justification for your re-design idea(s). I think there is always room for improvement, and after this weeks readings, I definitely think this assessment should be re-imagined and structured to motivate more students to want to do well rather than complete it as a means to an end. I think including a reflective piece or maybe a short answer portion where students write their own problem would be one way I could attempt to improve the design and learner motivation. Another idea would be to include some sort of project or performance task where learners complete the proof of the Pythagorean Theorem using manipulatives. Although, that is already a formative task we do earlier in the unit. I do think that some sort of hands on task would be a way to reach learners who are better at orally explaining what they know or physically showing what they know.

I think that the assessment I made is designed well in relation to the content and skills I want to assess and in terms of the information I hope to get form the assessment. Prior to this point there have been several formative assessments embedded within instruction and feedback has been provided several times daily, so my students have been able to diagnose weak areas and improve them before the summative. Perhaps, instead of giving the assessment online with all of the skills on one test, I could break the summative into six separate assessments so the learner has a clearer understanding of what skill is being assessed, although, reasoning to decide what the actual problem is or what the question is asking and then deciding how to complete the task is an important feature of the design of the summative test that covers all six skills. I think that separating the skills into separate assessments may trivialize the assessment all together. Part of what I am looking for is whether students know when to apply the Pythagorean Theorem or its Converse and whether or not they know which method, formula, and/or theorem they need to complete real world and mathematical tasks.