Math Preparation

The ability to count and all of the ramifications of being able to do so is critical in our present world. Counting leads to measuring. It allows us to predict. It permits us to define the world around use in terms other than our own subjective beliefs. “I know my first 10 letters of the alphabet.” “I know all 400 words in my basic reader.” “I am learning 5 new words each day.” “I read one book each week this summer.” When will you be empowered to the point (exhibit mastery) that cramming for and taking NCLB standardized tests will be, “just a waste of time?”

I learned my math on a sheet of paper. A large square was drawn. The square was divided into four squares. Each of these was marked off with four horizontal and four vertical lines. I could count to 100 by filling in the cells. I could count by 2s, 3s, 4s, and 5s, which was really multiplying by 2, 3, 4, and 5. I could count backwards, which was subtracting. I learned to estimate the answer to any math question so I had some judgment if I might not be right (I actually spotted a failing Marchant calculator. One of the wheels failed to stop at nine when it should have, but continued on to four). Later I learned square and square root. And finally logarithms, where addition is multiplication and subtraction is division (to three significant digits on a slide rule). The experience of learning the multiplication tables not only is essential in math but also carries over into learning other things that are not as limited and well defined. Hand calculators allow students to skip the basics and suffer the consequences.

The oldest, time tested, math downloadable listed by the Educational Software Cooperative teaches counting, addition, and subtraction. Next multiplication was included. Educational games and puzzles have always been popular, I think in part, because the authors have fun creating them. In a free enterprise economy, a successful game can support the author and a business is born. Those who directly benefit pay the cost of development rather than taxpayers or a non-profit that obtained its funding from a taxable free enterprise activity.

Word problems for grades 1-8 can now be presented by software. Unique calculator and statistical software are available to supplement the myriad of hand calculators. Some of this software is free. The same is true for graphing calculators. All of these are under listings and math downloadables.

Fractions and algebra are still available as downloadables from Merit Software even though these are much further developed in its online software. Evallutel Multimedia presents algebra and geometry, and more. Math downloadables are listed under classroom tests, educational games, math, and teaching aids. The online offerings in the prior two posts on reading and writing; vocabulary, phonics and spelling; also include math.

All of these lessons in software are designed to free teachers to teach, and students to learn, the subject rather than to spend time trying to memorize answers to questions they guess will be on a standardized test. Use this software to give students the opportunity to develop the sense of responsibility needed to learn at all levels of thinking. They will then be ready for Knowledge and Judgment Scoring, quantity and quality, and as also in Winsteps and Amplifier.

With subject mastery at the proper levels of thinking, there should be very little concern about passing current NCLB standardized tests that are scored at the lowest levels of thinking. IMHO it is failure on the part of school administrators to understand this miss match that locks many failing schools into continued failure. Preparing for a lower level of thinking scored test using lower level of thinking experiences dooms students to failure now and even more so in the future. In math especially, students need to be able to do and to understand, not just be aware of what a teacher has presented.

Students functioning at lower levels of thinking are dependent upon their teacher for maintaining their knowledge and skill levels. Students functioning at higher levels of thinking are capable of relearning as needed. They need a teacher for direction and for the expansion of their abilities, not for the maintenance of their knowledge and skill. The more you develop students, the easier it is to teach and to learn. This is the reason that well prepared third graders survive and flourish.

Vocabulary, Spelling and Phonics

Before assessing reading ability, one must be able to read. Before one can read, one must acquire a vocabulary. Given the complexity of American English, one must also know how to spell.

I did research on this matter with underprepared college freshmen in a remedial biology class. The campus computer system presented a sentence from assigned reading with a word missing. Students could enter one letter at a time to build the complete word (they called it Wheel of Fortune). Many students could not enter hints is this way. They insisted on typing an entire word. They had learned to read by the look-say method that does not stress spelling. The most unusual student read each word out loud, expect for tri-syllabic words or larger, for which she inserted, “buzz”. Her explanation was that long words, “really don’t count”.

