Blog #5

Differentiate instruction by offering various levels of challenge or alternative approaches for students with different learning needs.  Differentiating instruction requires that all students’ educational needs are taken into consideration.  This may include level of mathematical skill, but can also include how students learn most effective, students’ attitudes toward math, and other factors.  Students with weaker skills need opportunities to strengthen those skills.  This may require getting creative about how you might meet some of those needs.  Students with more advanced skills need to be challenged just beyond their current ability and encouraged to think about math in new and different ways.  Regardless of their skill level, students need choices that help them to learn in the most effective manner possible.  It is a tall order, and as an already busy and overwhelmed teacher, it is a daunting task.  How can you meet EVERYONE’S needs EVERY DAY with EVERY LESSON???  The truth is…you can’t.  But you CAN offer DIFFERENT opportunities and approaches on DIFFERENT days that will help students with DIFFERENT needs feel seen and supported.  Here are a few approaches I have used in my teaching that “mixes it up” a little for students.

Practice/Homework Alternatives

• If you have students who have difficulty writing, have poor writing, or just prefer the computer to paper and pencil, try assigning practice problems on an online format.  My favorite is Deltamath.com.  If is a free platform with paid upgrades, but even the free version is great!  You can sort the available problems by course or by standards within a course.  You can choose the problems that you want, how many of that type you want, how many students must get correct to move on, and how many tries they get.  Problems are a mix of multiple choice and free response, and it is easy to see student results when you set up a class.  You may find that you like this so much that you decide to assign practice to everyone this way.  You can also create assessments that provide all the students in one class with different versions of the same types of questions.  You can toggle on/off whether explanations are available to help a student while working a problem.  If you upgrade to the Plus level, there are also video explanations available (if you choose) for nearly all problems.  At the end of each problem, there is also an explanation so that if the student missed it, they can learn from their mistake and try another problem.  Students get instant feedback (again, if you set it that way) and teachers get great analytics to see where mistakes are being made.  I am a big fan of this website!!  (Here is a link to an overview on YouTube if you are interested.)

• If you have students who are all over the place when it comes to completion of practice problems, you could set up assigned problems into must/should/can sections.  Assign MUST problems that are the bare minimum that you expect students to do.  This makes the time commitment for students who take longer or are struggling to work out problems more reasonable and less overwhelming.  This also gives students who may have home lives that don’t allow for a lot of homework time a reasonable amount to complete.  Encourage students to also complete the SHOULD problems.  These may be a slightly higher level of thinking, or may look at the math skill from a different perspective.  The MUST and the SHOULD problems together are what a “normal” practice/homework assignment would be.  Then you can add a few CAN problems.  These are the critical thinking problems that you challenge students to see if they can do it.  Those students with more advanced skills will likely want to figure them out.  Those with on-pace skills will probably give them a try, but may not persevere.  And those with weaker skills can be aware that these are not problems they need to worry about.  Explain to students that if they are shooting for a HIGH grade in the unit, whey should consistently be completing the MUST and the SHOULD problems.  But if they are solid with the MUST problems, they can still pass the assessment.  (Then make sure the assessment and the assigned problems are aligned to reflect that statement.)

Mathematical Modelling

I wrote about mathematical modelling in my first blog on August 7, so I won’t go into great detail here.  But I do want to mention it again because a modelling problem that is well designed offers multiple entry points for multiple different students at multiple different abilities.  It is collaborative, so weaker students can learn from the more advanced students, but the weaker students can still contribute ideas because the problem is about something familiar to them.  Students will be more likely to truly work together if they feel everyone can and should have something to contribute to the success of the group.

