Why Is It Important To Teach Long Division For Dividing Polynomials.

 

This is one of those topics I really hate teaching, especially right now because most students have difficulty doing regular long division.  This has become even more apparent due to COVID and I have so many students who cannot divide without a calculator.  Although there is a wonderful shorter method referred to as synthetic division but it only works in specific situations.  

What I've learned over the years is hat if a student struggles with regular long division, they struggle with polynomial long division due to the process being the same. So when teaching this topic, it may be necessary to backtrack all the way to regular long division.

There are many reasons for students to learn long division with polynomials.  First, since division is a fundamental operation, teaching them to divide polynomials is helping them to apply the algorithm to algebraic expressions. Understanding this is essential for higher mathematics classes such as calculus and Complete factorization is important for solving equations, finding roots, and simplifying expressions. 

Next, being able to divide polynomials by using long division is essential to  factoring polynomials because it is a systematic approach that can be used in multiple situations.  The long division algorithm provides a step by step method for dividing polynomials while reinforcing algorithmic thinking.  It also helps reinforce problem solving skills for the more complex problems.  

As far as problem solving goes, long division requires careful organization and attention to details. It encourages logical thinking,  The process has students analyze the problem, break it down into smaller steps, and apply the appropriate strategies to find the quotient and remainder.  These skills are transferable and can be used in other math courses and in real life.

It also provides a foundation for higher level mathematics. In addition, it is the foundation of other mathematical topics such as synthetic division.  Of course, students will ask "When are we going to use this?" Or "When is it used in real life."  This is fairly easy to answer. 

Polynomial long division is used in circuit analysis when they are analyzing electrical circuits with complex transfer points or calculating the stability of a system by diving the input by the output. Another place is in control systems to determine the stability of feedback systems. In economics, polynomial division to determine roots and critical point used to understand market equilibrium and economic behavior.  In data interpolation, one use is to determine missing points and values within a data set. Furthermore, it is used in error correction codes such as the Reed Solomon codes which help detect and correct data transmission or storage systems. 

Although students will argue why learn since there are calculators out there that will do it for them, it is still important for them to learn the process so they understand how it works.  Let me know what you think, I'd love to hear.  Have a great day.

Kirigami And Shape Shifting Materials.

 

Recently, people have applied the math behind Kirigami to shape shifting materials so that more can be done.  Kirigami is the Japanese art of paper folding and cutting to create cool three dimensional designs. Scientists have taken the concept of Kirigami and applied it to other areas such as shape shifting materials. 

 Now shape shifting materials are also known as smart materials or programmable materials. In other words, these materials can change their shape or properties as a direct response to external stimuli such as heat, electricity, light, or a mechanical force.The change these materials undergo is reversible and the transformations can be controlled so they can adapt to different forms or configurations.

When scientists combine Kirigami techniques with the shape shifting materials, so many possibilities open  for creating complex and adaptable shapes. With careful cutting and shaping of the shape shifting materials, it opens the way to designing objects that can change their shape, size, or functionality.  One use of Kirigami is to apply it to shape-memory polymers. These particular polymers are able to "remember" a specific shape and with an application of stimuli such as heat, are able to return to that shape. When Kirigami is combined with these shape-memory polymers, the result something that can undergo specific transformations.

On the other hand, kirigami can be used with meta materials which are engineered materials whose properties are not found in nature. certain structures are created.  These structures change their mechanical properties such as stiffness or flexibility by cutting or folding certain areas selectively. These are just two examples of how Kirigami is combined with shape shifting materials.

Now the question of how is this information used in real life.  It can be used in robotics, aerospace engineering, biomedical devices, flexible electronics, and other fields.  In robotics, this process creates a material that can be used to design adaptive and self reconfigurable robots who can change their shape so they can navigate in different environments. On the other hand, in the biomedical field, this technique can produce materials used in pacemakers that can adapt to the shape of the organs.

Combining Kirigami with shape shifting materials offer a future of new materials that can be used across a variety of multiple industries. This is a field that will continue developing due to its potential.  Let me know what you think, I'd love to hear.  Have a great day.

Skip Counting, Multiplication, And How To Get From One To Another.

 

As I have been doing more research on number lines, I realized that many of my students get to high school with the ability to skip count but didn't know their multiplication tables.  I've accepted that skip counting might be the only way they know but I've often wondered why they didn't make the jump from one to the other.

