References
The Common Core redefines what it is to be a good reader. We all know that it’s not enough to just understand what a textbook or digital passage says. Close readers not only clutch an author’s message, but they also take a look under the cover, so to speak. We should teach students to identify the author’s tone or perspective, the implications of the author’s word choices, and why a text is structured or organized as it is. Additionally, readers should go beyond a text, evaluating its quality or value, comparing it with other books, or determining its implications. It’s a lot to ask of students, but with appropriate scaffolding and support, they can do it.
Anyone with doubts, about how close reading ties into the Common Core standards should take a look at the organization of the reading standards.
Close reading is unique because it has those three interpretive goals. In the past, we may have thought students were good readers if they could tell that Goldilocks shouldn’t have been in the Bears’ house or if they could predict what Baby Bear would find in his bed. In a close reading, that’s not enough. Close readers would wonder why the author had Goldilocks try out Papa Bear’s, Mama Bear’s, and Baby Bear’s belongings in each episode, or why she is so hard on Baby Bear’s stuff. (Goldilocks seems to want to grow up, but trying out grown-up stuff isn’t getting her there, which raises questions about what it takes to be a grown-up). Great stories and other quality texts are coherent: How an author presents the text reinforces and extends the message itself. Good readers can make sense of this coherence and what it contributes to the meaning.
Since close reading requires that students examine the texts more thoroughly, a “one and done” reading is not enough. Students will need to read and reread the texts. Because there are three reading goals, plan to visit the text three separate times. The first reading will focus on what the text says, the second reading will emphasize how the text works, and the third will engage students in evaluating the text, comparing it with other texts, or thinking about its implications in their lives.
In many ways, each of these reads will look like the reading lessons you’re already accustomed to teaching. You would assign portions of the text to read and follow up with a series of questions aimed at getting students to think about those parts of the passage (For examples of the kinds of questions, see the bottom of the page.) Or students might read the entire story or article first to make sense of what it says, and then, after a retelling, you could have them reread particular parts of the text relevant to the goals of the second and third reads.
You’re ready to take your first journey through close reading. How do you set your students up for success? First, don’t keep it a secret that they’re going to read the text multiple times. We wouldn’t want them to think that we are going back because they missed something or did something wrong. Tell them about the kinds of things that they are trying to figure out by rereading. For example, you might say, “Good readers often read and reread a text, which is what we’ll do with this story. After we read it a first time, we’ll talk about what happened and who did what. After that, we’ll go back and reread some parts of the story to figure out how the text works and what choices the author made.” It may also help to pre-teach difficult vocabulary words. Some teachers have expressed concern that they are no longer permitted to provide such assistance, but that is not the case. This kind of preparation is still useful and appropriate.
You’ll also want to introduce the story briefly. There is no need for an extensive overview. Sufficient introductions for a first reading would include: “We are going to read a story. We’ll read it to find out what the main character, Goldilocks, does and what happens to her.”
The depth of knowledge questions that you’ll ask during each reading is critical because they should encourage a broad consideration of the text. These questions should also be “text dependent.” This means that students shouldn’t be able to answer them correctly if they haven’t read the text. Asking students, “How did Baby Bear feel about what Goldilocks did?” or “Why were the Bears upset?” are appropriate, but “Is it okay for children to go to someone else’s house?” would not be. That doesn’t limit you to low-level questions about what is stated explicitly in a text (for instance, “What was the little girl’s name?”). You can still require students to infer and interpret, but those interpretations should depend upon the ideas in the text. If the questions are indeed text dependent, then students’ responses can easily be explained or supported with “evidence” drawn from the text.
The Common Core envisions the transformation of all students into thoughtful readers. To make this vision a reality, you’ll need a variety of lessons aimed at creating close readers. Lessons can deliver to whole classes of children, to small groups, and even one-on-one. Large group lessons are useful for exposing all students to particular ideas, while smaller groupings encourage greater participation and allow for more observation.
Not every text deserves a close read. No one knows how many teacher-led close reads would be a good idea, but don’t overdo it; one or two close reads every couple of weeks (some taking place over multiple days) seems like the right dosage. I predict close reading will still be in fashion when skinny jeans are long gone. Sometimes it’s okay to be interested only in the story considerations of craft and structure, and deeper implications are beside the point. And classroom reads don’t always have to emphasize close reading; the key is to incorporate close reading into your instruction, not use it exclusively. And that is as it should be, given its emphasis on making children more thoughtful, independent readers.
First Reading: Determine what the text says.
Second Reading: Figure out how the text works
What does _____ (a word from the text) mean in this context?
Third Reading: Analyze and compare the text
What information do these illustrations add to the text? Or, how does this picture differ from what the author wrote?
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So in 2017 the transition to the CA CCSSM is getting closer to the nightmares brought onto teachers under the NCLB Act of 2001. While reflecting back, we have seen tremendous growth in elementary school test scores reaching 800 plus. The nation failed to reach the utopia 100% proficient by 2014. The reason for this failure was not in the curriculum or standards but the instruction. It is not the curriculum or the state test that is important. It is not the grade that matters. The question everyone should have been curious about was “Did student learning occur and if so how or when did we know it happened? Even more important is did the student know this was going on. Formative assessment will become even more important than summative assessments in 2016 and beyond for teachers of mathematics.
Formative assessment has become the most efficient way of knowing which students are learning, which are stuck and where, and which students just aren’t getting it at all. It is information teachers collect in deliberate ways: listening to class discussions, glancing over a student’s shoulder as he or she complete an in-class assignment, asking three opening questions, collecting papers for review, and so on.
