Motivation Math Benchmark Assessments Common Core The development of national standards for K-12 Mathematics was initiated and coordinated by the National Governors Association Center for Best Practices (NGA Center, 2010) and the Council of Chief State School Officers (CCSSO, 2010). Common Core Standards (CCS) are specific academic benchmarks and expectations for all students in public schools endorsing CCS. The Common Core Standards in Mathematics measure student proficiency in the acquisition of knowledge and skills covered by the curriculum at the specified grade level. Students should not be compared to each other but rather evaluated on how well they are individually meeting grade-level standards. These standards provide a consistent framework to prepare students for success in college and careers. The Common Core Standards (CCS) earmark a significant change in education and assessment. According to the consortia SMARTER Balanced Assessment (SBAC, 2012) and Partnership for the Assessment of Readiness for College and Careers (PARCC, 2012), assessments must contain rigorous item types beyond selected response items. The requirements include extended constructed response, performance task, and computer-enhanced. Researchers have indicated the importance of a balanced approach to assessments (Black, Harrison, Lee, Marshall, and Wiliam, 2003; Garrison and Ehringhaus, 2007). This approach focuses on summative assessments such as benchmark or interim, end of unit, end-of-course and formative assessments that occur during instruction and are intended to improve achievement. Motivation Math Benchmark Assessments Common Core Aligned are summative assessments that measure student progress in mathematics at three different points during the year. The federal requirements of the No Child Left Behind Act (NCLB, 2001), and the Individuals with Disabilities Education Act (IDEA, 2004) mandate that all students participate in the state assessment program. All students must be tested in mathematics content at their respective grade levels. Accountability rules of NCLB remain in effect until ESEA is reauthorized by Congress. Based on NCLB, the Annual Measurable Objectives (AMOs) increase each year until 2014. By 2013-14 all students are to be 100% proficient in mathematics. Summative and formative assessments are necessary and used for developing an accurate picture of a student’s overall academic achievement. Classroom benchmark assessments correlated to the Common Core Standards provide teachers ongoing interval measurements of student progress, thus the rationale for Motivation Math Benchmark Assessments Common Core Aligned. These benchmark assessments are designed to measure student acquisition of the knowledge and skills specified in the Common Core Standards at different intervals. The primary purpose of Motivation Math Benchmark Assessments Common Core Aligned is to provide a valid measure of the quality of mathematics education in the classroom or across the campus. Research shows that students score higher on standardized tests when they experience focused, aligned practice. Motivation Math Benchmark Assessments Common Core Aligned measure how well students have acquired the knowledge and skills taught during mathematics instruction. The assessments are designed to ensure students are learning at their grade level. Furthermore, Motivation Math Benchmark Assessments Common Core Aligned provide data to teachers, schools, and school districts to support improved instructional decisions. The Motivation Math Benchmark Assessments Common Core Aligned serve as accountability measures to help gauge or predict future performance that might occur on state assessments which are part of the Adequate Yearly Progress (AYP) requirements of the federal No Child Left Behind Act (NCLB). With the summative assessment data, educators can pinpoint areas that require additional attention and focus. Periodic exposure to benchmark assessments provides students with opportunities to experience a variety of assessment items and formats for each standard. These experiences will benefit students facing a common assessment. When assessment is an integral part of mathematics instruction, it contributes significantly to students’ mathematical learning (Stecker et al., 2005). Assessment should inform

Motivation Math Benchmark Assessments Common Core and guide teachers as they make instructional decisions. During the school year, students can take practice tests to evaluate their own work and progress. Teachers could create customized assessments by assigning students only the items that measure a specific standard. Students partake in these opportunities to demonstrate what they have learned. After students are supplied with immediate achievement feedback, then students may proceed to intervention settings to develop standard mastery and ensure performance gaps are closed prior to the state or common assessment administrations. As a result, Motivation Math Benchmark Assessments Common Core Aligned arm teachers with essential data or information that helps in the preparation of high-quality instruction. Results of the Motivation Math Benchmark Assessments Common Core Aligned provide information about the academic achievement of students. This information is used to identify individual student strengths, determine areas of challenge, and measure the quality of mathematics education across the campus. Utilization of results from various benchmark assessments help teachers monitor student progress in order to determine future plans for instruction. Students can use the Chart Your Success charts located in