Skip counting is often the first thing students are taught in their journey into multiplication.  From there , they move on to learning multiplication and multiplication facts but some students never make the jump.

It is never too late to do things to help students make the jump from skip counting to multiplication.  These steps can be done in middle school or high school as part of the scaffolding activities. First, think about using visual representations such as number lines, counters, or arrays to help make students see how skip counting and multiplication is related since both are a form of repeated addition.

Another activity using counters, cubes, or blocks is to have students arrange these manipulatives to represent skip counting. So if a student is skip counting by three's, arrange the manipulatives in groups of three so they count by three's, then they can ease over to the idea of counting the number of groups to arrive at the total. Both ways get the student to the total but one is strictly addition and the other ways shows the idea of groups times number in group gives total.

Look at having students explore patterns and extensions associated with skip counting.  For instance, list the pattern for four's skip counting and leave blanks such as 4, 8, ____, 16, _____, etc.  Extend this to the idea that one 4 is 4, two 4's is eight, so three four's is 12 which is the missing number.  This helps students make the jump from skip counting to multiplication.

Throw in some questions which require students to use skip counting in a real life situation such as buying 5 packages of 12 screws so a student might do 12, 24, 36, 48, 60 or 5 x 12 is 60. This provides a real life connection between skip counting and multiplication.  

Finally, give students a chance to practice, practice practice.  Provide students the opportunity to play games, make posters, and other methods to give them a chance to practice. Start with easier problems and move to problems that are more complex.

These are just a few ways to help students move from skip counting to multiplication.  Once students have multiplication down, it is important to include continued practice.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

If there are 480 skittles in a one pond bag, how much does one skittle weigh? 

Warm-up.

 

If there were 108,000 new registrations of the French bulldog in 2022 and they were the most popular breed. The number two breed is the Labrador with 21,000 less. What percentage more bulldogs were registered than labs?

Combining Like Terms

 

Combining like terms is one of those topics that students either get or struggle with. The standard way to teach it is to have students identify like terms, rearrange the terms so like terms are next to each other, simplify by combining like terms, and the remaining terms constitute your answers.  Sounds quite straight forward by it doesn't always work that way.

It doesn't always work that easily because some students have difficulty understanding the concept of like terms.  One way to help students identify like terms is to have them use circles, squares, triangles, diamonds, and other shapes. They would circle all terms that are constants, terms with x's are inside a square and x^2 are inside triangles.  This way they students can rewrite the terms so those in the circles are next to each other, squares, next to each other, and triangles gathered together.  

Another way is to use either physical or digital sticky notes in different colors.  Each color represents a type of terms such as constants, x's, or x^2's so write each term on the appropriate color so that when it is time to rearrange the terms, students can put terms on the same color notes together to make it easier to distinguish among terms.  

Then there is using base 10 blocks with the individual squares representing ones, the 10's become the x's, and the 100's represent the x^2's, so 2x^2 + 3x + 4 would be represented by 2 - 100 squares, 3 - 10 strips, and 4 - individual squares.  Once they've translated the terms into the base 10 blocks, the student can physically see which terms are alike and it makes it easier for them to combine like terms.  

Once students have been instructed in the concept of combining like terms, it is time to include a variety of activities to reinforce and practice this.  One activity is to whip out a game of combining like terms bingo.  Prepare a variety of cards with answers and pass the cards out to the students.  The other possibility is to like the answers on the board, hand out blank bingo cards, and have the students fill out their cards with the answers they've chosen from the board.  Always have more answers than squares so that students will not have all the same answers.  To start the game, have a container full of problems and draw one out.  Write it on the board and have students come the like terms.  When they have the answer, they check their cards to see if they have the answer.  When they are beginning, I always go over the problems so struggling students can see how to do it.  As they gain skill, I no longer of it or only do it for problems where many students struggle.

When students are more proficient at combining like terms, it is time to enjoy either jeopardy or Kahoot games.  For Jeopardy games, I like having students work in pairs and write the answer on a whiteboard so all the students who get the right answer will receive a score otherwise students who take a bit longer do not feel penalized.  