These are things that don’t normally end up in the grade book but are little feedback loops signaling the amount of progress we are making toward the end goal. Typically it is important to jot down the names of students the teacher will need to give some one-on-one attention to the next day, or perhaps invite to a tutoring session before school.
More professional development dollars should focus on empowering more teachers to learn how to use formative assessment. Teachers need to expand the idea that formative assessment should cover just the curriculum-related skills. We need to stretch this concept to include the standards of mathematical practice student skills that are vital to the larger task of learning.
Formative assessment done well can help amplify the effectiveness of a teacher. It creates a synergetic loop of information flowing from teacher to student and back to the teacher and then back to the student again. Teachers who master the use of formative assessment and feedback will know they are making a difference, and students will understand what they must do to be successful.
Today’s student have multiple resources beyond the textbook through the use of technology connected to the Internet using Web 2.0 tools. Students need to know how to access and use these instruments to support their learning. They need to know how to research for help through Performing an Internet search and evaluating which sources will best help respond to the question; knowing how to collect evidence to support an idea, inference, or conclusion; writing clear summations of our work; and so on.
Classroom assessment is essential for students to become deeply involved in their learning. Grades are no substitute. However, grades do not tell them much about what they need to learn or what they need to do better. Students need to have an idea of what to do to improve their skills. Students need feedback and not grades. Students need feedback to gauge their progress of learning to master the standards. Sometimes feedback is on the content of the curriculum and sometimes on foundational skills.
This 11-minute video features Jaime Bonato─a high school mathematics teacher in the San Juan Unified School District─demonstrating the formative assessment process as her high school math class discusses the relationship between the rate at which water fills a container and its corresponding graph (Posted 07-Jul-2016, CDE, 2016).
This 9-minute video features Travis Burke─a math professional development coach in the Santa Maria-Bonita School District─demonstrating the formative assessment process as his grade 6 students discusses different ratio combinations for the perfect glass of chocolate milk. Students teach each other different strategies for solving this problem and then attempt to convince classmates that their strategy is best (Posted 8-Apr-2016, CDE, 2016).
Smarter Balanced Digital Library
The formative assessment component of the Smarter Balanced Assessment System
CAASPP Teacher Guide: Smarter Balanced Assessments
Guides for teachers to deepen understanding of the Smarter Balanced Assessment, their alignment with the California Common Core State Standards, and their intended connection to classroom teaching (updated 01-Jul-2016).
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Dr. Boyd’s efforts are leading to the development of novel, and more efficient, therapeutics for individuals with brain damage, but they are also shedding light on broader applications. By learning new concepts, taking advantage of opportunities, and participating in new activities, you are physically changing who you are, and opening up a world of endless possibility.
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“These strategies, although appearing to be independent, frequently overlap and are synergistic. They can be implemented as stand-alone programs (i.e. mentoring or family involvement projects.) When school districts develop an improvement plan that encompasses most or all of these strategies, positive outcomes result. These strategies have been successful in all school levels from K-12 and rural, suburban, or urban centers” (Shargel, 2015)
To purchase the book click here
The Basic Core Strategies
Mentoring is a one-to-one caring, supportive relationship between a mentor and a mentee that is based on trust. Tutoring, also a one-to-one activity, focuses on academics and is an effective way to address specific needs such as reading, writing, or math competencies.
Service learning connects meaningful community service experiences with academic learning. This teaching/learning method promotes personal and social growth, career development, and civic responsibility and can be a powerful vehicle for effective school reform at all grade levels.
Alternative schooling provides potential dropouts a variety of options that can lead to graduation, with programs paying special attention to the students’ individual social needs and the academic requirements for a high school diploma.
Many schools provide after-school and summer enhancement programs that eliminate information loss and inspire interest in a variety of areas. Such experiences are especially important for students at risk of school failure.
Early Interventions
Birth-to-three interventions demonstrate that providing a child educational enrichment can modify IQ. The most effective way to reduce the number of children who will ultimately drop out is to provide the best possible classroom instruction from the beginning of their school experience.
Research consistently finds that family involvement has a direct, positive effect on children'[s achievement and is the most accurate predictor of a student’s success in school.
Early interventions to help low-achieving students recognize that focusing on reading and writing skills is the foundation for effective learning in all subjects.
Making the Most of the Instruction
No sustained and comprehensive effort to keep students in school can afford to ignore what happens in the classroom. Strategies that produce better teachers expand teaching methods to accommodate a range of learning styles, take advantage of today’s cornucopia of technological resources, and meet the individual needs of each student can yield substantial benefits.
Teachers who work with youth at high risk of academic failure need to feel supported and need to have an avenue by which they continue to develop skills, techniques, and learn about innovative strategies.
When educators show students that there are different ways to learn, students find new and creative ways to solve problems, achieve success, and become lifelong learners.
Technology offers some of the best opportunities for delivering instruction that engages students in authentic learning, addresses multiple intelligences, and adapts to student’s learning styles.
A customized individual learning program for each student allows teachers flexibility with the instructional program and extracurricular activities.
Making the Most of the Wider Community
Students who come to school bring traces of a wider community; when students leave school, either before or after graduation, they return to that community. It’s impossible to isolate “school” within the walls of the school building. Effective efforts to keep students in school take advantage of these links with the wider community.
Systemic renewal calls for a continuing process of evaluating goals and objectives related to school policies, practices, and organizational structures as they impact a diverse group of learners.
When all groups in a community provide collective support to the school, a strong infrastructure sustains a caring environment where youth can thrive and achieve.
A quality guidance program is essential for all students. School-to-work programs recognize that youth need specific skills to prepare them for the larger demands of today’s workplace.
A comprehensive violence prevention plan, including conflict resolution, must deal with potential violence as well as crisis management. Violence prevention means providing daily experiences at all grade levels that enhance positive social attitudes and effective interpersonal skills in all students.
