What makes mathematics exam questions difficult

I think I can sympathize in that I made the similar mistake of writing "interesting" i. That simply never works. My rule of thumb now is that each test question needs to be completely transparent to me on first sight.

Writing the answer sheet should take at most one-quarter of the time available to students. If I look at a problem and think that it's "interesting", then that's a red flag that it needs to be cut from the test. If you're new to teaching or just unsure of what direction to go in , then I recommend reading Steven G. Keep the course learning goals in mind.

Your exam questions should be a chance for your students to demonstrate competency. If you ask me how many there are for a general n letters, I don't have the slightest idea, and honestly, when you think about it, it's indeed extremely difficult. Part of the problem is the "extra spice" you're giving them during the test. Why are you surprising them with extra spice for the first time during the test? That's literally the worst possible time to introduce new material!

This suggests a standard blocking vs interleaving illusion. Many textbooks are organized by concept and procedures rather than by difficulty, so students:. Students and teachers conclude "Holy cow, look at all these right answers, this is amazing, we're really getting it! How much should each person get?

The students used section titles of textbook to select the operation correctly instead of the meaning of the word problems. This is an illusion of understanding. When those section titles are not there on the exam, those non-meaningful habits continue and students are forced to guess somewhat randomly, which, of course, is terrible in a math class. Try interleaving! It drastically reduces speed and accuracy in the short run but forces meaningful thinking and retention in the longer run, and effect sizes are huge.

Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Students understand during course but can't solve exam Ask Question. Asked 3 years, 1 month ago.

Active 3 years, 1 month ago. Viewed 2k times. Improve this question. Another comment is that I think exam questions should usually be easier than the homework questions, so whatever twist is added on the exams probably shouldn't increase the difficulty as compared to the homework.

No matter where you are in your math studies , you can excel if you backtrack far enough to reinforce your foundation. You must fill in the holes with a deep understanding of the basic concepts you encountered in middle school math. No matter where you start and where you struggle, you must make sure you acknowledge any weak spots in your foundation and fill the holes with practice and understanding!

Actively scan device characteristics for identification. Use precise geolocation data. Select personalised content. Create a personalised content profile. Measure ad performance. Select basic ads. Create a personalised ads profile. Select personalised ads. Apply market research to generate audience insights. Measure content performance. Develop and improve products. List of Partners vendors. Once you've got a good idea of your current level and percentile ranking, you can set milestones and goals for your ultimate SAT Math score.

If you're currently scoring in the or the range on SAT Math, your best bet is first to check out our guide to improving your math score to be consistently at or over a before you start in trying to tackle the most difficult math problems on the test.

If, however, you're already scoring above a on the Math section and want to test your mettle for the real SAT, then definitely proceed to the rest of this guide. If you're aiming for perfect or close to , then you'll need to know what the most difficult SAT math questions look like and how to solve them.

And luckily, that's exactly what we'll do. WARNING: Since there are a limited number of official SAT practice tests , you may want to wait to read this article until you've attempted all or most of the first four official practice tests since most of the questions below were taken from those tests.

If you're worried about spoiling those tests, stop reading this guide now; come back and read it when you've completed them. Now that you're sure you should be attempting these questions, let's dive right in! We've curated 15 of the most difficult SAT Math questions for you to try below, along with walkthroughs of how to get the answer if you're stumped.

Based on the equation, which of the following must be true? Therefore, statement I is true. The other option which is longer and more tedious is to attempt to plug in all of the answer choices for a and see which answer choice makes both sides of the equation equal. Again, this is the longer option, and I do not recommend it for the actual SAT as it will waste too much time. This equals. According to the Pythagorean theorem,. From the side lengths of triangle ABC,.

The incomplete table above summarizes the number of left-handed students and right-handed students by gender for the eighth grade students at Keisel Middle School. There are 5 times as many right-handed female students as there are left-handed female students, and there are 9 times as many right-handed male students as there are left-handed male students. Note: Assume that none of the eighth-grade students are both right-handed and left-handed.

Since the total number of left-handed students is 18 and the total number of right-handed students is , the system of equations below must be true:. This relationship is known as Little's law. The owner of the Good Deals Store estimates that during business hours, an average of 3 shoppers per minute enter the store and that each of them stays an average of 15 minutes.

The store owner uses Little's law to estimate that there are 45 shoppers in the store at any time. Little's law can be applied to any part of the store, such as a particular department or the checkout lines. The store owner determines that, during business hours, approximately 84 shoppers per hour make a purchase and each of these shoppers spend an average of 5 minutes in the checkout line.

At any time during business hours, about how many shoppers, on average, are waiting in the checkout line to make a purchase at the Good Deals Store? Since 84 shoppers per hour make a purchase, 84 shoppers per hour enter the checkout line.

The owner of the Good Deals Store opens a new store across town. For the new store, the owner estimates that, during business hours, an average of 90 shoppers per hour enter the store and each of them stays an average of 12 minutes. The average number of shoppers in the new store at any time is what percent less than the average number of shoppers in the original store at any time? Note: Ignore the percent symbol when entering your answer.

For example, if the answer is In the question, it states that, in the new store, the manager estimates that an average of 90 shoppers per hour 60 minutes enter the store, which is equivalent to 1.

Typing can give students with learning difficulties the confidence and skills they need to be successful! Maria used to type with two-fingers, slowly and often inaccurately. Now she types faster, with fewer errors, more competently and professionally. This has boosted her confidence in the workplace tremendously. She now recognises individual sounds in words much better, due to the auditory aspect of the multi-sensory approach in TTRS.

Her vocabulary has noticeably improved and she has found she can explain things and express herself more clearly in English after completing the course. At Bolton College we offer the TTRS course to self-study adult learners who have returned to education to improve their spelling, increase their familiarity with technology, and use word processors. In contrast, Touch-type Read and Spell provides a rewarding and positive experience for them when it comes to spelling.

How we think about math matters Math is one of those subjects that is poorly understood by both children and adults. Who struggles with math? Learners with math anxiety Research has shown that math is a subject in which success is highly affected by psychological factors, including anxiety. Children with dyscalculia Learners with dyscalculia have trouble doing basic arithmetic and may struggle to learn math facts.

Students with dyslexia Dyslexia is a different way of processing in the brain which can make it more likely that students flip number and letter shapes , reverse numbers, or mix up their order. Individuals with dyspraxia Dyspraxia can impact on the fine motor skills needed to hold a pen or pencil.

They can also struggle with the sequence of steps and correct order of operations in math. Learners with dysgraphia One of the most important parts of doing a math problem is being able to put your thinking down on paper. Individuals with visual processing disorders Learners with visual processing disorders may have difficulty with math problems that involve spatial reasoning, including geometry, reading tables, reading maps and both discriminating and identifying different numbers.

How teachers can make the math classroom more inclusive Make math relevant. Teach in a multi-sensory way. Drill vocabulary in advance. Learn more Assign note-taking buddies. Allow access to accommodations. Give students more time. A quick re-cap: Students with dyscalculia, dyslexia, dyspraxia, attention difficulties, dysgraphia, visual processing difficulties and anxiety can struggle with math. About the Author. Meredith Cicerchia is a teaching affiliate at the University of Nottingham, an education consultant, and a freelance writer who covers topics ranging from speech and language difficulties and specific learning differences, to strategies for teaching English as a second and additional language.

Reviewed by. Chris Freeman has a BA cum laude in Sociology, and has undertaken post grad work in education and educational technology. Read and Spell Blog Students struggling with math Estimated reading time:. Testimonials and reviews.