This is also the perfect item for students to do a scavenger hunt activity.  On a piece of paper, write down a problem and an answer but not the answer to the problem on this paper.  Write the answer down to another  problem.  On the next sheet, record the problem to the answer on the other paper, and write down the answer to a different paper.  Continue till you have 10 to 15 papers completed and post around the room.  Give each student an answer sheet so they can start at any paper.  They work the problem, and then search for the answer.  Once they find the correct answer, they do the problem on that page and search for the matching answer.  Continue until each students has worked all the way through the problems.

These are some ways for students to practice combining like terms.  Let me now what you think, I'd love to hear.  Have a great day.

Need To Make A Decision, Use A Scoring System.

 

When it comes to making a decision, most people look at it as a yes or no proposition.  You do it or you don't do it but others look at a decision being a choice of several possibilities, much as businesses approach a decision. When the decision is difficult, we often list and rank our alternatives to determine which is better.

The process of using a scoring system involves identifying the outcome, determining the criteria, assigning a weight to each based on importance, developing the actual scoring system, evaluating, totaling the score, analyzing and making a decision.  Although this is the normal system used, it is sometimes flawed.

Often decisions come out of a limited number of choices. If the decision is based on one criteria such as cost, then it becomes much easier but if there are more possibilities, then it involves the pros and cons for each one. This means there is a multi-criteria choice involved.

Most of the weighted systems used to make the decision. This process requires the decision maker to eliminate those options which are a no go before ranking the remaining ones according to preference and assigned a score based on each criteria. The scores usually range from 1 to 5 or some similar ranking for each possibility, then multiplied by a weight, and the scores are totaled to find an overall score.  

Unfortunately, the weakness with this the when it comes to assigning the value because the value is based upon the human evaluation. The better approach. is to consider using a scoring system that contains negative numbers with an adjustment to keep the values between 0 and 10. The actual formula is 

                                    weighted score = (score – offset) × weight + scale_shift.

Offset refers to the midpoint of the score range and scale shift is the smallest number needed to make all values positive. Thus if the values are 0 to 10, then the offset and scale shifts are 5 and 50. 

This method still sees those that have the lowest numbers are not the best choice but what this alternate system does is that a low score does not immediately put it at a disadvantage whereas the normal system does. It was originally developed to use in engineering.

In the normal selection process, it is possible to get have several possibilities end up with a zero regardless of their importance and depending on whether they are along the left side or the bottom, determines whether they are zero regardless of importance or the choices are penalized against unimportant criteria.  In the alternative system, unimportant scores are neither good nor bad. 

This is just another way of looking at weighting choices. Although it originated in engineering, it is a methods that could easily be using in other places such as businesses.  Let me know what you think, I'd love to hear.  Have a great day.

Planning a trip.

 I am on my way home from spending the last week in Bulgaria. The idea of traveling provides the basis of a great project for the class. 

For this project students choose a place they would love to visit. They will need to research various airlines to find the best price. I know from personal experience that if you look at Iberian Air, they have prices that range quite a lot. Some prices represent their low cost airline while others are Iberia itself and the most expensive tend to be a codeshare with American Airlines. 

In addition, many of these overseas carriers offer three different air fares for economy, two for business class and may not have a first class. Other airlines such as Icelandic Air offer a free stop over for free. 

They will have to search for a hotel and this means deciding what type of hotel or hostel to stay in, it’s location, and will it offer breakfast, a shuttle, or even wi-fi. There are places in this world that do not offer wi-fi as part of the package. When I went to Fiji, I had to find a place that offered it in the rooms and didn’t charge extra for it. I use booking.com to look for a place to stay because I can put in things like free shuttle, breakfast, swimming pool, etc. 

If the hotel does not offer a shuttle, then one has to decide how they are going to get there. Will they take a taxi, bus, or train. I found if the hotel does not have a shuttle, it is usually cheaper to arrange for transportation before leaving on the trip. I usually do this either when I book my hotel or later through either viator or trip adviser. 

Then one needs to figure out what to do while visiting the place. Again, I like either viator or trip advisor when I look for things to do. I also look at Google map to see what things are available around my hotel that I might want to do. I look for museums, gardens, etc so I can plan short activities between the all day tours. I usually try to sign up for food tours so I can learn more about the local cuisine.

