Happy Memorial Day

 

Warm-up

 If it takes 3 oranges to make one cup of juice, how many quarts of juice will you get from 305 oranges?

Warm-up

 If you get 305 oranges from a tree in one year, how many oranges will the tree produce after 20 years?

How Effective Is Computer Based Instruction?

 Last semester, I put my students on a computer based program as a way of helping scaffold their foundational knowledge.  I'd say about a third of the students worked hard, attempting to learn.  Another third did some but did it since it was assigned but they didn't make much progress, and the last third spent more time trying to play games when I was not near them so they never actually did any of the assignment.   I know that we've had to rely on computers so much more since COVID hit, that I wondered if computer based instruction is as effective as we think. 

I came across a paper which looked at the effectiveness of using computer based remediation in two and four year colleges.  The premise is that students do most of their learning via the computer and the instructor is a facilitator rather than the primary instructor. The study was done to determine if technology centered instruction works well for students who are underprepared for college, academically.

In general, students are tested when they enter college and if their skills are not good enough, they are enrolled in developmental classes designed to help them bridge their gaps and get the skills they need to pass the college level classes.  Research indicates that only half the students who enrolled in this type of class actually finished it, and those who do not finish the classes are less likely to complete the degree requirements.

The use of technology driven instruction can be both good and bad. A positive effect is that the instruction is consistent across all classes allowing for a more even levels of preparation for higher classes. Another advantage, is that time is freed up so faculty can spend more time providing individualized rather than whole class time instruction. This means they receive more assistance when they need it, rather than having to wait for office hours or lab time. In addition, there is a clear time line for assignments, quizzes, and gives the instructors a chance to mentor student mastery of the material.

On the other hand, not all students do well learning on computer based programs and have the self motivation to work their way through the material without getting bored. These programs are designed with the expectation that students have the ability to regulate their time so they work through the program at the appropriate pace to finish the material.  It also assumes students will not be distracted by the possibility of surfing the web, checking mail, etc.

Furthermore, it also assumes students will actually work the problems rather than guessing their way through the answers until they hit the right one which raises questions of potential mastery and engagement in learning.

The conclusion to the study indicates that taking a computer based class did not improve the number of students who passed their remedial math class.  In fact, the number of students who went on to pass their first college based math class actually decreased and they were less likely to complete fewer credits over a period of six terms. Furthermore, they were less likely to get an associate degree or finish any credential within a 6 year period.

One suggestion for why students didn't do well in their first college level math class is simply due to the class having an actual instructor rather than letting student progress at their own rate on the computer.  Although these results are for college level, I think it is important to keep these results in mind since many high schools rely on computer based classes as a method for students to recover credit for classes they've failed.  Later next week, I'm hoping to look at programs that adapt as students work their way through the program.  Let me know what you think, I'd love to hear?

How Far Behind Are Students In General And What To Do About It?

 

I ran across information the other night in which someone shared the research on how far behind our students have fallen during the pandemic.  The article went beyond just reporting the results, it also suggested several research based ideas to help students catch up within one to two years.  It was wonderful seeing some real data and real solutions to this question which plagues every school district.

First off, the research focused mostly on elementary and middle school students rather than high school students.  We know that when children get behind in elementary school, they struggle for the rest of their time in school and they are more likely to drop out.  In addition, the data came from across the nation so it was not focused on just one state. The research compared the student achievement growth in the prepandemic period from 2017 to 2019 against the growth in the pandemic years of 2019 to 2021. The data came from the information collected by NWEA, the people who offer MAPS testing which is used in multiple districts across the nation.

Fortunately, it is known that the pandemic officially hit the United States in early 2020 and just about every school ended up going remote with methods ranging from the use of packets, television broadcasting, zoom, or what ever method the district could manage. Unfortunately, the results were quite discouraging.  In low poverty schools, students lost the equivalent of about 13 weeks of of unperson instruction while students in high poverty areas lost the equivalent of around 22 weeks or a little over a half a year.  

If you look at the results along racial lines, African American and Latino students lost four to five weeks more than caucasian students.  They also discovered the districts that returned to in person instruction sooner only lost between seven to ten weeks of learning. In other words, the longer schools stayed closed the wider the gap.

