Math Methodology is a three part series on instruction, assessment, and curriculum. Sections contains relevant essays and resources.
This page continues part 2 on Assessment, providing Assessment Resources.
Part 1: Math Methodology: Instruction
Part 2: The Role of Assessment
Part 3: Curriculum: Content and Mapping
Keep up-to-date on Progress toward Assessments for the Common Core State Standards in Mathematics
Visit the consortia that are working toward developing assessments for the Common Core State Standards (CCSS) in Mathematics:
The Partnership for Assessment of Readiness for College and Careers (PARCC) is a consortium of states working together to develop the K-12 assessments in English and math related to the Common Core State Standards. See PARCC's sample test items and performance tasks for the Common Core State Standards in mathematics.
In January 2014 PARCC made available computer-based sample test items for ELA and Math for grades 3-5, 6-8, and high school. There are also tutorials that demonstrate how students will navigate the test.
Raising the Bar: Becoming Assessment Ready (2014, February) is a white paper sponsored by Education Networks of American in collaboration with the Consortium for School Networking (CoSN) and the eLearn Institute. You'll learn about key considerations, including why online testing, the assessment consortia, PARCC and SBAC implementation, network infrastructure and support considerations, device considerations, IT support considerations, instructional design and preparation considerations. There are readiness recommendations and a checklist, school district case study briefs, and a list of resources.
Prepare for Common Core Online Testing:
Do you have the necessary technology?
Hot News for 2014: The State Educational Technology Directors Association (SETDA) developed a website called The Guide to Technology Requirements to support states for implementing online assessments. It will help you identify your technology needs in terms of computers and other devices, network and infrastructure, and provide assistance for determining student, educator, and school system readiness. "The website provides interactive charts, filtered by individual state and consortium, that enable the viewer to read and report on those requirements relevant to a school or district depending upon its specific assessment needs." Charts for six testing consortia are included: PARCC, Smarter Balanced, WIDA, English Language Proficiency Assessment for the 21st Century, DLM Alternate Assessment System, and the National Center and State Collaborative. After selecting your state, the chart revealed will show only consortia in which your state participates. (About this Project section)
December 4, 2012: SETDA released Assessment Readiness guidance in Technology Readiness for College and Career Ready Teaching, Learning and Assessment, which "is targeted to policymakers and K-12 school leaders interested in addressing school technology readiness needs for college and career ready teaching, learning and assessment. As guidance regarding minimum technology specifications are released by PARCC and Smarter Balanced, education leaders must consider this information in the context of the full range of technology issues schools are addressing today," according to SETDA. A primary consideration for teachers per SETDA is the following:
"Digital testing requires digital learning. Students using technology to take high--stakes tests must have significant opportunities to develop and demonstrate master of tested knowledge, skills and abilities via substantially similar technology prior to being tested. Teachers must be prepared to support this shift in instruction" (p. 1).
SETDA also addressed The Broadband Imperative. Among its recommendations is that schools target an external internet connection of "At least 100 Mbps per 1,000 students/staff" by the 2014-15 school year and "At least 1 Gbps per 1,000 students/staff" by 2017-18 (Fox, Waters, Fletcher, & Levine, 2012, p. 2). Schools can test their broadband performance using the National School Speed Test from the Education SuperHighway.
SBAC and PARCC released guidance for the minimum hardware specifications for new K-12 technology purchases that may be needed to ensure that schools are equipped to deliver the new Common Core online assessments beginning in 2014-2015. There are some commonalities to those specifications in terms of hardware, operating system, networking, and device type. NOTE on Updates to Specs: SBAC indicated that "the minimum and recommended specifications in the Technology Framework documents have been clarified as of 11/1/13." Technology Guidelines for PARCC Assessments (updated February 2014) "provides minimum and recommended specifications for computer hardware, input devices, and security requirements; and suggests recommended levels of bandwidth that will support schools instructional and assessment needs" (PARCC description).
Pearson has also developed Considerations for Next-Generation Assessments: A Roadmap to 2014, which focuses on five steps to make a successful transition to online assessments, benefits to online testing, case studies, and other considerations. It is available in webinar format and in print. Those steps include to conduct a needs analysis, develop a realistic transition strategy and plan, ensure interoperability, communicate proactively, and anticipate ongoing change.