the back of the assessment booklet to chart assessment data, self-monitor individual progress over time in mathematics, and compare the knowledge and skills to previous assessments. The involvement of students in assessment promotes student engagement in individual learning targets. Students need to know what learning targets they are responsible for mastering, and at what level (Stiggins, 2007). Marzano (2005) states, “students who can identify what they are learning significantly outscore those who cannot.” A class diagnostic chart is available at www.mentoringminds.com/ccsma which enables teachers to view and determine students’ strengths and weaknesses. After the analysis of assessment data, findings may indicate students require additional instruction to address deficits in order to achieve skill mastery and close learning gaps. If skill deficits exist, then teachers are encouraged to explore different strategies in order to improve student achievement. Teachers may design learning experiences to revise their curricula, develop formative assessments, examine instructional methods of delivery, target specific populations for remediation and enrichment, create student academic assistance interventions, and/or develop individual plans for student improvement. For a balanced assessment system, formative assessments must play an essential part of classroom instruction. Formative assessment focuses on improving student performance during classroom instruction whereas summative assessment focuses on accountability and often sorts or classifies students. In formative assessment both teacher and student share responsibility for assessment. The student and teacher share a common understanding of the standards that define quality work. Both student and teacher compare performance to these standards as they assess the work task in progress and when it is completed. Following the assessment, teaching and learning activities are adjusted to close the gap between the student’s performance and the standard. The teacher not only assesses the student’s performance, but also provides feedback to the student. The feedback informs the student as to the next steps to take for improvement in future performance. The teacher will also assess and adjust instruction based on the assessment. Research on formative assessment suggests that students should be aware of their learning target, their present status, and the next steps in reaching that goal or closing any gaps (Atkin, Black, and Coffey, 2001; Black, Harrison, Lee, Marshall, and Wiliam, 2003). Such knowledge helps students keep track of their achievements, know how close they are to their learning targets, and determine future steps to advance their learning. When students are aware of their achievement gaps and teachers motivate students with continuous feedback linked to the expected outcomes and criteria for success, students are able to surge ahead and close performance gaps in mathematics. Black and Wiliam (1998) note there is evidence to support a strong relationship between interactive feedback and student achievement. Although Motivation Math Benchmark Assessments Common Core Aligned are summative in nature, the item coding to standards provides teachers optional formative assessment opportunities to administer only select items that relate to the standards being taught. That action would negate the use of the assessment as a benchmark at a later date. However, formative assessments should be used during instruction to advance teaching and learning. Then, benchmark tests provide accountability in determining student learning after instruction. This entire process provides evidence that assessment and instruction are intertwined.

Motivation Math Benchmark Assessments Common Core Available for Levels 2-5, Motivation Math Benchmark Assessments Common Core Aligned are diagnostic and prescriptive in nature. These practice assessments provide educators with detailed information on student progress as well as promote flexibility of use in a variety of classroom settings. For each grade level, there are three different versions of the assessments (Forms A, B, C) bound into one student assessment booklet. Each form contains 60 test items. The standards for each grade level are addressed in at least one assessment item. This allows for additional items for some standards or the subcategories of the standard. Each assessment form has 48 selected-response items. Following the selected-response items, open-formatted items complete the 60-item assessment. These open-response items are comprised of constructed-response items followed by extended-response items. While this resource does have an online version, the assessment items are not computer-adaptive, but the online benchmarks do offer randomized assessment items. Test items are presented in a “real-world” context when possible. As shared by the United States Department of Education (2003), No Child Left Behind noted the importance of assessment items that align with the depth and breadth of the academic content standards. Therefore, all assessment items in the Motivation Math Benchmark Assessments Common Core Aligned are coded to the standard, to the Depth of Knowledge level (DOK), and to the Rigor/Relevance (R/R) Framework® level. The model Depth of Knowledge (DOK) was developed by Norman Webb (Webb, 2002a; 2002b). Dr. Webb advocates the necessity of assessment items matching the standard. Webb also wanted educators to be aware of the level of demonstration required by a student when a test item was developed, thus the development of his four levels of DOK. Level 1 assessment items