The strategies were developed by Dr. Jay Smink, Executive Director of the National Dropout Prevention Center at Clemson University, the associates of the Center and Mr. Franklin Schargel. They have been recognized by the U.S, Department of Education and the National Education Goals Panel as “the most effective strategies to help prevent school dropouts.”
To purchase the book click here
]]>When students and educators have a growth mindset, they understand that intelligence can be developed. Students focus on improvement instead of worrying about how smart they are. They work hard to learn more and get smarter. Based on years of research by Stanford University’s Dr. Dweck, Lisa Blackwell Ph.D., and their colleagues, we know that students who learn this mindset show greater motivation in school, better grades, and higher test scores.
Students are enthusiastic, hard-working, persistent learners. They take charge over their own success.
Failure to anticipate the need for credit recovery during the summer, and instructional modifications for alternative education environments.
Failure to realize that the traditional benchmarks are not relevant for preparing students for the SBAC performance task and that students will require multiple exposures to this type of assessment.
Smith, J. B., Jr. (2015). Secondary mathematics intervention and CAHSEE mathematics performance (Order No. 3736727). Available from Dissertations & Theses @ University of Phoenix; ProQuest Dissertations & Theses Full Text. (1746672427). Retrieved from http://search.proquest.com/docview/1746672427?accountid=458
The Common Core State Standards for Mathematics build on the best of existing standards and reflect the skills and knowledge students will need to succeed in college, career, and life. Understanding how the standards differ from previous standards—and the necessary shifts they call for—is essential to implementing them. The following are the key shifts called for by the Common Core:
Focus: Greater focus on fewer topics
The Common Core calls for greater focus in mathematics. Rather than racing to cover many topics in a mile-wide, inch-deep curriculum, the standards ask math teachers to significantly narrow and deepen the way time and energy are spent in the classroom. This means focusing deeply on the major work of each grade as follows:
This focus will help students gain strong foundations, including a solid understanding of concepts, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the classroom.
Coherence: Linking topics and thinking across grades.
Mathematics is not a list of disconnected topics, tricks, or mnemonics; it is a coherent body of knowledge made up of interconnected concepts. Therefore, the standards are designed around coherent progressions from grade to grade. Learning is carefully connected across grades so that students can build new understanding onto foundations built in previous years. For example, in 4th grade, students must “apply and extend previous understandings of multiplication to multiply a fraction by a whole number” (Standard 4.NF.4). This extends to 5th grade, when students are expected to build on that skill to “apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction” (Standard 5.NF.4). Each standard is not a new event, but an extension of previous learning. Coherence is also built into the standards in how they reinforce a major topic in a grade by utilizing supporting, complementary topics. For example, instead of presenting the topic of data displays as an end in itself, the topic is used to support grade-level word problems in which students apply mathematical skills to solve problems.
Rigor: Pursue conceptual understanding, procedural skills and fluency, and application with equal intensity.
Rigor refers to deep, authentic command of mathematical concepts, not making math harder or introducing topics at earlier grades. To help students meet the standards, educators will need to pursue, with equal intensity, three aspects of rigor in the major work of each grade: conceptual understanding, procedural skills and fluency, and application.
Conceptual understanding: The standards call for conceptual understanding of key concepts, such as place value and ratios. Students must be able to access concepts from a number of perspectives in order to see math as more than a set of mnemonics or discrete procedures.
Procedural skills and fluency: The standards call for speed and accuracy in calculation. Students must practice core functions, such as single-digit multiplication, in order to have access to more complex concepts and procedures. Fluency must be addressed in the classroom or through supporting materials, as some students might require more practice than others.
Application: The standards call for students to use math in situations that require mathematical knowledge. Correctly applying mathematical knowledge depends on students having a solid conceptual understanding and procedural fluency.
Reference
Corestandard.org (2015). Key shifts in mathematics. Retrieved from http://www.corestandards.org/other-resources/key-shifts-in-mathematics/
]]>It is a critical mistake for secondary teachers to not research, read, study, analyze, take notes to comprehend and use the information contained in the California Common Core Mathematics Framework to design curriculum, instruction, and assessments for the secondary level of mathematics instruction. A professional teacher needs to conduct research to properly prepare curriculum, instruction, and assessments to prepare students for the 11th grade summative Smarter Balance Assessment. The following figure displays the Smarter Balance Assessment System for California.
The standards specify K-12 expectations with a goal of all students leaving high school college and career ready. The Smarter Balance Assessment is for reporting college and career readiness assessments for accountability. The digital library is only accessible for those who search for it or whose educational leadership directs the review of literature. The interim flexible and open assessments should provide actionable feedback. The field testing of the SBA did not reveal any information that is usable by the teacher or educational leaders.
Teaching the common core state standards and preparing students for college and career requires focus, coherence, and rigor (NCTM, 2014). The Common Core State Standards for Mathematics in California (CA CCSSM) adoption required a major revision to the mathematics framework (CDE, 1997). The preparation for teaching the CA CCSSM must beginning with a review of literature. The following are links to germinal documentation for secondary mathematics that were released in 2013. Most of these documents are not published or released to the average mathematics teacher.
