Dear Aunt Sally vs Common Core math test, 5.2

PEMDAS is an acronym that is taught in school classrooms across the nation. It helps students remember the priority, or Order of Operations, used to solve expressions involving strings of numbers and operators. It stands for: P(arenthesis) E(xponent) M(ultiplication) D(ivision) A(ddition) S(ubtraction) A familiar mnemonic widely used in place of PEMDAS is: Please Excuse My Dear Aunt Sally. Thus the name of this application... Kind of an inside joke for the mathematical types. Computers, including smart phone calculators, desktops, etc. have built in functionality to properly interpret such expressions so we don't have to. But have you ever wondered what algorithms the CPU executes to get the right answer every time? This app demonstrates one such algorithm called the Shunt Yard, developed a few years back by Professor Edsger W. Dijkstra. We’re going to take a closer look under the hood at Order of Operations algorithms. It will interest programmers and school students alike; for programmers, the use of queues and stacks will reinforce previous computer science learning; for students, it allows them to write an expression, then analyze it using Order of Operations rules, step by step. The Quiz mode generates random expressions of user selected lengths and magnitudes and checks the student's answer. Incorrect answers can be examined using the same step by step process. In the SOLVE mode, algebraic expressions are entered free hand using an internal keyboard which limits entries to the five common mathematical operators (+ - / * ^) as well as one level of parenthesis. There is a maximum term limit of ten variables, but no limit to their magnitude in this mode. In the QUIZ mode, between two and ten variables can be selected, their maximum value and which operators that are eligible. The program then randomly generates an algebraic expression using these parameters. Both modes make available an analysis page which is used to step through the solution. Stack/Queue dynamics are displayed.

The Common Core math tests can be a source of anxiety for students because there is pressure to pass them and it is a very unusual test compared with tests they often take. Unlike tests students often take, the Common Core tests are typically done on a computer and the type of test questions often require multiple steps and a deeper understanding of math. This app has four full-length (30 questions each) math tests that are modeled on actual Common Core test questions that have been published by State Departments of Education. But it does more than just get students used to taking a test on a computer: it aims to fill in skill gaps and teach them how to answer similar questions on the real test. After the student answers a question, s/he is given immediate feedback as to what the correct answer is and is then given access to read a 1 to 4 page detailed, colorful explanation that assumes minimum prior knowledge of the key concepts. Each question is tracked as being correct, incorrect or unanswered by changing the button’s color so the student may ensure s/he completes the test and can review difficult questions again. If the educator wishes, the student’s results can be printed showing her/his name, date, time, the test version, the concept for each question and whether the student answered it correctly, incorrectly or did not answer it. Such a report may be helpful when generating an individualized lesson plan, and to monitor progress if subsequent test versions are used. This is the second set of tests for the 5th grade, which is why the icon shows 5.2 in the calculator display. Some students may find taking just one test reassures them of their skills and they may not need to take additional tests. Other students may have difficulty with one or more questions and can then repeat those questions or entire tests to help fill in skill gaps and build their confidence for the actual State exams. When the student returns to the main menu, all the answers are reset to unanswered. That way, the test may be administered to different students or even to the same student(s) after a prolonged break. If the adult permits, the student may turn on an option to get a quick break in the form of fun photos from nature if a questions explanation is short. This may also encourage the student to check the explanations for all questions just to see if there is a fun photo there, and hopefully read the full explanations too. After each correct answer the student gets lots of smiling emojis and, if the adult permits, at the end of the test a celebration screen with animated balloons and music. The app does not connect to any websites so it can be used off-line. There are no in-app purchases, subscriptions or 3rd party advertisements. The app is fully functional and never expires. The app does not collect or send us any info and when turned off it does not save any data. This is one of many products we've made that we hope will make learning fun.