have students recall information. Level 2 items ask students to think beyond reproduction of responses. Students use more than one cognitive process or follow more than one step. Students at Level 3 demonstrate higher levels of thought than the previous levels require as these items are more complex. Responses may have multiple answers, but students must choose one and justify the reasoning behind the selection. Assessment items at Level 4 require students to form several connections with ideas. Typically, performance assessments and open-ended responses are written at this level of thought. The Rigor/Relevance Framework® is a tool designed by the International Center of Leadership in Education (ICLE, 2012) to examine curriculum, instruction, and assessment. Knowledge of this framework enables educators to prepare instruction and design test items that challenge students to think in increasingly complex ways and apply knowledge through meaningful experiences in their lives, complementing the CCS. This framework uses four quadrants (A, B, C, D) to describe learning or student performance. The expectation for Quadrant A (Acquisition) is that students choose responses to show they can remember, recall, or understand knowledge. Students in Quadrant B (Application) use acquired knowledge to solve problems, design solutions, and complete work. Questions at this level require students to apply knowledge to new and unpredictable situations. Quadrant C (Assimilation) questions lead students to extend and refine their acquired knowledge in order to use that knowledge automatically and routinely to analyze and solve problems and create solutions. When students respond to Quadrant D (Adaptation) question items, they exhibit competence to think in complex ways, applying their knowledge and skills. Even when presented with complex problems, students show they are able to use extensive knowledge and skills to create solutions and take action that further develops their skills and knowledge. As previously stated, the national shift towards preparing students to survive in the global market will impact the type assessments undertaken by students. Assessments that focus on the Common Core Standards will not only demonstrate if students can succeed in school but also in the real world. Assessments will indicate if students are both college and career ready. For the purpose of the Motivation Math Benchmark Assessments Common Core Aligned, the various DOK and R/R codings are utilized to reflect the rigor and depth in levels of thought required by students on the benchmark assessments. Assessment items displaying rigor require students to use higher-levels of thought, exhibiting a more challenging 21st Century learning environment. Students may be asked to use such processes

Motivation Math Benchmark Assessments Common Core as examine, create, prioritize, decide, produce, assess, generate, or classify. Assessments items reflecting relevance require students to work with real-world tasks that have more than one solution. Over the past years, changes in accountability and test¬ing have led to data playing a major role in the education of students. The U.S. Department of Education advocates the importance of using data for guiding instruction and improving student learning. Schools are being strongly encouraged to respond to assessment data, using it to identify students’ academic strengths and needs (U.S. Department of Education, 2009). As educators face increasing accountability pressure from federal, state, and local entities to improve student achieve¬ment, data should become the central element in how students’ aca¬demic progress is monitored and how instructional practices are evaluated. There is no single assessment that provides a complete picture of student performance. Motivation Math Benchmark Assessments Common Core Aligned offer three forms in order to keep a pulse on the progress of student performance, rather than a single snapshot assessment. Each assessment plays a prominent role in determining if quality teaching and learning are occurring. As correct and incorrect assessment answers are analyzed, teachers are able to observe the patterns of thought in which students experience difficulty or exhibit success. This data is informative in that teachers may appropriately adjust and revise instruction to more appropriately address the diversity of needs within classrooms. Thus, assessments have important implications for instruction. Research indicates it is essential that assessment data be used to make well informed instructional decisions (Armstrong and Anthes, 2001; Feldman and Tung, 2001; Forman, 2007; Liddle, 2000). Benchmarks provide student achievement data on the Common Core Standards throughout the school year, including the ability to report student achievement approaching, falling below, or exceeding the standards. With three forms of assessment per grade, these assessment instruments are capable of providing data to measure mathematics progress and proficiency throughout the year. These benchmark assessments for math are summative in nature as they are given at three different intervals during the year. If assessment items, that aligned to the specific standard from whence instruction was delivered, were extracted from the benchmark assessments and utilized during instruction followed by timely and descriptive feedback, then that usage becomes formative in nature. Formative assessments provide rapid and meaningful results to teachers to improve instruction. The adjustment to instruction could lead students to master the standard(s) at hand. Motivation Math Benchmarks