such a good point Teachers - Formative evaluation - Informal evaluation of Students' article Knowledge in Mathematics
While there can be overlap in the middle of some types of formative and summative assessments, and while there are both informal and formal means to correlate students, in this article, I will primarily offer suggestions for informal, formative estimate for the mathematics classroom, particularly in the first of the three categories recommend by Clarke & Wilson:
Teachers - Formative evaluation - Informal evaluation of Students' article Knowledge in Mathematics
The student's mathematical content knowledge. The student's mathematical processes, such as reasoning, communicating, qoute solving, and development connections. The student's mathematical disposition, such as attitudes, persistence, confidence, and cooperative skills.
If you agree with the plan that words are labels for concepts, then you will want to use the 1, 2, 3, 4, 5 idea shown below:
Indicate your knowledge of each word by writing a 1, 2, 3, 4, or 5 in front of the word. The numbers signify the following five statements:
I've never even seen the word/phrase.
I've seen the word/phrase, but I don't know what it means.
I know the word/phrase has something to do with...
I think I know what it means in math
I know the word/phrase in one or several of its meanings, together with the meaning for mathematics.
------------ Unit 2: Using Measures and Equations -------------
continuous opposites line distance of a segment ray central angle of a circle complementary angles vertical angles right triangle solving an equation rational number perfect square discrete scientific notation endpoint midpoint angle right angle additional angles acute triangle equation equivalent equations irrational number perfect cube absolute value segment congruent segments vertex of an angle right angle congruent angles obtuse triangle solution quadrate root real number cube root
I prefer to use this as both an informal pre- and post-assessment. At the starting of a new unit or episode (and again at the end), I give students a sheet similar to the one shown above, with vocabulary terms for the unit listed. [The first time you use this idea, it is significant to go over the five different levels of word knowledge, but students as a matter of fact understand the idea that there are words they have never heard of and words that they know in several ways (and all things in in the middle of these two).] It is prominent to verbalize the words as the students read them and rate their own level of knowledge of the word because there are words that students identify when they hear them but don't identify when they see them. Then, to correlate content knowledge, for all words that the students rated as 4's or 5's, ask them to write their best comprehension of what that word means in mathematics. This is not used for a grade but rather, as formative estimate to give an idea of students' understandings of the concepts before and after the unit of instruction.
A second way of assessing students' content knowledge, is giving students a sheet with 5 rows and 4 columns at the starting of the week. Then, each day, whether as students enter class, or as the conclusion action for the day, four problems from a old day's episode or homework are given, and students enter each qoute (and solution) in the four spaces for the day. The trainer can check these swiftly or have a row grader check them. These may be collected each day or at the end of the week, depending on the teacher's plan for using the estimate information.
The third advice for formative estimate of content knowledge is operation assessment. entire articles (and books) have been written on the next advice for formative estimate of mathematical content knowledge, but even though I cannot fully interpret it in the context of this article, I would be remiss not to mention the idea of operation assessment. operation assessments are assessments "in which students demonstrate in a range of ways their comprehension of a topic or topics. These assessments are judged on predetermined criteria" (Ascd, 1996, p. 59). Baron (1990a, 1990b, and 1991) in Marzano & Kendall (1996) identifies a estimate of characteristics of operation tasks, together with the following:
are grounded in real-world contexts involve sustained work and often take several days of combined in-class and out-of-class time deal with big ideas and major concepts within a discipline present non-routine, open-ended, and loosely structured problems that need students both to define the qoute and to compose a strategy for solving it need students to rule what data are needed, regain the data, narrative and portray them, and analyze them to discuss sources of error necessitate that students use a range of skills for acquiring data and for communicating their strategies, data, and conclusions (p. 93)
Begin exploring varied formative estimate tools with your students to rule their content knowledge in mathematics. You will learn a great deal - and then be able to help your students learn even more!
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