Introduction to Higher Mathematics Courses (PDF; Posted Sept-2015)
Algebra I (PDF; 1MB; Posted Sept-2015)
Geometry (PDF; Posted Sept-2015)
Algebra II (PDF; Posted Sept-2015)
Mathematics I (PDF; 1MB; Posted Sept-2015)
Mathematics II (PDF; 1MB; Posted Sept-2015)
Mathematics III (PDF; 1MB; Posted Sept-2015)
Precalculus (PDF; Posted Sept-2015)
Statistics and Probability (PDF; Posted Sept-2015)
Calculus (PDF; Posted Sept-2015)
Advanced Placement Probability and Statistics (PDF; Posted Sept-2015)
Universal Access (PDF; Posted Sept-2015 )
Instructional Strategies (PDF)
Supporting High Quality Common Core Mathematics Instruction (PDF; Posted Sept-2015)
Technology in the Teaching of Mathematics (PDF)
Assessment (PDF)
Instructional Materials (PDF)
Appendix A: Course Placement and Sequences (PDF)
Appendix B: Financial Literacy and Mathematics Education (PDF)
Appendix C: Possible Adaptations for Students with Learning Difficulties in Mathematics (PDF)
Appendix D: Mathematical Modeling (PDF)
Appendix E: Higher Mathematics Pathways Standards Chart (PDF)
Appendix F: Methods Used for Solving Single-digit Addition and Subtraction Problems (PDF)
Glossary (PDF)
References (PDF)
CDE (2012). Mathematic framework. Retrieved from http://www.cde.ca.gov/ci/ma/cf/draft2mathfwchapters.asp
]]>Response-to-Intervention (RtI) is the practice of providing high-quality instruction/intervention matched to student needs. Progress is closely monitored, and changes in instruction are based on data collected from on-going assessment. RtI represents an educational strategy to close achievement gaps for all students, by preventing smaller learning problems from becoming insurmountable gaps.
What do the tiers mean?
Tier I ALL students receive Tier I interventions, also know as “Best Practices.” Tier I interventions will prosper with 80- 90% of the student population. Classroom teachers provide Tier I interventions and supports (Shen, 2012).
Tier II Based on academic school-wide screening, students who are not meeting grade level benchmarks and for whom Tier I interventions are not supportive enough will receive Tier II interventions. They receive the same instruction as students in Tier 1 as well as targeted interventions. Tier II represents 5-10% of the population. Tier II interventions are provided by the classroom teacher as well as support staff when necessary (SCSD, 2012).
Tier III Students who are not making adequate progress at Tier II will receive Tier III interventions. Tier III interventions include intensive instruction, specific to the student’s highest area(s) of need. Tier III should only represent 1-5% of the population. Tier III interventions are provided by the classroom teachers as well as specialists in the particular area of skill deficit. (SCSD, 2012).
Common Core Math RTI?
Clearly, the best intervention is excellent instruction in the classroom (Tier I). Teachers need to self-reflect upon his or her teaching practices. We need to plan our instruction and differentiate as needed. We must begin by assessing and understanding our students. As a Marine Officer, I was successful when I knew each of my Marines and allowed a transfer of control to my personnel in which I was leading. As a teacher of mathematics, I need to release control to my students to become a facilitator and mentor of learning. The above descriptions of RTI did not help explain what I should be doing in the classroom. So first, I will give a teacher-centered description of RTI and then tell you from experience what works in my classroom.
Eight Steps of RTI (Quinn, 2012)
Step 1 – Universal Screening. Identify the students you will be monitoring during the Tier I instruction.
Step 2 – Tier One Full-Class Instruction. Use a research-validated curriculum. The Mathematics Vision Project curriculum is a research-validated curriculum for the common core integrated pathway based on independent data from the State of Washington. It has been validated as an efficient Tier I intervention standard core intervention.
Step 3 – Fidelity Check. Having another adult observe the teaching and make sure that the curriculum proceeds correctly.
Most teachers are doing steps 1-3.
Step 4 – Progress Monitoring during Tier I. We measure the students identified in the Universal Screening accomplished two to four times a week. It should be recorded and graphed.
Step 5 – Small Group Intervention (Tier Two). Instruction delivered to a small group of students in the classroom; These targeted students do not take a test, but it is through the teacher’s observation and how they respond to the classroom instruction. A small group forms with students with the same problem.
Step 6 – Small Group Intervention Fidelity Check. Has another adult come into the classroom to make sure the intervention is taking place? The adult should check for the process and the amount. The response requires the right amount of intervention. This response to intervention needs 20-30 minutes and 2-3 days a week. The paperwork should include the Universal screening, the full class curriculum, the fidelity check, the graph from the progress monitoring, the small-group intervention and the accuracy check off that small group intervention.
Step 7 – Small-Group Intervention Progress Monitoring. Record the results to see if it is increasing with 10 to 12 results over aa period of 4-6 weeks.
Step 8 – The Tier 3 intervention is ready to look at Special Educational Services or eligibility for SES. It could also mean an eye on a 50-minute intervention 3-4 days a week with intensive instruction on a particular intervention.
Common Core Implementation of RTI
The implementation of the new common core teaching and practice standards will require teachers to do universal screening carefully to begin RTI. We must plan for the intervention for our students that we know will be needed. We are aware that all students will not be prepared for the new common core.
Reference:
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The implementation of common core mathematics will require a shift in the thinking about traditional benchmark testing. Herman and Baker (2005) wrote that despite the glitz and gee-whiz appeal of assessment products, information about their effectiveness in improving student learning is generally hard to come by. The implementation of the common core mathematics has introduced three forms of testing. They include the Smarter Balance Assessment Consortium (SBAC), the PARCC Consortium, and the American Institutes for Research, or AIR Consortium. – See more at https://www.testingmom.com/blog/parcc-vs-sbac-test/.