Is your school's Internet access fast enough for digital learning?
Find out at SchoolSpeedTest.org, an initiative of the EducationSuperHighway. By following four steps noted at the website, "In less than a minute you'll know the speed of your school's Internet access and the types of digital learning it can support."
Is your school and district prepared to handle technology failures and legal liabilities?
Online testing might pose challenges to bandwidth and the network. When it fails and affects learner performance on those tests, including for learners with special needs and IEPs and for those whose performance might be tied to graduation requirements, there is the potential for legal issues. According to Justin Bathon (2013):
"Preparations might include reviewing contract language with wireless and bandwidth providers, having a device charging plan or policy to ensure access to an adequate charge for the exam, reviewing the district filtering policy for activities during test administration, strategizing for the administrative response in the event of a technical failure, and consulting with the district legal counsel in an effort to prepare all for potential eventualities" (p. 19).
Authentic Assessment Toolbox, by Jon Mueller of North Central College in Illinois, is a how-to hypertext on creating authentic tasks, rubrics, portfolios and standards for measuring and improving student learning. The Toolbox also contains a glossary of terms associated with authentic assessment and examples.
Assessment in Math and Science: What's the Point? is a video workshop for K-12 teachers with eight 90-minute video programs, workshop guide, and Web site. Examine current assessment issues and strategies in real K-12 math and science classrooms through videos interspersed with lively discussions of practicing teachers and content experts. Graduate credit is available. There is no fee to view the videos, which are brought to you by Learner.org.
Balanced Assessment in Mathematics was originally developed at the Harvard University Graduate School of Education. The library, now available at the Concord Consortium, contains over 300 assessment tasks for grades K-12, which you can use in your classroom for free. Tasks are categorized as primary (K-2), elementary (3-5), transition (5-7), middle school (6-8), high school basic, high school, high school advanced, and technology based (7-12). You will also find reports on how to assess mathematical understanding and skills effectively, scoring assessment tasks, and a spreadsheet to assist you with the scoring system for the tasks.
Fair Isn't Always Equal: Assessing & Grading in the Differentiated Classroom (2006) by Rick Wormeli will help middle and high school educators to make decisions on differentiation and assessment on several topics. Section 1 provides a rationale for differentiated instruction and delves into acceptable evidence of mastery. Section 2 addresses assessment in a differentiated classroom, types of assessments, tiering assessments, and creating good questions. Section 3 on grading helps educators to decide if they should incorporate effort, attendance, and behavior into academic grades; what approach they should take to grade homework or allow learners to re-do assessments, and setting up grade books and report cards for the differentiated classrooms. Section 4: Implementation and the Big Picture contains 36 tips toward implementing successful practices and answers the question, "How do differentiating teachers assess and grade differently?"
Formative and Summative Classroom Assessments from Park University includes advantages and disadvantages of both types of assessments. Classroom techniques for formative assessments, including journal writing are provided. There are guidelines for enhancing summative assessments and writing test items with expanded tips for several forms: true/false, matching, multiple choice, portfolios, alternative and authentic assessments, essays, and short answer. Grading strategies, including development and use of rubrics, add to the value of this resource.
Forms of Assessment by Dr. James Atherton (UK) contains current forms of assessment, including the description, indications (when to use), contra-indications (when not to use), and special precautions. Methods include case studies, collaborative/group projects, direct observation, essays, exams (unseen and seen/open-book), multiple-choice tests, oral questioning after observation, performance projects, portfolios, practical projects, presentations, problem sheets, self-assessment, simulations (forms of games), viva voce (oral) exams.
How to Create and Use Rubrics for Formative Assessment and Grading by Susan Brookhart (2013) includes two sections. In Section 1, Brookhart lays out the basics of rubrics, explains their importance, discusses common misconceptions, and how to write or select effective rubrics. She identifies various kinds of rubrics and their essential components. In Section 2, she explains how to use rubrics for formative assessment and grading.
Instructional Tools Related to Quality Test Construction from Dr. Bruce Frey at Special Connections, University of Kansas. Tools relate to Bloom's Taxonomy, writing a table of specifications, item analysis, multiple choice, matching, and testwiseness and guessing.