Once students have acquired all this info, it is time to have them put it together into a budget so they know what the complete cost will be. This gives them practice for the future when they are out of school and on their own. Let me know what you think, I’d love to hear.

Warmup

Create a word problem using the numbers 34, 192, and 1/2.

Warmup

 5.   7.   8.   2.    1

Use these digits and four operations to end up with 13

Visualizing Binomials

 As is well known, it is great if we can provide a way to visualize math concepts so students understand the topic better. Sometimes, it is more difficult to do this because algebra tends to be taught without providing ways to visualize concepts. I've looked for something to use but haven't had any luck in figuring it out so I had to come up with my own version.

So the way I do it is to begin with a base 10 manipulative. I talk about x being a set length as shown to the right.  So if we see X + 1, this says we are adding one unit to the length we started with. I tend to add the extra one in a different color as seen with the next one.

This is a physical way to show the adding one length. I also talk about this using a few numbers such as X represents 10 units and we just added one more to it.

On the other hand, when showing X - 2, start with the basic 10 strip, just like we did before. So instead of adding one, we take away two units. This shows a strip that is two units shorter than the original.

 

Unfortunately this doesn't translate well when it comes time to teach binomial multiplication, so the other way I show X - 2 is to do it like X + two negative values so it looks like this 

This just show that you have two small units that are negative but this one sets it up to slide into binomial multiplication visually.

To visually show binomial multiplication such as (X - 2) time (X + 1) I set it up this way.

I have the X - 2 along the top and the X+ 1 along the left side.  I didn't bother showing the X's in any color other than blue because they are both positive and I wanted the -2 and +1 part to stand out so students could see what was up.

So the next step is to show that X times X gives you X^2 or visual it shows a square with each side that is X units in length.  This allows the students to see where the X^2 term comes from.  

  The final two steps shows that the X times a negative gives a negative so X times - 2 gives you a -2x while the +1 times X results in a plus one X, easy to see.

Finally, the + 1 times -2 gives -2.  From here it is easy to show the parts of X^2 - 2x + 1x -2 or as we see when its all done, X^2 -x -2.  I like using this model for introducing binomial multiplication to my lower performing students because they can see the parts much better and do not have to remember the "FOIL" method.  

Let me know what you think, I'd love to hear.  Have a great day.  See you on Monday.

Using Number Lines In The Math Classroom.

Up until recently, I've never used number lines because I thought they were meant only for the younger grades. However, I've decided that number lines can be used to show older students so much and are a great addition to strips.  In addition, they can be used with different vocabulary when working with older students so they get a much better idea of positive and negative.

For instance, most students have been exposed to number lines in terms of addition and subtraction but they need the same exposure when working with positive and negative numbers.  For older students, this is where you can talk about the positive and negative relating to directions on the number line.  It can also be used to show by a double negative turns into a positive number.

Number lines in early elementary are used to show numbers and their order but number lines can also show order for fractions and decimals along with positive and negative numbers.  Furthermore, it is used to show addition and subtraction of whole numbers but it can be used to show addition and subtraction of decimals or fractions.  As long as the students have multiple number lines available, they can see that 2/5 < 3/5 or .4 = 2/5. In fact, you can have one number line with fractions on the bottom and decimal equivalents on the top. 

This is important because using number lines to show fractions helps provide a base for students to learn to read rulers and measuring tapes. I have so many students who cannot read measurement so they struggle when doing anything that requires it.  It is just a short step from using a number line to reading a ruler or measuring tape.  

Although I've never done it, I can see using number lines to show multiplication by showing that 3 x 5 is three jumps that are 5 units in length or 5 jumps that are three units long.  The same could be said of division by having students divide a total number into that many units.  In other words, show that 15 divided by 3 means you take the length of 15 and either divide it into 3 equal groups or into sections that are 3 units long.

What about having students use a number line to help solve word problems.  Students can mark the information on the number line to help them visualize everything, thus giving them a way to figure out how to solve the actual problem. This can really help students rather than just having to read numbers and guess the solution.  

For students who are more advanced, have them use number lines to create a problem which they turn into a word problem.  This helps students see that most word problems follow a set pattern.  Usually the information is provided with the question on what they need to find being one of the last things in the problem.  