My own experience in building a vocabulary was given a gigantic boost after taking a series of aptitude tests at the Johnson O’Connor Research Foundation in New York City during my second year in the USAF. I won an Air Force wide contest to attend the IBM Customer Engineering School at Endicott, New York, but the aptitude testing ranked me in the bottom 10% on vocabulary! “A person’s vocabulary level was the best single measure for predicting occupational success in every area.” And further, “…vocabulary is not innate, … it can be acquired.” 

I then spent several months while on duty in Japan reading through the two-volume edition of The Johnson O’Connor English Vocabulary Builder. It worked! I tested out of freshman English at Mizzou two years later, but enrolled in both semesters anyway. You can still buy the book. Or you can use related software from WordSmart’s. We are not talking flashcards here. The point is to embed a word in a meaningful matrix of relationships, such that it has a meaning, for which the word is the label. The Vocabulary Builder also presents good examples of grammar.

The Educational Software Cooperative (ESC) lists a number of authors teaching vocabulary, spelling and phonics. The key to success is that the student wants to learn. Vocabulary empowers. The high performance teacher has that unique ability to promote student engagement, in person or by way of software (educational games). Crossword puzzles are a fun way of teaching spelling and vocabulary. Crossdown and “other cool sites” let you create puzzles from your current spelling lists and other topics, as well as play online.

The oldest, time proven, phonics, spelling and vocabulary program to be listed under English, Animated Beginning Phonics, uses animation to entice young students to persist. An animated character speaks the word or you record the sound for the student to hear in the next advancement listed under Vocabulary and Spelling. Next comes the software for teaching word recognition, meanings, and origin by Merit Software. Today this software is fully developed online as are the remaining ESC offerings in this category. Spelling and vocabulary are included in the reading and writing online software discussed in the previous post. You must check each list and software category for the one that fits your needs the best.

How students use the software determines what they get out of it. Reading aloud and spelling can be conducted at the lowest levels of thinking with any in-person or software presentation. An empowering vocabulary is created when the student wants to learn and the words are truly labels for meaningful observations and relationships. The reader then experiences what the words represent. The accomplished reader can then command a given situation by use of meaningful words. The world would be so different if people took the time to actually understand one another. IMHO that would mean the end of traditional right count scored multiple-choice NCLB tests. If not the end, at least scoring for quantity and quality (as found in PUP, Winsteps and Amplifire) would be offered as an alternative choice to the current gambling.

Reading and Writing Preparation

The standardized testing being created by the two consortia (PARCC and SBAC) and Pearson is predicted to produce comparable test results among states (less cheating at all levels). The next level of assessment is standardized student certification: students passing the test will have predictable performance in future courses and in the workplace. Pearson, based in London, the largest education company in the world, over 70% of the revenues, is making great strides toward this goal (valid assessment must be coupled with appropriate instruction).

All of this must start with students being capable readers. The main problem found to date, indicated by students dropping out of high school, is that they were not good readers by the end of the third grade. They remained passive captives of the classroom until they could no longer stand the boredom; or the prospects of passing a NCLB standardized test to pass a course seemed impossible; or they were missing, disenrolled or triaged to increase the school’s rank.

To actually know something, to make it your own, requires that you do something with that knowledge or skill. Visualization works with both real and imaginary situations. Performance requires doing the real thing or working with a close mock up. Questioning, answering, and verifying do this for the self-educating student.

The passing rate on NCLB standardized tests makes a good example of how this can work out in a complex system of state and federal agencies. Some states visualized an ever-increasing rate of passing, but with each increase a bit smaller then in the previous year. The idea was to maintain the minimum annual yearly increase until the politicians in Washington, DC, would correct the initial error of requiring the impossible standard of 100% of students passing in 2014. Of course, that did not happen.

The politicians are now five years behind in correcting their original errors, and state departments of education must now explain why their new tests are producing such low passing rates, with about the same low scores. The passing rate was a Ponzi scheme at the state level based, as much on luck (the right count scored multiple-choice test), as on student ability. We really need a way to educate individual students and evaluate each for what each one knows and can do. Teaching to the middle of the class and assessing with the popular right marked scored multiple-choice test cannot do that when the result is low scoring tests. The vision was doubly faulted: instruction and assessment.

