What To Think About When Creating Any Assignment.

Yesterday, I discussed some general points to think about when creating an assignment but today I’ll be exploring parts of the assignment in more detail. When looking at creating an assignment, it is important to think about what the assignment being anything that is assigned to students from the warm-up to the exit ticket and everything in between including the actual assignment focused on learning the content.

  

First one needs to look at the type of assignment being given.  Is it a short task of under 15 minutes such as bell ringer, journal entry, or the exit ticket or is it a task spread out over two days or is it a project that takes longer than two days such as a performance task.  Does the assignment focus on content standards associated with the grade level or does it use standards from other grades.  Does the assignment include any mathematical practices.  Are the directions clear and easily interpreted by the student.  

Next, does the assignment require high levels of cognitive thinking of the students.   If the assignment does not require higher levels of cognitive thinking, look at how you can change  or adjust it so it demands more.  This includes warm-ups, journal entries, and exit tickets.

Think about the rigor involved in the assignment.  Does it allow students to develop mathematical understanding of the skills and processes as well as concepts.  Does it provide opportunities for developing an authentic understanding of math via the use of multiple representations. It is important to use multiple representations of the material because that makes it better for students to learn the material.

Does the assignment help students learn to discuss topics mathematically?  Does it ask students to provide a response to an argument, justify a response, or explain their thinking to others while using the language of mathematics.  Did the assignment include opportunities for whole class discussion, small group conversations, or talking between peers. It is important for students to develop the ability to converse mathematically.

Does the assignment help students bridge their understanding from unknown to known and does it make the math feel relevant to students even if the material feels foreign.  Does the assignment provide choices for students so as to support their autonomy.  In math the choices could be in which problems they can do or the method of doing the problems such as flipgrid, or a video.  

Finally, is there scaffolding included in the assignment and what type is it.  Is there scaffolding written in for a part of the assignment or for the whole assignment?  If only a part of the assignment, what is the scaffolding and why is it used only for that part.  Is the scaffolding done via a graphic organizer? Is the material broken down into small chunks?  Does the student have a list of steps to follow?  

So when you are thinking about creating assignments, especially now after students having been out of school since the beginning of the fourth quarter, it is important to include scaffolding and to look at all of these items to create assignments so they are the best for students.

Creating Effective Assignments

 

I suspect the books you use in math are similar to the ones I have in that the teachers edition has recommended problems for basic, normal, or advanced.  The assignments are a bunch of different problems students are expected to complete and turn in.  The problems are always in order and coincide with all the examples.

Unfortunately, that is not the best way to assign problems especially if you want students to learn.  Today, I'm touching on a few changes to make the assignment better.

1.  Figure out what the objectives are that you want students to meet and decide how they will show they've met that objective.  To do that, begin with rewriting the learning objective as "I want my students to be able to: ____________".  In addition, use active verbs when writing the objective such as compare similarities or discuss differences, or explain the steps necessary to solve this type of problem.

2.  Try to make the assignment more interactive and interesting than just straight problems.  See if there is a way of designing the assignment to make it creative and challenging while motivating students at the same time.  Think about how you can change the assignment up so it is no longer the "do every third problem".  Perhaps you can change it to "Write a letter to a friend explaining how to do the problem because they were sick that day" or "Create a video showing how to check your work for this type of problem."

3. If the assignment does include problems from the book, make sure the problems are not in the same order as in the book.  Instead of assigning "Every third problem", maybe do 2, 10, 22, 4, 12, 24 so the problems are mixed up.  This helps students learn the math better.

4.Once you've created the assignment, go back and make sure the assignment still meets the learning objectives.  If the learning objective requires students to compare and contrast two things and you only have the comparison in the assignment, you'll need to go back to include the contrast part. 

5.  Think about how to order assignments so skills are built in the proper order. You want students to build the necessary skills incrementally and make sure students see the connection between what they already know and what they are learning. If you plan to end the semester with some sort of project, make sure the smaller assignments build all the skills they need to complete the project.  

6.  Determine the frequency of assignments and how often they need to be turned in. Will students complete an assignment for each section or for two or three sections with a few problems from each section.  Normally, I'd recommend  having a calendar of assignments and due dates completed prior to the beginning of the semester but with the coronavirus, that might not be as easy to do.