California has chosen the SBAC and created a new assessment system called the California Assessment of Student Performance and Progress (CAASPP). The following is the testing schedule for 2015-2016. LEAs are administering two types of tests in 2015:
Smarter Balanced Tests:
English Language Arts/Literacy and Mathematics in grades 3–8 and 11
Paper-pencil tests:
California Standards Tests (CSTs) for Science—grades 5, 8, and 10
California Modified Assessment (CMA) for Science—grades 5, 8, and 10 who meet the eligibility requirements to take this instead of a CST for Science
California Alternate Performance Assessment (CAPA) for Science—grades 5, 8, and 10 who meet the CAPA requirements
The California Alternate Assessment (CAA) Online Field Test will be administered to all CAPA students in grades 3-8 and 11.
These state test will be given during the spring and the results will not be available until the beginning of the next year. These state directed test are for accountability reporting and cannot be used to modify instruction in real time. It is for this reason that many Local Education Agency’s have been giving benchmark tests since the enactment of the NCLB Act of 2001. The CAASPP is changing the state test and the CAHSEE is being suspended for 3-4 years. Districts are scrambling to develop new benchmarks. Many of school districts will still be using the same approach by using the traditional benchmark test.
Reference
Menken, K. (2006). Teaching to the test: How No Child Left Behind impacts language policy, curriculum, and instruction for English language learners.Bilingual Research Journal, 30(2), 521-546.
Is Benchmark Testing Really needed anymore?
Yet the quality of the assessment is essential: There is little sense in spending the time and money for elaborate testing systems if the tests do not yield accurate, useful information. If the information is flawed or erroneous, it is unlikely to provide good guidance for instruction or to support better decision making. The whole rationale for conducting the assessment falls apart; it merely creates the illusion that something is being done and people are paying attention. The validity, or quality, of an assessment is derived from an array of evidence showing the extent to which that assessment provides sound information for particular purposes (Herman & Baker, 2005).
The purpose of benchmark testing is to provide both accurate information about how well students are progressing toward mastery of standards and useful diagnostic feedback to guide instruction and improve learning. There are six criteria that determines the validity of benchmark tests: alignment, diagnostic value, fairness, technical quality, utility, and feasibility (Linn, Baker, & Dunbar, 1991). The following recommendations reviews the important aspects of the criteria for educators in California summarized from Herman and Baker (2005).
Alignment – The benchmark should align with the CA CCSSM. Teacher should decide what specific content to assess and at what level of intellectual demand. The performance task should include the application of complex learning. To create benchmark tests that enrich student learning opportunities, focus on the big ideas of a content area and counteract curriculum narrowing by designing benchmark tests that allow students to apply their knowledge and skills in a variety of contexts and formats (Herman & Baker, 2005).
Diagnostic Value – Enhance the diagnostic value of assessment results through initial item and test structure design. Use extended-response items to reveal student thinking and potential misconceptions. Build distracters into multiple-choice items that reveal common student misunderstandings (Herman & Baker, 2005).
Fairness – Ensure the fairness of benchmark assessments for all students, including English language learners and students with disabilities. Avoid unnecessarily complex language or specific contexts that could unfairly confound some students’ ability to show what they know (Herman & Baker, 2005).
Technical Quality - Insist on data showing tests’ technical quality. Study psychometric indices to determine the reliability of assessments (Herman & Baker, 2005).
Build in utility – Design reports of test results to be user-friendly and to provide guidance on how to appropriately interpret and use the results (Herman & Baker, 2005).
Evaluate Feasibility – Hold benchmark testing liable for meeting its purposes. Creating good benchmark tests and ensuring their wise use for improving student learning requires systematic design and continual evaluation (Herman & Baker, 2005).
References
Herman, J.& Baker, E. (2005). Making benchmark testing work: Six criteria can help educators use benchmark tests to judge student skills and to target areas for improvement. Educational Leadership. 63(3) 48-54.
Linn, R. L., Baker, E. L., & Dunbar, S. B. (1991). Complex, performance-based assessment: Expectations and validation criteria. Educational Researcher, 20(8), 15–21. (ERIC Document Reproduction Service No. EJ 436 999)
What is the Insanity Theory? Insanity: doing the same thing over and over again and expecting different results. ~ Albert Einstein.
The flexibility of implementing the common core provides teacher leaders the opportunity to change instruction of mathematics. The change in the standards for mathematics requires a corresponding change from traditional instruction and assessment. The task-based, problem-centered learning shifts from direct instruction to student-centered learning environment using daily mathematical discourse. This instruction change will require different methods for formative assessment models designed to meet the six criteria as stated above. The old benchmarks using multiple choice questions do not meet to meet the six criteria for efficient use of benchmark testing. A different approach needs to be field tested and this will also require a change in our formative assessment methods (diSessa & Minstrell, 1998; Ericsson, 2002).
References
diSessa, A., & Minstrell, J. (1998). Cultivating conceptual change with benchmark lessons. In J. G. Greeno & S. Goldman (Eds.), Thinking practices in learning and teaching science and mathematics (pp. 155–187). Mahwah, NJ: Erlbaum.
Ericsson, K. A. (2002). Attaining excellence through deliberate practice: Insights from the study of expert performance. In M. Ferrari (Ed.), The pursuit of excellence in education (pp. 21–55). Hillsdale, NJ: Erlbaum. Mahwah, NJ: Erlbaum
Read more at http://www.brainyquote.com/quotes/quotes/a/alberteins133991.html#2Cj0B704yl0oMBvZ.99
Why doesn’t this feel right?
Recently I was working on the new MVP curriculum implementation materials. Our educational leaders urged for a benchmark. Because of my research I was not in favor of creating a benchmark test because it just felt like the same old thing that did not meet the six criteria above and it would only be a benchmark on paper only. This was disturbing and caused a “Red Flag”. Last year during the field testing students did not attempt the performance task because it was overwhelming to them because they had no practice or experience with this type of problem. Secondly it had no value because it did not count in their grade. Our LEA policy will include two performance tasks each year. The teachers from our site decided our students would need more practice and are planning to give five additional performance tasks. In search for performance tasks I discovered that the work had already been done because of a grant from the Bill Gates Educational Foundation. We are incorporating lessons and assessments from the Mathematics Assessment Project.