The Educational Software Cooperative (ESC) was formed in 1992 (incorporated as a non-profit in 1994) to provide a means for teachers and software authors (who were mostly teachers) to empower individual students to become proficient learners (both quantity and quality, knowledge and judgment, are important) regardless of the academic environment of their schooling. Software lessons can also be non-judgmental and have everlasting patience.

ESC members have continued to teach by way of ever changing software that improves in the level of thinking addressed with every advance in technology. The oldest currently listed downloadable reading software is Animated Alphabet for Windows. It teaches letter sounds and vowels with silly animation to prevent boredom when learning at the lowest levels of thinking. Directions are read aloud for pre-readers. The level of thinking is in balance within instruction, learning, and assessment.

The most advanced downloadable reading software listed, such as AceReader, promote reading, fluency and comprehension. I have never seen such a course in all of my schooling. I took the Evelyn Wood’s Reading Dynamics course in 1967 in Honolulu, Hawaii, when on a two year sabbatical with the USDA, Agriculture Research Service. The most successful students in the class performed at phenomenal reading speeds when they were able to change from sub-vocalizing each word to forming visualizations from groups of words. You actually see, experience, what the author is writing about rather than remember the words used. It is a neat experience. Successful students must be efficient and proficient readers. Yet how often do students in public schools get a chance to learn to read at this level, or even be aware that it exists? It was a new experience to me.

Another example of replacing words about a subject with the experience of doing is Smart Science. Sub-vocalizers think they are reading well because they have never experienced a higher level of reading. Cookbook laboratory manual exercises, followed one word at a time (at lower levels of thinking), do not generate the experience of doing science (at higher levels of thinking). The words are a poor replacement for the real thing. Smart Science teaches the important process of science and scientific habits of thought by way of real virtual labs. This is reading, observing, thinking, and writing using all levels of thinking. It is much more than record keeping at the lowest levels of thinking.

The most recent offerings take advantage of the Internet to supplement individual student learning and perform classroom record keeping chores. Merit Software produces award winning software for the home and the classroom that teaches reading and writing. Essential Skills Software produces both CDs and online versions for use in classrooms that are closely aligned with state reading and writing standards. Please check the ESC list for others.

Teaching by way of software is now well developed. The Common Core State Standards has created an environment in which free enterprise can thrive. Good government has a positive effect that costs the taxpayers nothing. The two consortia however are struggling with computer scored essays (at the lowest levels of thinking comparable to human fast scoring), online assessment (with right count scoring at the lowest levels of thinking) and millions of taxpayer dollars.

The Internet pipeline for full online interactive assessment is needed to manage cheating at all levels. Once in place it can then be reversed and used for individual student instruction. At this point I would hope that all levels of thinking could then be accommodated. I also predict the dominate testing company may well become the dominate instruction company. The traditional classroom will no longer be needed. The creativity that produces new educational software will always be needed. 

Currently, to my knowledge gained in writing this post, student ability is still assessed within school courses. Software teaches as a supplement to, or a replacement of, a part of a course. Each year more teacher friendly features are included: record keeping, etc. Even the software I have named as examples have many more features than I have mentioned. Each author, teacher, has a unique approach to creating software. You must check out each offering for the one that fits your needs the best.

At some point software should have the same weight as a correspondence course. This is coming about as a natural experiment in what is now being called  “flipped” instruction. Students do the lower level of thinking portion at home by CD or online. They are then ready to question and discuss at higher levels of thinking, and to know where they may need help, in class.

This method of instruction worked very well in my remedial biology course. The textbook was presented with questions on the campus computer system to help students learn to read by questioning and relating (meaning making). Biweekly multiple-choice tests scored for quantity and quality (accurate, honest, and fair – no guessing required) promoted student development from passive pupil to self-correcting scholar. Today we can also add Winsteps and Amplifire (see previous post).