7.  Think about the ability of students to get the assignments done.  Will they have enough time or so they struggle and need additional time?  This is important when creating assignments because more is not always best.  Do students really need to complete 20 problems for every section or will 10 be enough especially if you ask them to discuss how to do it or talk about issues they had working the assignment.

This is just an overall look at creating good assignments but on Wednesday, I'll be looking at questions one needs to answer in more detail when creating an effective assignment.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

One of the largest cakes ever made in the world has a diameter of five feet across and weighs 50 stone.  If one stone equals 14 pounds, how many pounds did the cake weigh?

Warm-up

The World's largest pizza is 122 feet 8 inches in diameter and weighed 26,883 pounds.  How many pounds is that per inch?

Using Multiple Choice Questions In Class

 

Personally, I don't like using multiple choice questions in class but many standardized tests such as ACT or SAT use them and most of my students struggle with this type of question.  On many of the standardized tests given by the state have the right answer, two wrong answers that students will come up with if they don't take the problem to it's natural conclusion or only get half done and one that is totally wrong. 

Even though I don't like giving this type of test, it is important that students learn to take them and not just guess.  In my textbook, the pre-tests for each chapter are multiple choice along with certain questions in the problems for each section.  Many students need to be taught how to take multiple choice tests effectively.

There are strategies to help students when taking multiple choice questions.  First, students should cover up the potential answers without even looking at them before they read the problem because they need to know exactly what the problem is asking.  If they cover the answers, they do not get distracted and they can reread the question multiple times to understand it. 

In fact, it is recommended that students rephrase the question to themselves, before trying to answer it in their mind first. If the problem requires calculations or simplification, students should try to answer the question before they look at the answers otherwise, many students tend to guess rather than trying to do the problem.  If the problem requires them to find an equivalent equation or find a fraction closest to a number, they should still cover the answers to they are focused only on the question before going through each answer slowly to see if the answer goes with the question.

Secondly, have students highlight key words, especially words like always, never, sometimes, not and others that place limits on the situation.  The question might ask you to find the probability of not drawing a red or green ball, rather than asking for the probability of drawing a certain colored ball.  Many students miss the qualifiers if they don't highlight certain key words.

Next, after reading the question and highlighting key information, students should read through the answers to eliminate any that are obviously wrong.  If a student does not see any that are obviously wrong, then there is another technique to use.  If the answer required is an actual number, one can substitute the answers back into the original equation to see which one makes the whole problem correct.  I've used this last one myself on multiple choice questions.

One person analyzed over 2400 questions from 100 different tests to determine the four strategies to help increase a person's chances of getting multiple choice questions correct when they don't know an answer.  First, if you have see "None of the above" or "All of the above",  one of these is likely to be the correct answer over half the time.  Secondly, two questions in a row seldom have the same answer.  For instance if you don't know the answer to question 2 but know the answer to question 1 is a and the answer to question 3 is d, then chances are question 2 will not be either a or d.  Next, the correct answer is more often than not the longest answer because the people who write the test want to make sure the correct answer is definitely correct.  They are not going to take as much care with an answer that is wrong.  Finally, eliminate any questions that are out there.  Often, on math tests, people can eliminate answers that are too small or too large just by using estimation.  

I also tell students to keep an eye on the time if the test is timed.  Always do the questions you know how to do first, followed by those you sort of know, and leave the ones for last that you have no idea how to do.  You can do this for some computer tests but not for all and it works well for paper based tests.  I advise students to spend no more than two minutes if they get stuck on a question otherwise they'll get frustrated and not be able to complete the test.  I also include some practice questions with their homework.  Let me know what you think, I'd love to hear.  Have a great day.

Always, Sometimes, Never?

I've occasionally seen and used always, sometimes, and never statements but I've never made a practice of it because I've not been sure what they accomplish.  As stated earlier, for the first few weeks of school, I have to send work home for part or all of the week and after reading up on these, I think they will be a good addition to the packet. 

If you've never seen or done one of these activities, they are fairly simple.  Students are giving between two and five statements to look at.  They have to decide if the statement is always true, sometimes true or never true.