Common Core Aligned Forms A, B, and C can be used in different ways: as practice, as a diagnostic instrument, and as a teaching tool. Students need opportunities to practice and develop test-taking skills. These tests focus on the skills students will be expected to demonstrate on assessments of Common Core Standards. A diagnostic chart is available on the Mentoring Minds website mentoringminds.com/ccsma. This chart enables teachers to determine students’ strengths and weaknesses. Teachers can view the chart to determine specific area where additional practice for mastery of skills is warranted. Data from the assessments will help the teacher to identify areas where additional instruction is necessary, thus, using the assessments as teaching tools. Studies support the use of several measures from which to gauge student achievement. The Mathematics Product Development Team recognize that assessment systems should include a balance of formative and summative data to be most effective in improving outcomes and in making a significant impact on mathematics education. The development team studied available guidelines released by the assessment consortia SMARTER Balanced Assessment Consortium (SBAC, 2012) and Partnership for the Assessment of Readiness for College and Careers (PARCC, 2012). PARCC and Smarter Balanced consortia have both released a range of sample items and item specifications regarding the assessment of mathematics. This information was considered by the Mathematics Product Development Team in order to design assessment items and tasks that measure a deeper understanding. Some assessment items contain multiple assessments within the item. Members of both consortia indicate that students must be more than smart test takers as they must demonstrate not only procedural skill in mathematics but conceptual understanding. Information appears to show

Motivation Math Benchmark Assessments Common Core that the common assessments will contain a variety of item types: adaptive multiple choice, extended-constructed response, technology-enhanced constructed-response, and performance tasks. For Motivation Math Benchmark Assessments Common Core Aligned, a balance of item types were developed with all items aligned to the Mathematics Common Core Standards. Although common assessment test items are reported to be computer-based or computer-adaptive, the format for Motivation Math Benchmarks Common Core Aligned will be paper-pencil or an online version of each form. As the school year progresses, the students who are proficient in the various benchmarks can determine how they may perform on the state or common assessments in math. The three forms offered at each grade enable the benchmarks to be spread out over the year, leaving a window of time for the state or common assessments to be administered. As the Motivation Math Benchmark Assessments Common Core Aligned data is examined, teachers can identify students who are performing at the grade specific standard level, those who are exceeding the standards, and those who are approaching or are functioning below the standard. Teachers can also determine and chart the data for the various subgroups (i.e., ethnicity, disadvantaged, special education, and English Language Learners). All subgroups must make sufficient growth in order for the school to achieve the adequate yearly progress (AYP) status per the No Child Left Behind law. The developers of Motivation Math Benchmark Assessments Common Core Aligned reviewed relevant reform efforts on teaching and learning in mathematics, studied the Common Core Standards, perused the available and released item specifications released by both consortia, and employed individual expertise and col¬lective judgment as they designed a resource to lead students into the 21st century. Motivation Math Benchmark Assessments Common Core Aligned focus on the grade-level standards and subcategories of each standard for mathematics. This focus ensures the assessment items align with the assessed standard, resulting in appropriate and effective assessment items based on current information. Webb’s Depth of Knowledge and the Rigor/Relevant Framework® were the basis for designing items that stimulated students’ higher order thinking skills, encouraging rigor and depth in thinking. With the Common Core Standards as the key guiding points, the Mentoring Minds Product Development Team developed Motivation Math Benchmark Assessments Common Core Aligned as a resource for assessing and strengthening mathematics education. Bibliography for Motivation Math Benchmark Assessments Common Core Armstrong, J., & Anthes, K. (2001). How data can help: Putting information to work to raise student achievement. American School Board Journal, 188(11), 38–41. Atkin, J. M., Black, P., & Coffey, J. (2001). Classroom assessment and the national science education standards. Washington, DC: National Academy Press. Black, P., Harrison, C., Lee, C., Marshall, B., & Wiliam, D. (2003). Assessment for learning: Putting it into practice. Maid¬enhead, UK: Open University Press. Black, P., & Wiliam, D. (1998). Assessment and classroom learning. Assessment in Education, 5(1), 7–74. Feldman, J., & Tung, R. (2001). Using data-based inquiry and decision making to improve instruction. ERS Spectrum: Journal of School Research and Information, 19(3), 10–19. Forman, M. L. (2007). Developing an action plan: Two Rivers Public Charter School focuses on instruction. In K. P. Boudett & J. L. Steele (Eds.), Data wise in action: Stories of schools using data to improve teaching and learning (pp. 107–124). Cambridge, MA: Harvard Education Press.