The Mathematics Assessment Program (MAP) aims to bring the Common Core State Standards (CCSSM) to life in a way that will help teachers and their students turn their aspirations for achieving them into classroom realities. The project materials exemplify CCSSM in explicit down-to-earth performance terms and were produced as part of a collaboration between the University of California, Berkeley and the Shell Center team at the University of Nottingham, with support from the Bill & Melinda Gates Foundation. The team works with the Silicon Valley Mathematics Initiative and school systems across the US and UK to develop improved assessment.
You’re probably rolling your eyes at the screen. If you’ve been anywhere in the remote vicinity of the education realm in the past couple years, you’ve heard of and have probably seen efforts to blend online and offline learning in your classrooms and schools.
On a very basic level, Blended Learning is simply the use of online learning (via the web, digital program, or other digital means) and offline learning (traditional brick-and-mortar setting, group-based projects, discussion, etc.) as a means to personalize instruction within the classroom.
Below is one of four major Blended Learning models, each providing students and educators flexibility and learning environment variety.
The Rotation model has one simple requirement: students motion through learning activities that cover different modalities, with at least one of these activities being administered online. However, the method and order of these activities often vary dramatically from class-to-class.
Station Rotation: This method offers educators quite a bit of instructional flexibility. Students rotate through a variety of learning stations/activities, ranging from group discussion to individual online learning and everything in between. The teacher schedules the rotation from one modality to another at their own discretion, whether its a fixed/timed or needs-based.
Lab Rotation: The Lab Rotation model has been around almost along as weve seen computers in schools. The idea is that students participate in offline learning activities in the traditional brick-and-mortar setting, and then go participate in online learning activities in a media or computer lab. Lab rotation requires students to physically change rooms between activities, which sets defined, different environments for the online and offline learning. If your class maintains a computer or media lab, youve used the Lab Rotation model.
The Flipped Classroom: Lab Rotation and Station Rotation are rather traditional when it comes to blending online and offline learning. Simply put, the Flipped Classroom is not. In the Flipped Classroom model, students learn face-to-face with an educator in a brick-and-mortar setting. They are then assigned online activities or homework to be completed in a remote setting, i.e. at home, at the library, coffee shop, etc. Once again the learning environment is separate, but in this case, they are not both necessarily located on school grounds.
Individual Rotation: Obviously, the key word to this subset is individual. In the previous three subsets, the students are given roughly the same curriculum path (regardless if the path is online or offline). But, with the Individual Rotation model, the individual student motions through a variety of activities and stations defined either at the teachers discretion, via an algorithm-driven learning path, or a combination of the two. It’s also important to note that the student may not necessarily rotate or switch to each available station or activity, only to those listed in the individual curriculum path.
Click Here to Learn More About Rotation Model – Blended Learning
Snagit lets you share what can’t be put into words. Easily create custom images and videos that grab attention and keep it. Snag images and insert them directly into presentations and handouts, or record quick videos to show students how they can improve their homework. Then share your content instantly with just one student or your entire class. No matter what you’re working on, Snagit helps you eliminate confusion and provide students with personal, meaningful content.
Record high-quality videos in no time with Camtasia’s advanced screen recorder. Capture smooth, high-quality videos with Camtasia’s world-class screen recorder. Record a window, region, or your entire screen with just a click. TechSmith Fuse, our free mobile app, makes it easy for you to get photos and videos from your mobile device straight to Camtasia for editing. Personalize your videos by recording webcam video or importing existing videos. Add photos, music, and more to create unique videos that stand out.
In a flipped classroom, students learn through online instruction outside of class; “homework” is done in the classroom. Students are much more likely to watch or create a video at home than they are to read a textbook or write a paper. Teach new and difficult topics with video. Use animation to simplify complex ideas. Illustrate word problems. Use video at open houses, back-to-school nights, assemblies, staff meetings, and other events. Teachers can “check for understanding” with video assignments. Students on the Autism spectrum find animated videos to be a great way to communicate and share their feelings.
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Mathematics instruction should engage and encourage learning. If the instructional methods do not encourage students to engage in the learning activity then no learning will occur. As Michael J. Fox stated, “If students can’t learn from the way you are teaching, then maybe you should change the way you teach.” The task-based learning approach from the Mathematics Vision Project integrates both the Standards for Mathematical Practices and the Mathematical Teaching Practices using an integrated pathway approach (MVP.org, 2014). It encourages the use of mathematical tools and the strategic use of online tools such as the Khan Academy.
Teachers need to plan instructional activities that will encourage, promote, and enhance student learning activities facilitating mathematical discourse connections to real life activities. Students need to experience mathematical thinking about real life applications. This experience must also be anchored through connections to real life to provide relevance, rigor, and establish mathematical relationships. The relationships and experiences helps to create a conceptual understanding of mathematics. The engagement in learning by a student of mathematical concepts lays the foundation for practice of procedural skills. The creation of common core math videos may be entertaining and engaging to students. It is how and when the video is used during the instruction that matters. The following video was used to introduce students to factoring quadratics. Westerville South Senior High School has produced several videos. These students are engaged through music connection to mathematical functions and procedural fluency for factoring quadratic equation.
Click Here to Learn More About Use of Common Core Math Videos
Students should become aware of the wide variety of strategic tools that can help deepen his or her understanding of mathematics. A calculator such as www.desmos.com/calculator is a useful tool for graphing of functions. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.Click Here to Learn More About Mathematical Tools for Understanding (SMP 5)
Teaching to the Test Did not Work!!