Multiple Choice Construction Checklist by Dr. Robert Runté (2001) contains tips for better multiple choice questions, true/false questions, matching and completion tests. Reporting test results and item analysis are also included in this set of checklists.
National Center on Student Progress Monitoring has a library of "downloadable articles, PowerPoint presentations, FAQs, and additional resources about student progress monitoring, Curriculum-Based Measurement, applying decision making to IEPs and other researched based topics," which will help educators to implement student progress monitoring at the classroom, building, local or state level.
Rubrics for Assessment is a collection of rubrics posted at the University of Wisconsin for assessing virtual learning in simulations/games, portfolios, cooperative learning, the research process, PowerPoint projects, podcasts, oral presentations, web pages, blogs, wikis, math/art/science/writing, and other Web 2.0 projects. There are also rubrics for primary grades and resources for creating your own rubrics.
Rubrics for Web Lessons from San Diego State University.
Test Accessibility and Modification Inventory (2010) is an evaluation tool designed to facilitate a comprehensive analysis of tests and test items, including analysis of computer-based tests. It was written by Peter Beddow, Ryan Kettler, and Stephen Elliott of Vanderbilt University. Analysis considers the passage/item stimulus, the item stem, visuals, answer choices, page/item layout, fairness, depth of knowledge level. Computer-based test analysis also considers the test delivery system, test layout, test-taker training, and audio.
Developing Performance Assessment Tasks from Prince George's County Public Schools includes the definition of performance assessments, characteristics of effective performance tasks, research on the value of those, the design process, and evaluation process for performance tasks.
How to Design Questions and Tasks to Assess Student Thinking by Susan Brookhart (2014) provides guidance on how to assess higher-order thinking and manage assessment of it, how to view assessment questions and tasks as problems to solve, writing multiple-choice question to assess higher-order thinking, and using open-ended and close-ended questions. She delves into performance assessment tasks: the basics, varying the amount of structure, controlling cognitive level and difficulty, and provides an idea bank of performance assessment tasks. Multiple examples from K-12 content areas are included.
HOT for CCSS: Illustrative Mathematics Project is a work in progress to produce illustrative tasks that students would be expected to do related to each of the Common Core State Standards for Mathematics. Sections address illustrations for the K-8 and High School standards. The project is an initiative of the Institute for Mathematics & Education and the Bill & Melinda Gates Foundation.
Introduction to Performance Tasks from Area Education Agency 267 in Iowa contains a step by step guide on how to write performance tasks/performance assessment tasks, when to use them and why they should be used. From this link, you can also access a number of general teaching strategies.
HOT for CCSS: Mathematics Assessment Project (MAP) is funded by the Bill and Melinda Gates Foundation. A collaborative team from the University of California at Berkeley and University of Nottingham in the UK is developing assessments that will help educators to implement the Common Core State Standards (CCSS). At MAP you will find both summative tests or tasks and formative assessment lessons. Tasks available are for high school and middle school. Tasks are grouped into novice, apprentice, and expert levels and "variously ask students to use their mathematics in routine or non-routine situations to design, plan, estimate, evaluate and recommend, review and critique, investigate, re-present information, explain, define concepts, and show their skills in routine technical exercises." Further, "MAP thus provides a source of tasks for assembly into tests that teachers can use for periodic summative assessment during the school year and, where appropriate, in substantial end-of-year examinations. They also provide a model for designers of high-stakes tests who aim to develop valid assessments of the mathematics described in CCSS." (Summative assessment section)
HOT for CCSS: Mathematics Common Core Toolbox has sample task items for elementary, middle, and high school from the PARCC Prototyping Project, posted by The Charles A. Dana Center at the University of Texas at Austin.
Mathematics Performance Task Bank provides "the classroom teacher with resources to assist in learning about and implementing performance-based math assessments in the K - 8 classroom" (Introduction section). You'll find resources organized by grade level and math strand. This site is from Albuquerque Public Schools: Research, Development, and Accountability.
