NCTM vs. NJCCCS

1. NCTM vs. NJCCCS Presentation by Beth Meichenbaum

2. Comparison of: NJCCCS 4.4 A. Data Analysis B. Probability NCTM Data Analysis & Probability Standard

3. NCTM Standard is Broken into 4 Basic Subtopics 1. Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them 2. Select and use appropriate statistical methods to analyze data 3. Develop and evaluate inferences and predictions that are based on data 4. Understand and apply basic concepts of probability

4. Subtopics are Further Divided Subtopics are further divided into sub �standards (like NJCCCS CPI strands) by grades Pre-k - 2 3-5 6-8 9-12

5. Major Differences NJCCCS strands are more general in nature than NCTM sub-standards, but more specific in what should be done by end of grade level. NCTM sub-standards practically recommend what activities should be done in the lesson, whereas the NJCCCS standards only cover a topic or concept to be learned.

6. Major Differences NJCCCS repeats many of the strands at each grade level but certain strands are added as grade levels increase so students progress along Bloom�s Taxonomy (knowledge, comprehension, application, analysis, synthesis and evaluation) NCTM sub-standards do not tend to repeat at each grade level verbatim

7. Similarities Both sets of standards are similar at the older grade levels � especially �using simulations to explore the variability of sample statistics from a known population.� Both stress �students making inferences and evaluating arguments based on displays and analysis of data.� However, NCTM introduces this at grades 3-5, whereas NJCCCS doesn�t mention it until grade 7!

8. Lesson Idea for NCTM Standards# 1 �Representing Data� To fulfill subtopic 1, �Formulate questions�� In grades 6�8 all students should �� � select, create, & use appropriate graphical representations of data, including histograms, box plots, & scatter plots. Have students obtain data from around the school and create an appropriate representation of the data (histogram, scatter plot, etc.)

9. Lesson Idea for NCTM Standards # 2 �Mean, Mode or Median� To fulfill subtopic 2, �Select & use �� In grades 6�8 all students should �� � find, use, and interpret measures of center and spread, including mean and inter-quartile range. Give students different sets of data in which either mode, median or mean are the most important statistical method used. Example for median: List of students� heights

10. Lesson Idea for NCTM Standards# 3 �Coin Toss� To fulfill subtopic 3, �Develop & evaluate �� In grades 6�8 all students should �� � use observations about differences between two or more samples to make conjectures about the populations from which the samples were taken; Have several groups of students record the results of 100 coin tosses. Discuss the differences between 2 or more sample groups and make conjectures about the populations from which the samples were taken.

11. Lesson Idea for NCTM Standards# 4 �Smoking Statistics� To fulfill subtopic 3, �Develop & evaluate �� In grades 9�12 all students should �� � evaluate published reports that are based on data by examining the design of the study, the appropriateness of the data analysis, and the validity of conclusions; Have students review a published report on smoking � one by a tobacco company and one by a cancer research company. Teaching the concept of skewed statistics in high school is controversial.

12. Lesson Idea for NCTM Standards # 5 �Complementary or Not?� To fulfill subtopic 4, �Understand & apply �� In grades 6�8 all students should �� � understand and use appropriate terminology to describe complementary and mutually exclusive events; Give students examples of instances of each and have them identify which is mutually exclusive (outcome of first has no effect on second) and which is complementary (outcome of first has effect on outcome of the second).

13. Questions?