Finally, Alway include the number line when reviewing and reinforcing what they've already learned using one.  This can be done by creating games that use the number line. I hope this gives you a few ideas for using number lines in your classroom.  Let me know what you think, I'd love to hear.  Have a great day.

Fraction, Decimal, And Percent Strips

 

This past week when I was researching whether digital or physical manipulatives were better, I came across a lovely website that had tons of virtual manipulatives from geoboard and geoshapes to analog thermometers, to money.  In amongst the list, I found the usual fraction strips but right next to those, there were decimal strips and percent strips.  I felt like I had a light bulb go off in my head.  This is the first time I've ever seen 

The decimal and percent ones are set up the same way that the fraction strips are designed to work in the same way as fraction strips. The decimal one has strips for 1, .5, .25, .4, .3, .125, or .1 while the percentage manipulative has 100%, 50%, 25%, 40%, 30%, 20%, etc to. match up with fraction strips.  

When I saw these, I realized that I could easily use these to help students when they struggle to learn about equivalents between fractions, decimals, and percents.  Think about letting students taking a 1/2 fraction to line up with a .5 tile and a 50% tile.  They can physically see they are the same size so they'd know they were equivalent.  This is the same technique we use to show that 1/2 is the same as 2/4 or 4/8.  They line the tiles up and they can see they are the same lengths.  

I am not saying one should use all three at once but as students learn to convert fractions to decimals, they can use those two so that they see the relationships between each fraction and its equivalent decimal.  When they work on converting decimals to percents, they can use those two strips and they can use all three if they are looking at all three.

I wanted to find more information on this topic but there really isn't any that I could find. I found a lot on using fraction strips or decimal strips or percent strips, but very little on using either decimal or percentage strips. I also didn't find much at all on using fraction, decimal, or percent strips together. 

Unfortunately, This site only offers the strips individually, not together so you can't compare these virtually.  I also went looking for individual physical representations for fractions, decimals, and percents. I found lots of fraction strips, I found a few fraction and decimal strips that seem to be about half and half but I didn't find any percentage strips.

On their other hand, you can make your own.  It is possible to find blank fraction strips.  These can be printed on card stock and students can fill the values in for decimals or percents.  This way they have their own strips to use while they learn the concept rather than just memorizing the facts.  This may help student make the connections they need.

Since I'll be working with some 6th and 7th graders next year who will probably be light on the knowledge of what fraction equals what decimal and percent so this is a great way to help them.  Let me know what you think, I'd love to hear.  Have a great day.

Warmup

 

You are paying a company $38 dollars per 1000 square feet to aerate your lawn.  Your yard is 52 feet by 250 feet but your house covers 1,450 square feet.  How much is the company going to charge you to aerate the remaining lawn?

Warmup

 You need to fertilize your back yard.  The rate is 10 pounds of fertilizer per 1,000 square feet.  If your back yard is 52 feet by 78 feet, how much fertilizer will you need?

Physical versus Digital Manipulatives.

 I've been wondering which type of manipulatives are better to use in the classroom.  I see advantages for both and usually end up using the digital ones because it's impossible to lose pieces, break them, stab them to death, or throw them at others.  I do know that the feel is not the same so today, I'm looking into both to see if one is better than the other. 

For definitions, physical manipulatives are the ones that students can hold in their hands, move around, and feel.  Digital or virtual manipulatives are web-based or app based representations of the physical ones. The virtual ones allow students to interact with to a higher degree than the physical ones.

As you know, math manipulatives offer students the opportunity to interact with concepts and can be any thing from base 10 to fractions to clocks. Research as far as using physical manipulatives helps students learn better than those who do not use them but note that it is not the manipulatives themselves but the context in which they are used.

The use of digital manipulatives has not been explored as much as the physical ones but early results indicate one should use both forms for the best results.  There are advantages to either one.  Digital manipulatives offer flexibility in that the virtual ones often can be broken into smaller parts or put together in ways physical ones cannot.  Digital ones also offer the opportunity to create more if there are not enough since physical manipulatives come in a predetermined number so if the student needs more, they have to find a second set.

In addition, the digital version is accessible from home or school and only require a tablet or phone to get to. It is easier to keep sets whole because one doesn't have pieces to lose, account for, and the teacher does not have to make sure sets are complete. The classroom always has the right number of sets.

