go to the website Teachers - Formative estimate - Informal estimate of Students' content 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 compare students, in this article, I will primarily offer suggestions for informal, formative evaluation for the mathematics classroom, particularly in the first of the three categories recommend by Clarke & Wilson:
Teachers - Formative estimate - Informal estimate of Students' content Knowledge in Mathematics
The student's mathematical content knowledge. The student's mathematical processes, such as reasoning, communicating, question solving, and manufacture connections. The student's mathematical disposition, such as attitudes, persistence, confidence, and cooperative skills.
If you agree with the idea 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, including the meaning for mathematics.
------------ Unit 2: Using Measures and Equations -------------
continuous opposites line length 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 further angles acute triangle equation equivalent equations irrational number perfect cube absolute value segment congruent segments vertex of an angle straight 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 beginning of a new unit or part (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 necessary to go over the five distinct levels of word knowledge, but students beyond doubt 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 leading to claim the words as the students read them and rate their own level of knowledge of the word because there are words that students recognize when they hear them but don't recognize when they see them. Then, to compare content knowledge, for all words that the students rated as 4's or 5's, ask them to write their best insight of what that word means in mathematics. This is not used for a grade but rather, as formative evaluation 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 beginning of the week. Then, each day, whether as students enter class, or as the closing action for the day, four problems from a previous day's part or homework are given, and students enter each question (and solution) in the four spaces for the day. The teacher 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 evaluation information.
The third suggestion for formative evaluation of content knowledge is execution assessment. whole articles (and books) have been written on the next suggestion for formative evaluation of mathematical content knowledge, but even though I cannot fully by comparison it in the context of this article, I would be remiss not to mention the idea of execution assessment. execution assessments are assessments "in which students demonstrate in a collection of ways their insight 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 number of characteristics of execution tasks, including 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 gift non-routine, open-ended, and loosely structured problems that need students both to define the question and to manufacture a strategy for solving it need students to settle what data are needed, obtain the data, article and portray them, and analyze them to discuss sources of error necessitate that students use a collection of skills for acquiring information and for communicating their strategies, data, and conclusions (p. 93)
Begin exploring assorted formative evaluation tools with your students to settle 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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