Your Choice of Multiple-Choice Testing

Doing PARCC, SBAC, waiver or no waiver? Your choice of multiple-choice makes a big difference in what you get for your money. Today you have a choice. You are not bound to the traditional, right count scored (RCS) version.

• Traditional RCS multiple-choice works very well at the mastery level, 90% cut score; it is an easy way to score classroom tests, 75% average score and 60% cut score; it is gambling below a score of 60% (meaningless ranking where quantity and quality scores are identical).
• Independent quantity and quality scored multiple-choice provides the same freedom for students to report what they trust they know and can do as when using short answer, essay, projects, and reports when scored at all levels of thinking. The quality score can range from that found on a RCS test up to 100%, independently from the quantity score: the number of right marks (both the examinee and the examiner know what the student knows and how well knowledge and judgment are used). No forced guessing or gambling is required, just fair and honest reporting.

You have several ways to implement the student empowering features of independent quantity and quality scoring.

• Both right count scoring and Knowledge and Judgment Scoring (KJS) are featured in Power Up Plus (PUP). This is a classroom friendly implementation. It allows students to select either right count scoring (at the lowest levels of thinking) or KJS (at all levels of thinking). Research has shown that after two experiences with KJS, over 90% of students switch to KJS. It takes a couple of experiences for them to see and believe that they do better taking responsibility for what they know and can do than just marking a test and hoping for good luck. They then change study habits from memorizing random bits of non-sense (to hopefully match on a RCS test) to making sense of each assignment so they can now correctly answer questions they have not seen before.
• Winsteps, the software many states have used on NCLB testing, contains a Partial Credit Model (PCM) analysis feature. Using item response theory (IRT), it produces the same scoring as classical test theory (CTT) in PUP. It calculates the unexpectedness of each student mark. PUP now colors the student and test performance charts using the unexpectedness values from Winsteps.
• Amplifire by Knowledge Factor contains the most powerful implementation of independent quantity and quality scoring. Instead of mixing quantity and quality, half and half, for a test score (as is done in PUP and Winsteps), Confidence Based Learning (the forerunner incorporated into Amplifire) mixed three parts quality with one part quantity (knowledge). This is justified in high-risk occupations and in rigorous academic training (mastery). Amplifier, a patented instructional system, includes fast response coaching in such a timely manner that the seemingly impossible standard set by the high quality requirement can be met in a reasonable amount of time.

Today there is no reason to continue using traditional RMS multiple-choice tests when the average score falls below 75% and the cut score is below 60%. Below these points, the tests tell us nothing useful about student performance (other than a questionable rank on the test). From the same test, same preparation, same scanning, we can also get what each student actually knows and how well that knowledge or skill is used.

We get an insight into the level of thinking being used (teaching and learning) in the classroom. We get a student view of the test as well as teacher and test maker views. Misconceptions are distinguished from difficult questions. We get an insight into the development of the student, what levels of thinking are friendly and useful; and which students are taking charge of learning and reporting (highly teachable, meaning makers); and which students are still waiting for the teacher to teach, to test, and to tell them how many right marks they got gambling on a traditional RCS test.

All of the above test benefits are also available at the state department of education level. One of the difficulties of holding students, teachers, schools, and state departments of education accountable (see prior post) has been the use of a ranking system that has had little to do with what students actually knew or could do at the cut score. The cut score was often selected for political reasons. A valid 90% passing at a mastery level was as unsettling, as 24% passing because the scoring was too low, or 90% passing because the cut score was set too low. The additional information from independent quantity and quality scored testing reduces this problem.

The only change in standardized testing required is to offer Knowledge and Judgment Scoring, or PCM scoring, and RCS on the same test. My experience has been that this eliminates the politics of implementing a different scoring method. It is also crucial to allow students the freedom to make the choice that fits their development. This freedom is consistent with taking responsibility for selecting questions to mark when opting for Knowledge and Judgment Scoring or PCM scoring.