New York City Department of Education: Tasks, Units & Student Work. "NYC educators and national experts are developing Common Core-aligned tasks embedded in a unit of study to support schools in implementing the Citywide Instructional Expectations. These resources include task descriptions, teacher-annotated student work representing a range of performance levels, rubrics to assess student work and instructional supports including Universal Design for Learning (UDL) principles" (About the Tasks section). You can search tasks and units by keyword, grade level, subject area, and standard.
PALM (Performance Assessment Links in Math) from SRI International is an "on-line, standards-based, resource bank of mathematics performance assessment tasks indexed via the National Council of Teachers of Mathematics." Tasks are grouped by grade band, and include "student directions and response forms, administration procedures, scoring rubrics, examples of student work, and technical quality data calculated from field testing." (What is PALM? and About tasks sections)
Engrade is a totally free online gradebook suite, which includes the gradebook, an online calendar for homework and events, attendance book, student reports, and online messaging for parents and students.
Jumprope is a web-based platform, free for teachers. It includes standards-based gradebook in which teachers can write their own standards, use state standards, or align curriculum to the Common Core. Teachers can record attendance, track student behavior and character development. There are curriculum design tools based upon the principles of backwards planning. Jumprope also provides administrative tools for school-wide reporting.
Kickboard was a 2014 SIAA CODiE classroom management solution finalist. It's a standards-based gradebook. It stores teacher-developed tasks and rubrics, captures student artifacts, enables teachers to form and manage groups and to add weight to assignments. There are multiple grading formulas from which to choose. Attendance, behavior, and character strengths can also be collected. Teachers can request a free classroom account.
LearnBoost is a free online gradebook and classroom management system, which also has support for use with the Apple iPad. Some features include "managing and creating lesson plans, tracking attendance, maintaining schedules, integrating calendars including Google calendars, [and] seamless tagging of Common Core State Standards" (About section).
Sifu is an online gradebook with the Common Core standards pre-loaded. It is subscription based. It is available on MAC, PC, Android, and IOS devices and includes a feature called "Motion Graph" for a visual viewing of student progress over time.
ClassMarker is online quiz making and grading software with several formats for developing questions. Choose from two testing options: class-based or external testing. The standard account for class-based testing includes full functionality for creating and administering online quizzes and is free. External testing allows you to "embed tests within your website or link directly to them (optionally password protect your tests)" and there is also a free version. Nominal fees are connected to the professional version for each option.
EasyTestMaker.com is a free test generator for multiple-choice, fill-in-the-blank, matching, short answer and true and false questions. Insert instructions, create multiple sections and alternative versions, and generate the answer keys.
ProProfs.com has a free online quiz service--Quiz-School. Create and customize your quiz. You can share it with others. You can post the quiz on any webpage, including at your classroom website, or link to it from any webpage. You can create printable versions, too, add discussion on the quiz, set criteria for passing, and provide feedback on what the correct answer should have been. Assign keywords to your quiz for easy retrieval. The site also has a section for creating flashcards for free.
Quia for the Web from IXL Learning is a low-cost annual subscription service with a range of options for creating 16 types of games and learning activities, quizzes with any of 10 types of questions, and sharing your activities with others. There are over 1900 shared activities for math alone. You can create classes and track quiz results, create class pages for communicating with students, and maintain an online schedule and calendar. You can upload images and audio clips, and copy/modify any of Quia's activities to suit your own needs. IXL Learning also has a site called IXL Math, with practice problem sets in math for grades preK-8 and sections for algebra and geometry.
Quizlet allows you to make digital flashcards for free. You can import existing questions and answers on your computer or from a web site or type them in directly. There are several modes for students to interact with content: familiarize mode, learn mode, test mode, and then games (e.g., the matching game called Scatter and video game simulation called Space Race). In test mode questions can be matching, true-false, multiple choice, short answer and any combination of those with a scoring capability. Students can keep track of their progress. You can view quizlets created by others; there are multiple quizlets available in K-12 math.
Edulastic is free for teachers. "K-12 teachers can craft homework assessments aligned with the Common Core, track mastery, and collaboratively share their proven curricula with other teachers. They can also create constructive, non-evaluative, practice spaces for students" (About section). A valued feature is the option to create Common Core aligned assessments for specific standards using questions in Edulastic's open resources. You can also create your own from over 40 different technology enhanced Common Core-aligned question types.
