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?
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
4. Why do we need standards?
• To make sure that
• To produce quality
• To deliver quality
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
– 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.
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
– investigate the relationship between fractions and
– explore, know and understand the concept and
value of a decimal number.
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
– divide decimal numbers of values up to the hundredths
and solve problems involving these numbers.
– manipulate ratios and solve problems involving ratios
– know and understand the concept of percent and to
solve problems involving percents.
8. Mathematics Competencies for Grade 5
– 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.
9. Mathematics Competencies for Grade 5
– 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
– describe the area of a circle, measure and use it to
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
– 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
11. Sources of Information on Student
• Assessment Results
– Classroom Assessment: Quarterly Test, Quizzes
– National Assessment: NAT Results (Grade 6)
12. Sources of Information on Student
– Paper and Pencil
– Alternative forms: Performance, authentic, Portfolio
– Assessment “of” learning
– Assessment “for” learning
13. Assessment Literacy
• (1) Assessment comes with a clear purpose
• (2) focusing on achievement targets
• (3) selecting proper assessment methods
• (4) sampling student achievement
20. ASSESSMENT OF LEARNING AND ASSESSMENT
Effect of Previous Practices:
rank students on
achievement by graduation
New Expectation: Assure
competence in Math,
Reading, Writing, etc.
Assessment and grading
procedures should help
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
• Assessment is a tool to ensure student
mastery of essential standards.
22. ASSESSMENT FOR LEARNING
• Mistaken beliefs about how to
use assessment to support
1.High-stakes tests are good for all
students because they motivate
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
23. MISTAKEN BELIEFS
4. The way to maximize learning is to
5. It is the adults who use assessment
results to make the most important
24. MISTAKEN BELIEFS
Teachers and leaders don’t need to understand
sound assessment practices – the testing people
will take care of us.
They do need to understand sound assessment
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
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
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;
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;
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.
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
• they also provide feedback to students so they
can improve their performance
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.
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
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
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
• 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.
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
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?
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.
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
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.
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.
43. Teaching for Mastery
(1/4 of instruction time)
(3/4 of instruction time,
• Role playing
• Focus on one mathematics
• 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