Accountability
Classroom Scenario:
9th Grade Mathematics
Mrs. Born had a new 9th grade classroom in 2003. Her second period class has 30 students. What skills did they have, and what did they need? Mrs. Born is Math teacher. She decided to look at the 8th grade state assessment Math scores for one of her classes. The scores were low! She had to find some way to prioritize them. Then she compared the scores to the state Just Proficient Mean (JPM) to see what the passing score was for all state 8th graders.
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Let's
look at what she found: Mrs. Born's
9th grade class.
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What cluster areas needed less help? She wasn't really sure about the language arts literacy scores because they did not look TOO low. But the Math scores were definitely noticeably lower than the JPM.
Mrs. Born decided to explore a little further before deciding on her priorities. She decided to compare her class scores with scores by students who made advanced proficient scores.
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Mrs.
Born compared her 9th grade class with students who made advanced
proficient scores on the 8th grade test. See Math
scores.
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What cluster areas seemed to pose the most difficulty for Mrs. Born's Math class? Where should she focus her attention for maximum student achievement?
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Mrs.
Born noted that all Math clusters scored low, but the Knowledge
cluster was particularly low. She decided that her students had
not learned the math concepts necessary for the 8th grade statewide
assessment and that she needed to focus on most
of Math - she decided not to worry about problem solving for
now.
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Mrs. Born immediately
began helping the class by targeting the mathematics standards, and by
reviewing grade 8 standards as she went. She decided to emphasize
knowledge around standards, and not to worry too much about problem solving.
Her students would have to work very hard! She used the Math
standards matrix.
| Standard 4.1 (number and numerical operations). All students will develop number sense and will perform standard numerical operations and estimations on all types of numbers in a variety of ways. | Descriptive Statement: Numbers and arithmetic operations are what most of the general public think about when they think of mathematics; and, even though other areas like geometry, algebra, and data analysis have become increasingly important in recent years, numbers and operations remain at the heart of mathematical teaching and learning. Facility with numbers, the ability to choose the appropriate types of numbers and the appropriate operations for a given situation, and the ability to perform those operations as well as to estimate their results, are all skills that are essential for modern day life. |
| Standard 4.2 (geometry and measurement). All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena. | Descriptive Statement: Spatial sense is an intuitive feel for shape and space. Geometry and measurement both involve describing the shapes we see all around us in art, nature, and the things we make. Spatial sense, geometric modeling, and measurement can help us to describe and interpret our physical environment and to solve problems. |
| Standard 4.3 (patterns and algebra). All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes. | Descriptive Statement: Algebra is a symbolic language used to express mathematical relationships. Students need to understand how quantities are related to one another, and how algebra can be used to concisely express and analyze those relationships. Modern technology provides tools for supplementing the traditional focus on algebraic procedures, such as solving equations, with a more visual perspective, with graphs of equations displayed on a screen. Students can then focus on understanding the relationship between the equation and the graph, and on what the graph represents in a real-life situation. |
| Standard 4.4 (data analysis, probability, and discrete mathematics). All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data. | Descriptive Statement: Data analysis, probability, and discrete mathematics are important interrelated areas of applied mathematics. Each provides students with powerful mathematical perspectives on everyday phenomena and with important examples of how mathematics is used in the modern world. Two important areas of discrete mathematics are addressed in this standard; a third area, iteration and recursion, is addressed in Standard 4.3 (Patterns and Algebra). |
Benefits
arising from teaching these clusters: Students will increase their overall
math knowledge. Ensuring that assessments are designed to ensure that
the students are thinking beyond the lowest Bloom's taxonomy level will
help establish the knowledge.
• See the Thinking
is Critical section of the HSPA Helpful Hints Tutorial.
• An additional
rule of thumb for assessment is that the first three Bloom's levels (Knowledge,
Comprehension and Application) and excellent for formative assessment;
and the three other levels (Analysis, Synthesis and Evaluation) inform
the summative level. See Applying
Bloom's Taxonomy by Joan Dalton (http://www.teachers.ash.org.au/researchskills/dalton.htm)
which gives question stems and possible related activities. There are
many other references on the web.