When teaching mathematics, statements are made which are only true in certain contexts and usually the context is what is being taught.  This activity allows students to think critically about math to determine when things apply or don't apply.  Furthermore, it promotes mathematical reasoning and introduces the idea of counter examples to prove something isn't always true.  

It is important to have students provide counter examples for sometimes statements because it helps students see the context of when it is true or false and requires deeper delving into the statement as they think about it. Determining if the statement is always true, sometimes true, or never true requires higher level critical thinking skills rather.  In addition, this activity helps  identify misconceptions in student understanding.  

The always, sometimes, never activity also promotes dialog and communications because students are required to explain why the statement is always true, sometimes true, or never true.  It is a good activity to help students learn to "Justify their answer" which is often seen on tests.

Overall, always, sometimes and never activities are considered low floor with a high ceiling because students who have low mathematical reasoning skills can still participate by substituting numbers to see if it seems to always be true or find a counterexample.  It is high ceiling because students have to justify their conclusions. Furthermore, always, sometimes, and never is also a way to introduce logic statements to students without using straight mathematical language and theorems.  

Always, sometimes, and never also helps students develop perseverance as they look for examples or counter examples.  They build arguments while evaluating their logic and the logic of their peers arguments. It also has students engaging in authentic mathematical thinking.

When doing this with students, they often will try one number to see if it works but they will need to be guided into trying several possibilities such as zero, fractions, or negative numbers and not to just accept the first possibility.  Take the statement "Any number added to five gives a number larger than five" which on the surface seems to be true because people automatically assume one or above which makes this true but if you add a negative number to it, the answer will be less thus making the statement, sometimes true.

So if you want a way to help student develop mathematical thinking, this is a good way to do it.  Let me know what you think, I'd love to hear.  Have a great day.

Taking Notes From The Textbook.

Many schools are starting this virtually this fall complete with distance lectures and reading assignments.  Some students have the idea that one does not need to take notes because the material is all there but that is not quite true.  When students take notes, it can improve their reading comprehension, and helps them retain information.  

Currently, research indicates when students use pen and paper to take notes, they are better able to retain information when compared to using digital apps such as Evernote.  

Furthermore, when taking notes by hand, it means a person does not have to toggle back and forth between the class and pages or other note taking app.  One can also watch videos or streaming lectures while jotting notes down.  When students first learn to take notes, they try to take down everything they can. I know in college, I'd try to write everything down but I'd go over notes later to make them neater and to make more sense.

One should not try to write down everything because it can lead to information overload, which limits the amount of material a student is able to recall later.  Since most classes require reading, it is important to jot down notes while reading and don't be afraid to draw pictures or diagrams.

I want to focus on teaching students to take notes from their textbooks during the time they work at home since I won't have as much time available during class.  In math, taking notes is a bit different than for English or History and most of my students do not have those skills yet.  In addition, reading and taking notes from a math textbook should be done when the student is alert. 

It is recommended students write down definitions, key concepts, and theorems in their own words rather than copying them down verbatim.  If they find terms they don't understand, they should look it up and make notes.  When writing down definitions, they need to include examples of things that meet the definition and those that don't. As for theorems, students need to read those carefully and determine why they apply in various situations.  

When the student comes to the example or application of the theorem, they need to look carefully at them, working on understanding each step in the process, and once they've finished, they should try working the example or application of theorem without using the book or notes. In addition, as students work through examples, check the end of the chapter to which ones are like the ones just done and try those.  If there is something students don'e understand, they should ask the teacher.

Furthermore, students need to read the text slowly because mathematical texts are extremely information dense and they need to pay attention to understand everything.  Students need to be prepared to read and reread the material sentence by sentence, paragraph by paragraph to comprehend the written word.  Take time to analyze all the diagrams and pictures.  When looking at a picture, students need to identify how it relates the the topic.  

This is important to help students learn to take notes from the textbook.  For the first couple weeks, I have to send work home, I am going to include a partially started set of notes students can copy into their composition books and finish on their own.  This is the only way, I'm going to teach them to take notes when reading.  Let me know what you think, I'd love to hear.  Have a great day.