So what can schools do about it.  The following suggestions have been researched and shown they produce demonstrable results.  These are the best solutions we have at the moment.  It will require a bit extra spending and time but if any of them are implemented, students can make up their loses in one to three years.

One of the best recommendations is for students to implement is through high-dosage tutoring where a tutor meets three times a week with one to four students for the whole year.  This can result in up to weeks of instruction.  That is almost equal to the amount of time students have fallen behind in high poverty levels. 

Another suggestion is to place students in summer school where they work on missing skills.  This type of extra work can help students recover up to 5 weeks of instruction.  If that is not an option, add one extra period to the instructional day so students receive one extra period of instruction in math every single day for the full school year. This can result in a gain of 10 weeks of instructional gain.  The final suggestion is to lengthen the school year  just like most do to make up for unscheduled school days for the next two to three years.

Unfortunately, all of these require spending funds that districts may have earmarked for other things.  The last district I worked for had already earmarked all their COVID funds to help run the district for the next few years and none of it was earmarked for direct student instruction other than buying new books.  It seems to me that we need to spend the monies on these suggestions, especially the first one so we can help students catchup rather than enduing up with a lost generation of learners.  

The tutoring idea could be done by adding in an extra period, using peers, aids, janitors, kitchen staff, and parent volunteers to work with the students.  Yes, they would have to be trained but that can be done. The other, adding in one extra period a day of math so they get a double dose is doable, especially if they turn a six period day into seven periods.

We have the research, we have solutions, lets see if we can talk our districts into implementing them so our students get the best chance to get the future they deserve.  Let me know what you think, I'd love to hear.  Have a great day.

Why Use Multiple Ways To Solve Problems

 

One thing that is emphasized is to show students as many ways as possible to do something, but unfortunately, many teachers and textbooks tend to show only one way to do something rather than exposing students to multiple ways.  For instance, FOIL seems to be the main way students are taught to multiply binomials yet there are so many ways to do it.

I know when I was in school, teachers only taught one way to do any problem including only the FOIL method for multiplying binomials.  It's only since I began teaching that I've learned multiple other methods or rather how to use methods they already knew from earlier situations that could be applied to a situation.  Research indicates when we teach students to solve math problems in only one way, the method taught may not be the "best" way of doing other problems.  We need to focus on having students learn multiple methods so they can choose the method that works best for the situation and for them.

Teaching students multiple strategies to solve problems helps make them more flexible mathematical thinkers. This is because they have multiple methods to choose from to solve any problem and can select the one that works best for the situation rather than trying to figure out how to apply the one method to every single problem. 

In addition, when we teach students multiple strategies to solve problems, we are providing scaffolding so they find a place that has what they need. In addition to finding the strategy they can use, they are exposed to methods that may be beyond them at that point but which they may be ready for later on.  Furthermore, these strategies can be used as they go from one skill to another.  For instance, an elementary teacher taught me how to multiply using the lattice methods.  I saw it and realized I could use the same method with my high school students when they multiply binomials, or trinomials. Many of my students had this teacher in 5th or 6th grade so they knew the method and could easily use it. 

Furthermore, when students feel they can't do math, or don't like math, or don't have that math gene, they often are more willing to try doing problems when they've been taught multiple strategies. Teaching them multiple strategies allows all students to have an entry point  and a way of attacking problems at their level rather than feeling lost because they don't understand or can't do the method taught by the teacher. 

One thing that comes up again and again in research is to teach students how to visually represent the problem no matter what age or level of mathematics students are in. Another thing that show up is one thing that I have not always done.  Research indicates that in addition to teaching at least two ways to do every problem, the teacher should take time to compare and contrast the two methods because it helps build analytical thinking.  I've never done the compare and contrast part and need to start doing that.  It has been found that students benefit when they are expected to use multiple methods to find solutions. 

Once students are used to using multiple methods, teachers can then take time to start looking at why one method might be better for solving certain problems for its easy and efficiency.  In addition, it is suggest that teachers show methods that look like they would work but don't and then take time to lead a discussion on why it happened this way.

Finally, it is important for the teacher to create a culture of problem solving by having discussions where students show the different ways they used to find the solution.  This reinforces the idea that there is not one way to solve a problem.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

 

If it takes four pounds of fresh grapes to make one pound of raisins, how many pounds of raisins will you get from 2548 pounds of freshly picked grapes?