Infuse Learning provides a platform to "engage every student, on any device. Make informed decisions at the point of instruction with real-time, student feedback." The product enables learners to read, write, and participate in their native language. International collaboration via the internet is possible. Sign up for free. See video tutorials on how to use Infuse Learning at gettngsmart.com.
MasteryConnect has a free section for common assessment creating and sharing. "Share assessments of any curriculum type such as multiple choice, open-answer, rubrics, writing and oral assessments." You can also modify and remix assessments to suit your own class, and re-upload those to share with the community. MasteryTracker is also a free feature for monitoring and reporting mastery. Within it you'll also find standards resources and content tied to both state and Common Core standards.
Socrative "is a student response system that empowers teachers to engage their classrooms through a series of educational exercises and games via smartphones, laptops, and tablets." Socrative is by MasteryConnect and is free.
HOT for CCSS: Math Reasoning Inventory (MRI) is "is an online formative assessment tool designed to make teachers’ classroom instruction more effective. The MRI questions focus on number and operations and are based on content from the Common Core State Standards for Mathematics prior to sixth grade." There are three assessments in the MRI: whole numbers, decimals, and fractions. Each has two levels, an interview section done face-to-face with about 10-12 questions for assessing understanding and core reasoning strategies and then a written section completed by each learner individually. (About the Assessment section). MRI can be completed in a short time: about 10 minutes for the interview and 5-10 minutes for the written section, and would be appropriate for learners in upper elementary grades through middle school, about grades 4-8. MRI is free for teachers. Sample videos are at the web site that demonstrate how learners think and reason appropriately and also with lack of understanding. The MRI author team is led by Marilyn Burns, founder of Math Solutions. The project receives financial support from the Bill & Melinda Gates Foundation.
rCampus.com has Rubric Studio, a free comprehensive rubric design and assessment tool to build simple or complex rubrics with multiple sections and a flexible number of rows and columns. There is also a Rubric Gallery with a collection of rubrics made my members, organized by subject and type of rubric.
yourhomework.com allows registered teachers to post assignments online for their K-12 students. No more excuses for "I didn't know what the assignment was." The basic service is free.
Do you need help with online testing?
Online testing is a reality. New assessments are being developed by two consortia in connection with implementing Common Core State Standards in mathematics and English language arts. The Partnership for the Assessment of Readiness for College and Careers and the SMARTER Balanced Assessment Consortium are developing those for the general student population. The new online assessments will be implemented during the 2014–15 school year.
Assess4ed.net from the State Educational Technology Directors Association is a HOT resource that will assist "states and districts in making the shift to online and computer-based student assessment, including implementing the RTTA program by the 2014-15 school year. Assess4ed.net supports communication and collaboration between the private and public sectors, and – within states, districts, and schools –emphasizes the important roles for curriculum, assessment and technology staff necessary for implementation of the Common Core State Standards (CCSS) and their assessment." You'll find "webinars, resources, discussions, synchronous and asynchronous chats and other opportunities for communication and collaboration among assessment, curriculum and technology staff at the state and district levels regarding getting ready for online assessment" (About Us section).
All of the following include math. Some feature other content areas beyond which is described below.
American Education Corporation provides research-based core curriculum instructional software for K-12 and up. Among those are RTI and math.
Carnegie Learning, Inc. publishes research-based math solutions for middle school, high school, and post-secondary students.
Compass Learning for K-12, including RTI and math. Odyssey is the flagship product.
CTB/McGraw-Hill features assessment for preK-12 and adult learners. Acuity Common Core is a featured product for K-12
Curriculum Associates has K-12 solutions for math, RTI, test prep, and more. You can select your location to see products geared to your state. Note: Ohio educators might be interested in the Ohio Strategy-Specific Mathematics Kit for grades 2-8, which includes a built-in pacing chart and lesson plans for teachers, diagnosis followed by targeted and scaffolded instruction, assessment that tracks progress and skill mastery, and test simulation experience. Of particular interest to all states that adopt the Commom Core State Standards is the i-Ready Common Core State Standards Screener for grades 3-8, which is a one-hour online diagnostic per subject to help prepare for the CCSS testing. Per the web site, the program will help districts:
Discovery Education Assessment provides K-12 assessment solutions that measure and improve student achievement and predict performance on your state’s high-stakes exam, which were built from Vanderbilt University assessment research.