Guided Notes

Two years ago our school was training teachers how to better serve our EAL students in our classes.  One strategy that I felt made sense for me in my math class was to provide guided notes pages for the lessons.  I created them from one of the worksheets provided with our textbook, then edited them to fit our needs.  This gave me a starting place with images already included and made it much easier to create the guided notes than starting from scratch.  I also included practice problems (often copied and pasted from exercise worksheets provided with our textbook) so that students had the notes and examples to refer back to when they did the practice.  I handed out paper copies to all of my students for each lesson, but I also provided a pdf on our Learning Management System so that those who preferred using their tablets could download the pages.  I found that it helped my EAL students be able to manage all of the mathematical language being used and to focus on what was really important in the lesson.  I also found that it helped my distractable students because if they wondered off for a moment, it was easier for them to see where we were in the notes and get back on track.  One caution to doing this, however, is that the more advanced students think they know everything already and want to work ahead of you and not really pay attention.  You will need to make your expectations about that very clear and then have a few strategies for holding them accountable (walking around the room, asking different students to answer questions or show how they did an example, etc.)  To see an example of how I edited a worksheet into Guided Notes for a Geometry lesson on Trigonometry, click here.

Movement

Students sitting in seats while a teacher lectures has its place in a math classroom (in my opinion), but NOT ALL PERIOD EVERY PERIOD!!  Students get restless.  They start to hate the sound of my voice, even I start to hate the sound of my voice.  I love to combat this with getting students up and moving.  Sometimes it as simple as instructing them after trying a problem to go find someone not sitting beside/near them to compare their answers.  They are given a chance to get up out of their seat for a few minutes and THEY get to do the talking.  Other times I use more elaborate games or activities to get students moving.  One of my favorite activities is a Scavenger Hunt.  In a Scavenger Hunt, papers are posted around the room with an answer on the top half of the paper and a problem on the bottom half, but the answer and the problem do not go together.  There is also a letter in the upper left hand corner.  A student may start at any paper.  They write down the letter and work out the problem on the bottom half.  When they think they have an answer, they search for that answer on the top half of any other piece of paper.  When they find it, they move to that paper next, write the letter, and do the problem on the bottom half.  This continues until they have solved all of the problems and the last problem they solve takes them to the answer on the paper where they started.  If at any point they cannot find their answer, or if they end up back at the first paper before solving all of the problems, they know they have made a mistake somewhere.  I usually provide a page where they can record letters and work out problems to help them stay a bit more organized.  The students love this activity because they get to walk around, they get to talk to classmates when they are stuck, and they get to have fun.  Scavenger Hunts usually lead to laughter and “arguing” and great math talk among the students, and all you have to do as a teacher is hang up the problems.  Use this link to find a Scavenger Hunt for Simplifying Trig Expressions and Solving Trig Equations in my TPT Store.

Challenge Problems/Brainteasers

If you read last week’s blog, I talked about problem solving and critical thinking and ways to get students thinking a little differently.  This is especially important for the more advanced math students in your class.  Because math has been easy for them most of their school life, they start to feel/act like they already know everything.  They usually grasp mathematical concepts easily and can perform computations very quickly.  But ask them to think about math more deeply, from a different perspective, or in an application context, and they often struggle.  Since they are not used to struggling, they can give up easily because they don’t like the uncomfortable feeling of not getting a quick answer.  Therefore, it is important that we also look for ways to differentiate for those with advanced math skills.  They need opportunities to struggle and persevere and prevail with tough problems so that they will become more resilient.  An easy way to do that is to post a challenge problem/brainteaser of the week or month.  Something that makes students stretch their understanding of math.  Something that quick students can work on when they have extra time.  And maybe something that earns some sort of reward or recognition for solving the problem.

Again, I am not suggesting that you try to do all of these every day, but most of the ideas above are relatively easy to put together and can be integrated periodically.  Your students will feel that you are making an effort to help ALL of them grow by providing different approaches.  They may find something that works great for them on one day, and that may help them persevere more on another day when the approach doesn’t fit them as well.  Or better yet, they may pick up a strategy that worked on the one day and use the strategy independently on another day.  Doing whatever you can, within the time and headspace you have, WILL make a difference for how your students are able to learn math.  Your students will appreciate your efforts!