Physical math manipulatives work well for students who need to "play" with something.  It allows them to have a kinesthetic experience and they do not do well with the digital version.  In addition, many students find the use of physical manipulatives more motivating than using digital ones because the physical ones provide immediate feedback while improving their use of time. Consequently, physical manipulatives also engage students more, especial boys.  When boys use the digital ones, they are less confident and less involved. 

Although physical manipulatives come in specific sets, if one used homemade manipulatives, one can create as many as needed.  The pieces can be placed in sandwich bags and more can be made if students lose pieces. The bottom line is that both types of manipulatives can be used effectively to improve conceptual understanding.  Let me know what you think, I'd love to hear.  Have a great day.

Fraction Strips Vs Circles.

 

This past year, I had to teach a 7th grader fractions because he had absolutely no idea how they worked but he could do it on the calculator as long as the calculator had the "right" buttons.  I had him use the fraction strips rather than the circles but I wonder if I made a mistake in not having him use the fraction circle pieces.  So today, I'm looking at the two choices to see if one is better than the other or if I should have had him do both.

As you know fraction manipulatives are great for showing how many pieces equal one, for showing students that each fraction is equal, for equivalents, comparing, adding, subtracting, multiplication, division and so much more.  

If you've never used them, fraction strips or bars are strips that are used to represent the fractions and are straight whereas the fraction circles are like a pizza that is cut into various sets.  Either way, having students use manipulatives is a good way to determine if they understand the concept.  There is research out there that says if they cannot model fractions, they are lacking in understanding the concept. In addition, these manipulatives do not inherently give them the concept but they help facilitate understanding.

In general, circle manipulatives are used in the lower elementary grades and referred to as a pizza or a pie.  Although there is no definitive conclusion that these are the best to use because it depends on the way they are used: it was concluded that circle manipulatives are the most effective to help students form a visual picture of fraction.

On the other hand, the use of a fraction wall which is a static representation of fraction strips from one to twelfths is not as good as using the individual strips.  Having said that, it is good for students learning about the inverse relationships between the denominator and size of the fractions but they did not get a good understanding of the numerator and how it works. 

As far as fraction strips, these are considered better for physically comparing fractions.  These allow the students to physically line fractions up, one set on top and a different set on the bottom which is extremely difficult to do with fraction circles.  In addition, the strips allow students to see the lengths for each set of fractions get smaller as the whole is divided into more and more pieces.  

It sounds like the choice of strips versus circles depends on what age being taught and the purpose behind the use of manipulatives.  One thing did come out in researching this topic, although many classrooms have sets of pattern blocks, these are not considered the best ones to use to teach fractions because the shapes are all different whereas when using strips or circles, the shapes are the same for all fractions, just have different sizes.  

On Friday, we'll look at the differences between real life and virtual/digital manipulatives.  With many schools giving their students computers or tablets, it is often easier to put them online rather than facing the possibility of losing pieces.  Let me know what you think, I'd love to hear.  Have a great day.

Research Backed Digital Games.

I have been trying to find independent research showing which digital games do what they are supposed to do other than finding company based information.  I once taught in a school where I had to teach reading using one of those scripted programs and I went looking for independent research to show the program worked and the only study I found that was not on the company site, indicated the program was not as good as a literature based program. 

As far as digital games, I found a couple of independent sources not from the companies.  The first suggested game is Wazzit Trouble designed to help students conceptualize topics. This app is designed to have students help break a creature out of jail by working through the combinations of the cell.  This app was tested with 3rd graders and the results showed the students who played this game improved quite a bit.  This app does cost money. This study was done at Stanford.  

I have found articles that explain which programs are used by teachers, suggestions by a few places like Common Sense organization but few actual places that show the research. Common Sense has published a list of suggested sites one can use but many of them are geared more for elementary school and most are paid.  They do however provide a bottom line such as explaining one site's games focus on fluency but doesn't go beyond drills.  

According to an article on Education Week, several folks at McGill University evaluated 90 math related apps in the Apple Store and discovered that quite a few did not include the information needed by teachers and parents to properly evaluate quality.  The missing information included things like whether any researchers were consulted in the design, does the app meet any standards or is it aligned to any particular program or educational philosophy.Without this information, it is difficult to determine if the app will do exactly what you want it to do.  

Thus, it is up to teachers to really determine if the app does what it needs to do to help students improve mathematical thinking, fluency, and understanding of concepts.  So in that same article that talked about evaluating 90 apps, they go on to make four suggestions a teacher can use when evaluating apps for use in the classroom.

First, it is important to know what the purpose behind the app is.  Is it meant to drill students, to introduce new concepts or review older concepts, is it gamified, or is it designed to let the student explore through self direction?  It is important to look for apps whose purpose is closely aligned to the instructional goals. 

Next look to see if the app has feedback and scaffolding.  It is important that the app not just tell students if their answer is right or wrong but it should offer hints and scaffolding so that the student arrives at the correct answer. Aside from being important to learning, it keeps students engaged because they are less likely to give up. The app should identify when the student is in a cycle of struggle and adjust work so the student can get through it.  In addition, students should be able to start where they need to based on their abilities and it moves them to more complex problems as they show understanding.

The math should be integrated into gameplay such as with Dragonbox Algebra for Elementary students.  It asks them to move boxes around until both sides are balanced.  Once the student has the equation balanced, they have "won" the round. The whole app encourages mathematical thinking.  You do not want an app with lots of small unrelated mini-games as a break or reward because it can take the student's focus away from the mathematical thinking.

Finally, look at how easy it is to use the app.  Is the student able to input their answer correctly or does the app make it hard to enter the answer. If the app operates with a touch screen, does the screen move as the student wants?  If the student struggles to respond to the question or move the screen, then they will get frustrated and the app will not get a good feel of what the student actually knows.

Years ago, I found an app to hell my students practice their multiplication tables.  I didn't realize that it required students to just type in the missing number to make the statement true in order.  It did 9 x ____ = 9, 9 x _____ = 18, etc so the student would type in 1, 2, 3, etc.  It didn't require them to learn because they just typed the digits in.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

 If every 16 ounce jar of peanuts use 3 pounds of peanuts, how many jars of peanuts will you get from 5,000 pounds of peanuts from your acre of land?

Warm-up

 One acre of land planted in peanuts produces about 5,000 pounds of peanuts.  If you have 4.75 acres of land planted in peanuts, how many pounds of peanuts will you produce?

Data Science In High School

 

I think it is important to offer math classes to students that they can use in real life, especially if they are not planning to go to college.  I've offered a class to students so they could learn construction or trades math, a class on the math involved in some of the Pixar movies, and of course practical financial math that covered credit cards, loans, insurance, and just about everything they'd need once they left school.  A new course that I want to offer is one on data science. 

Data science is a field where people take data and try to make sense of it.  This requires the use of scientific methods, algorithms, and assorted processes to separate the data into identified trends.  Companies use this information to make informed decisions to help the business grow while making a profit.  It is important for companies to be aware of the latest trends so they make the proper decisions.

There are many reasons students should study data science.  First, it is one of the fastest growing fields out there and it is expected to grow over 36 percent between now and 2031. It is an in demand career. In addition, it is a field that pays well, over $100,000 per year on average. In addition, it offers a variety of possible jobs from data analyst, to a machine learning engineer, to data base administrator, to data scientist, to so much more.  The jobs available range from health care to manufacturing, to the financial sector, and more.  

Data science requires knowledge of programming, modeling and analysis, statistics and probability, linear algebra and calculus, being able to visualize the data, machine and deep learning, data wrangling, data base management and data processing.

By offering students a taste of data science in high school, it gives students the chance to see if they are interested in pursuing this in college.  It can also expose students to this topic who might not ever think about going into this field. Should you want to offer this at your school but don't know where to go.  Heard off to the data science course at youcubed.org. 

This course is a year long exploratory experience that gives students a taste of it.  The course is free and comes with professional development so you can feel confident in offering the class.  You can explore the first unit without signing up for the class. The first unit focuses on data ethics, types of data, creating visual representations, figuring out the story the data tells, and more.  This unit is designed to take about a month. 

The unit comes with everything from the resources, slides, student reflections, samples of student work, student concept organizer, student portfolio, and software requirements.  In addition, it view all the activities for each section of the unit so you can check everything out ahead of time for planning purposes.  I realize that many schools are unwilling to add new classes like this without going through a ton of hoops.  Let me know what you think, I'd love to hear.  Have a great day and weekend.