Motivation Math Benchmark Assessments Common Core Garrison, C., & Ehringhaus, M. (2007). Formative and summative assessments in the classroom. Retrieved Summer 2012 from http://www.amle.org/Publications/WebExclusive/Assessment/tabid/1120/Default.aspx Hamilton, L., Halverson, R., Jackson, S., Mandinach, E., Supovitz, J., & Wayman, J. (2009). Using student achievement data to support instructional decision making (NCEE 2009-4067). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved Fall 2012 from http://ies.ed.gov/ncee/wwc/publications/practiceguides/. Individuals with Disabilities Education Improvement Act (IDEA) (2004). PL 108-446, 20 U.S.C. §§1400 et seq. International Center for Leadership in Education (2012). Rigor/Relevance Framework®. Rexford, NY: International Center for Leadership in Education. Retrieved Fall 2012 from http://www.leadered.com/rrr.html Liddle, K. (2000). Data-driven success: How one elementary school mined assess¬ment data to improve instruction. Amer¬ican School Board Journal. Retrieved April, 2009, from http://www.asbj. Marzano, R. (2005). What works in schools (PowerPoint presentation). www.marzanoandassociates.com/pdf/ ShortVersion.pdf National Governors Association Center for Best Practices (NGA Center) and the Council of Chief State School Officers (CCSSO). (2010). Common Core Standards for Mathematics. Washington, DC. Retrieved Fall 2011 from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf No Child Left Behind. (2001). Washington, D.C.: U.S. Department of Education. Partnerships for Assessment of Readiness for College and Careers (PARCC). (2011). PARCC Model Content Frameworks: Mathematics Grades 3-8. Retrieved December 2011 from http://parcconline.org/sites/parcc/files/ PARCCMCFfor3-8MathematicsFall2011Release.pdf Partnerships for Assessment of Readiness for College and Careers (PARCC). (2012). Item and task prototypes. Retrieved August 2012 from http://www.parcconline.org/samples/item-task-prototypes Perie, M., Marion, S., & Gong, B. (2007). A framework for considering interim assessments. Dover, NH: National Center for the Improvement of Educational Assessment Retrieved November 13, 2007 from http://www.nciea.org/publications/ ConsideringInterimAssess_MAP07.pdf. Smarter Balanced Assessment Consortium (2012). Smarter Balanced Mathematics Item Specifications Grades 3-5. Retrieved April 2012 from http://www.smarterbalanced.org/wordpress/wpcontent/uploads/2012/05/TaskItemSpecifications/Mathematics/ MathematicsGeneralItemandTaskSpecificationsGrades3-5.pdf Stecker, P. M., Fuchs, L. S., & Fuchs, D. (2005). Using curriculum-based measurement to improve student achievement: Review of research. Psychology in the Schools, 42, 795–819.

Motivation Math Benchmark Assessments Common Core Stiggins, R. (2007). Assessment through the student’s eyes. Educational Leader¬ship, 64(8), 22–26. Retrieved Summer 2012 from http://www.ascd.org/publications/educational-leadership/may07/vol64/num08/Assessment-Through-theStudent’s-Eyes.aspx Stiggins, R. (2004). New assessment beliefs for a new school mission. Phi Delta Kappan, Vol. 86, No. 1, September 2004, pp. 22-27. Retrieved Spring 2012 from https://docushare.prsd.ab.ca/docushare/dsweb/Get/Version-563/Stiggins%20Paper%20(2).pdf U.S. Department of Education. (1990–2007). National Assessment of Educational Progress. National Center for Educational Statistics. Retrieved September 1, 2007 from http://nces.ed.gov/nationsreportcard/ U.S. Department of Education. (2009). Using ARRA funds to drive school re¬form and improvement. Retrieved Fall 2012, from www.ed.gov/policy/gen/leg/recovery/guidance/uses.doc. Webb, N. (2002a). Depth-of-Knowledge (DOK) levels for mathematics. Retrieved Spring 2010 from http://www.ride.ri.gov/ assessment/DOCS/NECAP/Science/DOK_Science.pdf Webb, N. (2002b). Depth-of-Knowledge levels for four content areas. Wisconsin Center for Educational Research. Wylie, C. (2008). Formative assessment: Examples of practice. The CCSSO Formative Assessment for Students and Teachers (FAST) SCASS. Washington, DC: Council of State School Officers. A paper prepared for the Formative Assessment for Teachers and Students (FAST) State Collaborative on Assessment and Student Standards (SCASS of the council of Chief State School Officers (CCSSO). Retrieved Summer 2012 from http://www.ccsso.org/Documents/2008/ Formative_Assessment_Examples_2008.pdf