Teachers proclaim: “They don’t know what 6 times 7, or fractions or decimals!” How can I teach them Algebra if they can’t solve multiple step equations or the order of operations. Why don’t the elementary and middle school teachers teach them the basics of arithmetic. Middle School Teachers state: ” Every year it’s the same thing, these students cannot multiply or divide. They refuse to do word problems and cannot do fractions.” The time for no calculators and computers restrictions for students is coming to an end.
I Flipped the Classroom
After researching and studying the CA CCSSM, the CA Mathematics Framework let the in depth study to other publications from the NCTM. The lesson study and the professional development for our school district’s new curriculum with Mathematics Vision Project made it clear that the traditional classroom had failed teaching mathematics to the current digital natives. So I flipped my classroom such that you will observe multiple learning strategies in the classroom. I am no longer the main focus in the classroom. I am a facilitator of learning. During summer school beginning in July I introduced my students to the use of technology and writing to self-teach mathematical concepts for the second semester of Algebra I for students who failed the subject as 9th graders. These students were now 11th graders. The results are amazing and remarkable. I had always dreamed of having students excel in math but would never have achieved this goal by continuing to teach using the traditional methods.
In 1968 there were no calculators. So when I went to school it was necessary to memorize multiplications tables. In 1978 I bought my first calculator and used it in my job performing multiple tasks in the United States Marines Corps for the management of personnel and equipment. Upon becoming a teacher in 2004 , I entered a system that still refused students to use technology to solve mathematical problems. Why?? Simply because they (the teachers) were taught this way. Education research for teachers of mathematics has pointed how this instructional strategy was wrong (NCTM, 2014). The Common Core Mathematical Standards are about embracing the correct way to teach mathematics through the use of using tools strategically to enhance understanding (Standards of Mathematical Practices.
Under the Common Core State Standards, High school students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. High school students should be sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations.
For example, high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. They are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. McCallum (2011) illustrates the need for understanding the structure of the mathematical practices.
There Are Two Standards for Mathematics
“The CA CCSSM include two types of standards: Eight Mathematical Practice Standards (identical for each grade level) and Mathematical Content Standards (different at each grade level). Together these standards address both “habits of mind” that students should develop to foster mathematical understanding and expertise and skills and knowledge—what students need to know and be able to do. The mathematical content standards were built on progressions of topics across grade levels, informed by both research on children’s cognitive development and by the logical structure of mathematics” (Corestandards.org, 2013)
According to McCallum (2011) the structure is divided into four main areas. Standard 5 requires students to use appropriate tools strategically. So if a student can not add, subtract, multiply or divide by the time they get to the 9th grade then it is OK for them to use a calculator to participate while learning mathematical concepts. Conceptual understanding of mathematics precedes procedural fluency (NCTM, 2014). Students need to model mathematics through the use and support of appropriate tools.
My doctoral journey forced me to understand the importance for a professional educator to become a scholar, practitioner, and a leader in their workplace, classroom, school, or Local Education Agency (LEA). In the primary role as a teacher, it is important to conduct research to find evidence to support their instructional methods. When we teach we must assess the progress of our student’s learning to identify shortfalls in our instructional methods and take ownership for the lack of learning. We must hold our students accountable for their leaning and we will accept an evaluation of our performance as teachers. The present textbooks are a mixture of previous publications stamped with the SMP’s strategically. A closer analysis of the common core mathematical practices for teachers and students do not connect to a content standard. The big idea of the common core is about learning mathematics correctly.
The content for high school mathematics remained the same for 9-12. However, the creation of specific standards for learning and teaching is what’s new. The complaints by parents goes along this reasoning: ” I don’t understand this, I was not good in math myself, I was never good with math test, and I can’t help my child learn this new way. I want them to get a good grade that includes credit for homework , attendance, classroom participation, and fun projects that I can help them complete.”
So my response to these concerned parents is as follows: ” Let me get this straight, you didn’t get math in school and only passed because of the extra stuff”, So now you are asking me to do the same thing to your children”. Is this correct?
]]>Office Mix allows you to turn your PowerPoint decks into interactive online lessons or presentations. It adds functionality to PowerPoint 2013 so you to record audio or video of yourself presenting, write on your slides as you speak to them, insert quizzes, polls, online videos, and more.
We will be joined by Microsoft Distinguished Scientist Anoop Gupta, the Office Mix godfather, who sold the concept to Steve Ballmer before a line of code was written and also leads the team who has built it. Download Office Mix at http://OfficeMix.com
Click Here to Learn More About Microsoft Office Mix Plug-In – Power Point
Haiku Learning revolves around your content. Create classroom pages, add and organize content blocks, change layouts, and publish whenever you’re ready. Embed content from YouTube, Google Docs, Maps, Skype and dozens of other third-party services or create your own from scratch. And when you’ve crafted the perfect classroom page? Resource sharing in Haiku Learning lets you share your classes, pages, and content blocks with any other Haiku Learning user–and use content in your own class created by other teachers.
Click Here to Learn More About Interactive, engaging online content in a few simple clicks
The 2015 issue of Annual Perspectives in Mathematics Education (APME) approaches assessment from a wide variety of perspectives. Its 21 chapters, written by leading mathematics educators and researchers, are grouped into four sections:
Assessment in Action
Design of Assessment Tools and Strategies
Professional Learning to Enhance Classroom Assessment
Assessment as Reasoning from Evidence
To most of us, learning something “the hard way” implies wasted time and effort. Good teaching, we believe, should be creatively tailored to the different learning styles of students and should use strategies that make learning easier. Make It Stick turns fashionable ideas like these on their head. Drawing on recent discoveries in cognitive psychology and other disciplines, the authors offer concrete techniques for becoming more productive learners.
Memory plays a central role in our ability to carry out complex cognitive tasks, such as applying knowledge to problems never before encountered and drawing inferences from facts already known. New insights into how memory is encoded, consolidated, and later retrieved have led to a better understanding of how we learn. Grappling with the impediments that make learning challenging leads both to more complex mastery and better retention of what was learned.
Many common study habits and practice routines turn out to be counterproductive. Underlining and highlighting, rereading, cramming, and single-minded repetition of new skills create the illusion of mastery, but gains fade quickly. More complex and durable learning come from self-testing, introducing certain difficulties in practice, waiting to re-study new material until a little forgetting has set in, and interleaving the practice of one skill or topic with another. Speaking most urgently to students, teachers, trainers, and athletes, Make It Stick will appeal to all those interested in the challenge of lifelong learning and self-improvement.
Click Here to Learn More About Make It Stick: The Science of Successful Learning
“This emphasis on principles poses a problem for popular techniques like Please Excuse My Dear Aunt Sally, a mnemonic device for remembering the order of operations that teachers complain is imprecise, and the butterfly method for adding and subtracting fractions. If correctly applied, the tricks always result in the correct answer, but math experts say they allow students to skip the sort of conceptual thinking the standards are trying to encourage in students.” (Felton, 2014).
References
Boaler, J (2015). Memorizers are the lowest achievers and other Common Core math surprises. Retrieved from http://hechingerreport.org/memorizers-are-the-lowest-achievers-and-other-common-core-math-surprises/.
Felton, J. (2014). Common Core math experts say teachers need to stop using shortcuts and math ‘tricks’. Retrieved from http://hechingerreport.org/common-core-math-experts-say-teachers-need-stop-using-shortcuts-math-tricks/
This post is about YouTube videos made by educators to help explain why we needed to change mathematics instruction in the United States. The common core math videos do not frustrate me. The comments do. The negative comments or rather lack of understanding provides evidence that educational leadership needs to do a better job of educating the parents and establishing support systems for them. I am sharing these videos about Common Core Math because the videos being displayed below in this post point out why the standards were developed. Many videos are being posted to the public on YouTube about common core math. I have reviewed over a hundred thus far. I can remember the frustration of my parent’s experience with the new math in the 4th grade in 1963. My parent’s could not help me with my math homework. There was no social media comments out bashing teachers for trying to implement something that was a directive from above. The first people being frustrated are the teachers.
I have read many of the negative comments about common core math before writing this post. I have read about their concerns. I am frustrated and disappointed from the comments and responses to these teachers. I can read the comments and discern who is knowledgeable and who is not. I have been a public school mathematics teacher for over twelve years. The United States is far behind in the world in mathematics (PISA, 2012).
“The results from the 2012 Program for International Student Assessment (PISA) show that teenagers in the U.S. slipped from 25th to 31st in math since 2009; from 20th to 24th in science; and from 11th to 21st in reading, according to the National Center for Education Statistics, which gathers and analyzes the data in the U.S.”
Read more: http://www.businessinsider.com/pisa-rankings-2013-12#ixzz3dFLBAn4y
The negative comments are coming from the individuals who did not get it (mathematics). This is the PROBLEM! If those parents were taught conceptually then they would be able to get it and would have remembered it! Let us not repeat the ineffective instructional methods to our present day children when we know that the evidence (educational research) states that it does not work. Educational leadership did not understand the common core math and the associated tasks that would be necessary to implement this curriculum and instructional process. Now that we know we can reach out to do a better job of communicating to teach the community!
The negative comments are coming from those who never were taught to develop a conceptual understanding of mathematics and are now frustrated parents like mine back in 1963. These two videos shows the difference between procedural fluency and conceptual understanding. Both are required in the common core math.
These are the good comments:
“However, what the author is saying is that if the students understand what is REALLY happening when you are using the boring method (like how/why the magic zero appears, etc.), they are much more likely to remember it in the long run.”
“The problem in the video was 45 x 24. Lets put a 3 in front of the 24, so now the new problem is 45 x 324. If the students were ONLY taught the procedure (boring/traditional way), they wouldn’t know what to do when they are now multiplying by a 3-digit number (there would end up being two magic zeros when multiplying the hundreds place, which is the 3). If the student was taught the common core way (and THEN the procedural way), their minds would have the flexibility to adapt and solve the problem correctly. Problem solving is another very large aspect of common core.”
“My main criticism of common core is that they (the higher-ups in education) rushed into this so quickly without much of a grace period that now students, parents, teachers, administrators, and even textbook authors are basically being hung out to dry. I’m just trying to play the hand that I was dealt”
I have included only the good comments as valuable
“I think standard method works in other countries because kids in other countries are taught number flexibility at a young age, preparing them for number manipulation at older ages. The typical stereotype about Asians is that they are good at math. Asian countries teach their kids the abacus. They learn to manipulate numbers in kindergarten. The US didn’t. They just teach kids to memorize things and expect them to be on the same playing field as kids who grew up manipulating numbers. The number flexibility/familiarity that is instilled in Asian children is being addressed with Common Core. This “dumb method” is creative thinking. It is analysis. It is recognizing patterns. It will definitely be used in later math and in life….”
“She understands the “why”. I tried several approaches of explaining it until I found one that worked for her described above. It’s actually the same concept as the regrouping homework that made no sense to her, but presented in a totally different way. But the arithmetic worked even before she understood it on a deeper level, which is the beauty of arithmetic. I’m not going to proclaim that I found “the” way to convey a deeper understanding of math. I found one way, and I would not require anybody else to use this method.”