Edmentum (formerly known as Plato Learning) interventions for K-adult learners.
Houghton Mifflin Harcourt -- see the section, At School, for curriculum and assessment solutions.
Kaplan K12 Learning Services. Select your state for how Kaplan meets your needs. Math intervention is principally addressed for learners who are below grade-level in skills or who need extra reinforcement of grade-level skills. Ohio educators will appreciate Kaplan's Test-Taking Strategies for the Ohio Graduation Test (OGT), which devotes up to 12 hours in reading and math for each subject.
McGraw-Hill Education publishes for pre-K through adult learning.
Measured Progress features the Common Core Assessment Program for grades 3–8 and high school among its assessment products. It includes Benchmarks, Testlets, an Item Bank, and professional development.
MetaMetrics "is focused on improving teaching and learning in grades K–12 by enabling educators, librarians and parents to use students’ scores from classroom and state tests to link assessment with instruction." Its free resource called The Quantile Framework for Mathematics "measures mathematics achievement and the difficulty of mathematical skills and concepts ... By placing the curriculum, teaching materials and students on the same developmental scale, Quantile measures help educators to describe which mathematical skills a student has learned, those that require additional instruction and new skills the student is ready to learn. Quantile measures better enable educators to target instruction, monitor student growth and forecast performance on high stakes tests. Parents also can use Quantile measures to support students’ mathematical development by connecting them with targeted mathematics activities at home" (Resources section: MetaMetrics Backgrounder). An extensive database of K-12 instructional resources and math textbooks is available to help educators and parents locate a list of specific skills and concepts that a student is ready to learn. Then "after searching for skills the student is ready to learn, teachers and parents can click on the links provided leading to resources such as worksheets, games, websites, mathematics textbook lessons, and more" (Resources section: What can teachers and parents do with the measure?).
Northwest Evaluation Association Computer Adaptive Assessments includes their Measures of Academic Progress. Also see the Common Core MAP.
Pearson Assessment Note: Pearson's Next Generation Assessments initiative includes white papers that will help states design and deliver new online assessments.
Peoples Education includes diagnostic and practice tests geared to state and national standards and Common Core State Standards. There are online assessments in Measuring Up Live, for example.
Renaissance Learning -- see Star Assessments, including for Math, for example.
Voyager Sopris Learning has math intervention products for grades K-9 and an algebra intervention. VmathLive is web-based for grades K-8.
i>Clicker "response devices are compatible with any brand of interactive whiteboard and any software application, making it a perfect audience response system ..."
Become Knowledgeable about Assessment Terminology
Each year you will be faced with interpreting test results particularly for mandated state assessments, and explaining those results to students and parents. It is a good idea to have a working knowledge of key terms. The following resources should help in this endeavor.
Add Rigor and Relevance to your Curriculum, Instruction, and Assessment Endeavors
The International Center for Leadership in Education developed a Rigor/Relevance Framework to examine curriculum, instruction, and assessment. It has two dimensions of higher standards and student achievement organized in four quadrants: acquisition, application, assimilation, and adaptation. The first dimension is based on the six levels in Bloom's taxonomy. The second dimension is an Application Model with five levels based on action: knowledge in one discipline, applying in one discipline, applying across disciplines, applying to real-world predictable situations, and applying to real-world unpredictable situations. Teachers might find it very helpful in planning instruction and assessment activities.
Bathon, J. (2013, July). For districts, online testing has legal liabilities. T.H.E. Journal, 40(7), 17-20. Retrieved from http://online.qmags.com/TJL0713#pg1&mode1
Fox, C., Waters, J., Fletcher, G., & Levin, D. (2012). The broadband imperative: Recommendations to address K-12 education infrastructure needs. Washington, DC: State Educational Technology Directors Association (SETDA). Retrieved from http://www.setda.org/web/guest/broadbandimperative
State Educational Technology Directors Association (2012). Technology Readiness for College and Career Ready Teaching, Learning and Assessment. Retrieved from http://www.setda.org/priorities/online-assessment/
See other Math Methodology pages: