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- 1. Strategies in Teaching the Least Mastered Skills Dr. Carlo Magno De La Salle University, Manila 1
- 2. Answer the following questions: • What important skills should be assessed in Mathematic? • How would you know if students have mastered the skill? • What do you do to teach for mastery? 2
- 3. Advance Organizer • Standards for learning • Sources of Information for Mastery – Assessment literacy – Reading Assessment results – Assessment for Learning • Teaching Strategies – Formative Assessment – Mastery Learning 3
- 4. Why do we need standards? • To make sure that everyone delivers quality work • To produce quality students • To deliver quality programs 4
- 5. Mathematics Standards for Grade 5 • Number and Number sense – Read and write large whole numbers and round off whole numbers to the nearest thousands and millions. – Find the greatest common factor and the least common multiple of given numbers. – apply divisibility rules for 2, 3, 4, 5, 6, 8, 9, 10, 11 and 12 on different contexts. 5
- 6. Mathematics Standards for Grade 5 – simplify a series of operations on whole numbers and solve problems involving these. – perform the four fundamental operations on fractions and mixed numbers and solve related problems. – investigate the relationship between fractions and decimal numbers. – explore, know and understand the concept and value of a decimal number. 6
- 7. Mathematics Standards for Grade 5 – add and subtract decimal numbers with values through thousandths and solve problems involving these. – multiply decimal numbers of values up to the hundredths and solve problems involving these numbers. – divide decimal numbers of values up to the hundredths and solve problems involving these numbers. – manipulate ratios and solve problems involving ratios and proportions – know and understand the concept of percent and to solve problems involving percents. 7
- 8. Mathematics Competencies for Grade 5 • Geometry – explore polygons with up to 10 sides. – explore circles. • Patterns and Algebra – solve for the unknown values in simple equations involving one or more operations on whole numbers and fractions. 8
- 9. Mathematics Competencies for Grade 5 • Measurement – describe the circumference of a circle, measure and use it to solve problems. the measure of circumference, area of a circle, volume of a cube and a rectangular prism and temperature. – convert units of measure for area and volume and select appropriate units and tools for consistency and accuracy. – describe the area of a circle, measure and use it to solve problems. 9
- 10. Mathematics Standards for Grade 5 – describe the volume of a cube and a rectangular prism, measure and use it to solve problems. – describe temperature, measure and use it to solve problems. – Probability and Statistics – construct, read and interpret a line graph and its corresponding table of data and solve problems involving data from a table and a line graph. – make simple predictions of events based on a probability experiment. 10
- 11. Sources of Information on Student Mastery • Assessment Results – Classroom Assessment: Quarterly Test, Quizzes – National Assessment: NAT Results (Grade 6) 11
- 12. Sources of Information on Student Mastery • Forms – Formative – Summative • Types – Paper and Pencil – Alternative forms: Performance, authentic, Portfolio • Approaches – Assessment “of” learning – Assessment “for” learning 12
- 13. Assessment Literacy • (1) Assessment comes with a clear purpose • (2) focusing on achievement targets • (3) selecting proper assessment methods • (4) sampling student achievement 13
- 14. Reading Assessment Results Levels of Proficiency 14
- 16. Reading Assessment Results Beginning Developing Approaching Proficiency Proficient Advanced 16
- 18. Reading Assessment Results • Mathematics NAT • 15 items – Place value = 1 – Fraction = 2 – Measurement = 2 – Multiplication = 1 – Division = 2 – Lines = 1 – Addition = 3 (Problem solving) – Ratio and proportion = 1 – Statistics = 2 (interpreting graphs) 18
- 19. Approach in Assessment Assessment of Learning Assessment for Learning Assessment as learning 19
- 20. ASSESSMENT OF LEARNING AND ASSESSMENT FOR LEARNING Effect of Previous Practices: rank students on achievement by graduation New Expectation: Assure competence in Math, Reading, Writing, etc. • Implications? Assessment and grading procedures should help students succeed. 20
- 21. ASSESSMENT FOR LEARNING • We need to close the gap between standards and students competencies • Risk: our society will be unable to productively evolve in social and economic sense. • Assessment is a tool to ensure student mastery of essential standards. 21
- 22. ASSESSMENT FOR LEARNING • Mistaken beliefs about how to use assessment to support school improvement: 1.High-stakes tests are good for all students because they motivate learning 2.If I threaten to fail you, it will cause you to try harder 3.If a little intimidation doesn’t work, use a lot of intimidation 22
- 23. MISTAKEN BELIEFS 4. The way to maximize learning is to maximize anxiety 5. It is the adults who use assessment results to make the most important instructional decision. 23
- 24. MISTAKEN BELIEFS PROFOUND MISTAKE Teachers and leaders don’t need to understand sound assessment practices – the testing people will take care of us. COUNTER BELIEF They do need to understand sound assessment practices. 24
- 25. Assessment “for” Learning • Assessment Crisis: The Absence Of Assessment FOR Learning • By Rick Stiggins 25
- 26. Assessment “for” Learning • School improvement requires: – the articulation of higher achievement standards, – the transformation of those expectations into rigorous assessments, and – the expectation of accountability on the part of educators for student achievement, as reflected in test scores. 26
- 27. Assessment “for” Learning • When they assess for learning, teachers use the classroom assessment process and the continuous flow of information about student achievement that it provides in order to advance, not merely check on, student learning. 27
- 28. Assessment “for” Learning • understanding and articulating in advance of teaching the achievement targets that their students are to hit; • informing their students about those learning goals, in terms that students understand, from the very beginning of the teaching and learning process; • becoming assessment literate and thus able to transform their expectations into assessment exercises and scoring procedures that accurately reflect student achievement; 28
- 29. Assessment “for” Learning • using classroom assessments to build students’ confidence in themselves as learners and help them take responsibility for their own learning, so as to lay a foundation for lifelong learning; • translating classroom assessment results into frequent descriptive feedback (versus judgmental feedback) for students, providing them with specific insights as to how to improve; 29
- 30. Assessment “for” Learning • continuously adjusting instruction based on the results of classroom assessments; • engaging students in regular self-assessment, with standards held constant so that students can watch themselves grow over time and thus feel in charge of their own success; and • actively involving students in communicating with their teacher and their families about their achievement status and improvement. 30
- 31. Teaching Approaches Formative Assessment Mastery Learning 31
- 32. Formative Assessment • Need not be graded as summative assessments (end-of-unit exams or quarterlies, for example) are. • They serve as practice for students • They check for understanding along the way and guide teacher decision making about future instruction; • they also provide feedback to students so they can improve their performance 32
- 33. Formative Assessment • For assessments to be accurate, teachers need multiple measures of student understanding. • Teachers need evidence gathered over time in different ways to evaluate how effective the teaching and learning process has been. • Tomlinson and McTighe (2006) suggest that when teachers gather a "photo album" rather than a "snapshot" of our students, we can differentiate instruction based on a more accurate evaluation of our students' learning needs. 33
- 34. Formative Assessment • 1. Student friendly targets from the beginning • 2. Models of strong and weak work • 3. Continuous descriptive feedback • 4. Teach self-assessment and goal setting • 5. Teach one facet at a time. • 6. Teach focused revision. • 7. Teach self-reflection to track growth 34
- 35. Formative Assessment • Group Assessment - allows you to quickly identify problems or misconceptions, which you can address immediately. • Individual assessment - Provide some feedback to the learner, perhaps in the form of a brief comment or, at the very least, a check, check-plus or check-minus, with a brief verbal explanation about what each symbol indicates 35
- 36. Formative Assessment • Summaries and Reflections .Students stop and reflect, make sense of what they have heard or read, derive personal meaning from their learning experiences, and/or increase their metacognitive skills. These require that students use content-specific language. • Lists, Charts, and Graphic Organizers Students will organize information, make connections, and note relationships through the use of various graphic organizers. • Visual Representations of Information Students will use both words and pictures to make connections and increase memory, facilitating retrieval of information later on. This "dual coding" helps teachers address classroom diversity, preferences in learning style, and different ways of "knowing." • Collaborative Activities Students have the opportunity to move and/or communicate with others as they develop and demonstrate their understanding of concepts. 36
- 37. Formative Assessment • Formative Assessment can be an integral part of instruction (Guskey, 2007): • (1) use assessments as sources of information for both students and teachers, • (2) follow assessments with high-quality corrective instruction, and • (3) give students second chances to demonstrate success 37
- 38. Formative Assessment • By varying the type of assessment you use over the week, you can get a more accurate picture of what students know and understand, obtaining a "multiple- measure assessment ‘window' into student understanding" (Ainsworth & Viegut, 2006). • Using at least one formative assessment daily enables you to evaluate and assess the quality of the learning that is taking place in your classroom and answer these driving questions: How is this student evolving as a learner? What can I do to assist this learner on his path to mastery? 38
- 39. Formative Assessment • Response to Intervention (RTI) model – Tier 1 interventions include monitoring at-risk students within the general education classroom, ensuring that each student has access to a high- quality education that is matched to his or her needs. – RTI focuses on improving academic achievement by using scientifically based instructional practices. – Use alternative assessment which utilizes quality interventions matched to student needs, coupled with formative evaluation to obtain data over time to make critical educational decisions. 39
- 40. Mastery Learning • Internalization of learning resulting in automatic or habitual change in behavior through repetition and application. • Shift from short term to long term memory 40
- 41. Mastery learning • Mastery learning breaks subject matter and learning content into units with clearly specified objectives which are pursued until they are achieved. • Learners work through each block of content in a series of sequential steps. • Students must demonstrate a high level of success on tests, typically at about the 80% level, before progressing to new content. • Those who do not reach the required level are provided with additional scaffold, peer support, small group discussions, or homework so that they can reach the expected level. 41
- 42. Stages of mastery learning • Stage 1: Unconscious incompetence – Student does not know at all • Stage 2: Conscious incompetence – Student discovers that he does not know and realizes he needs to know • Stage 3: Conscious competence – Learner receives instruction, tries to do it, does it again and again. • Stage 4: Unconscious competence – Proficiency, executing task without effort. 42
- 43. Teaching for Mastery Teacher direction (1/4 of instruction time) Students self-activity (3/4 of instruction time, time-on-task) Explanation, which includes: motivation presentation Examples through: demonstration concrete examples Exercise, oral work board work seatwork drill homework 43
- 44. Workshop • Role playing • Focus on one mathematics competency/standard • Demonstrate how to teach formative assessment and mastery learning to develop the competency selected • Before you begin the demonstration tell the audience the topic and the competency 44