TUVA Labs

 

As math teachers, we are always looking for data we can use in our classrooms that is authentic and interesting.  It has to be interesting to capture student attention and buy in.  This is where TUVA Labs come in.  The offer three types of information to use in the classroom for everything from bellringers/warmup to activities, to data stories.  Each one can be used for a specific purpose.

The material can be in data stories which allow students to generate their own questions, evaluate data found in different forms such as charts, tables, or graphs, or look for patterns and make observations.  Data stories are great for warm-ups, conversation starters, or an introductory activities.  These are short 10 to 20 minute activities.

They provide data sets complete with associated activities that are real-world, content rich, data sets obtained from sources such as NASA, the Census Bureau, NOAA, the CDC, and so many others.  The activities require that students analyze the data, and can be used as part of a classroom lesson. These are longer, taking from 20 minutes to a full class period. The final type is the task which has students applying what they've learned and can be used to challenge students or extend concepts.

They offer students the opportunity to create a dot plots, scatter plots, bar charts, histograms, and box plots, or construct their own mathematical models, while making predictions and interpreting data. In addition, they can look for patterns and apply mathematical or statistical concepts to situations that are real and authentic. They've got materials rated for grades 3 to 12.

Although, Tuvalabs offer both a free version and a paid version, the free version only allows you to access 10 free lessons, upload 5 data sets and set up basic student accounts.  The free lessons cover things such as dinosaurs, Atlantic hurricanes, devastating earthquakes,  the population of the Lynx and Snowshoe hares in Canada for science.  For math, there are lessons on comparing the profits between Pixar and Dreamworks, determining who is at the highest risk of getting measles, relationship between diameter and mass of M&M's and several others.

Each lesson can be accessed through google and each has an activity preview. The preview discusses learning goals while explaining the lesson step by step. In addition, you can look at all the case cards, see how many activities have been created, and how many students have used them. Now if your school lets you invest in the paid version, you end up getting access to every lesson, activity, data set, etc, all 267 of them.  There are unlimited uploads, premium student accounts, integration with google classroom and other LMS and other advantages.

The company does provide tutorials designed to help students learn how to do a variety of topics from how to do certain charts, to filtering data, to random sampling, and so many others.  Now I will say, this is something I would be more likely to do during an actual face to face class because I'd want to be there to monitor and answer questions rather than trying to run it virtually.  Next, I would strongly recommend you test drive this by signing up for the 10 free lessons to see if it would work well for your lessons.  let me know what you think, I'd love to hear.  Have a great day.

The Geometry Of Haircutting.

I never thought there would be geometry associated with haircuts until I got hooked on those hairdressers who look at "fails" and discuss what they did wrong and how to avoid it.  One of the guys mentioned geometry and haircutting in the same breath so of course my ears perked up. 

In general, geometry plays an important part in cutting hair since many cuts are based on geometric principles.  Take the wedge cut, bob, and bangs for instance. They are based on geometric angles.  In addition, a hairstylist has to know the angle they need to hold the scissors and comb to get the desired result.

Furthermore, a hairdresser has to know how to divide the head into various geometric shapes, as they divide the hair up into sections to cut the hair, dye it, highlight it. They have to know how cut layers so the layers look proper.  They don't want to do what has been advised on Tik-Tok because they will end up with chunks.  If you haven't seen it, the most common method is to either divide the hair into two pigtails which have elastic wrapped around the hair at the point they want to cut it and then they cut it.  This method results in a curved haircut which is shorter by the ears and longer in back with choppy edges.

The other method is to put your hair in a ponytail with the elastic band placed where you want to cut the hair.  Cut it just past the band and it is supposed to produce a layered look.  It sort of ends up that way but its in chunks so it doesn't look particularly great.  Hairstylists learn to cut hair so it doesn't chunk and ends up looking proper.

When hair is cut, stylists may use a beveled cut to accomplish the finished look.  Beveled cuts is a technique that uses diagonal cuts to make the stacked look in hair.  On the other hand,  they might cut hair in a convex line to create the U or V shape of the hairstyle or the concave to create a curved line like an arch. The concave lines are most often used at the back of the head or in bangs, or around the ears. 

The angle they actually use to cut the hair helps define the look of the hair.  If there is no angle or a zero degree angle is used for a one length cut as a horizontal line.  If hair is cut at a 45 degree, it produces a stack or a wedge, which is a triangular cut.  If the hair is cut at a 90 degree angle, its called a universal cut. but the 180 degree cut results in a layered cut.

In addition, math is used to mix the chemicals properly to straighten hair, perm it, bleach it, dye it, or highlight it.  Many hairstylists end up working as independent business people who rent a station in a beauty parlor and they have to figure out what to charge for their services so they can make money while still meeting all their bills.

So as you've seen, geometry plays a large part in cutting hair.  Let me know what you think, I'd love to hear.  Have a good day. 

Warm-up

 

If it takes 540 peanuts to make a 12 ounce jar of peanut butter, how many peanuts will it take to fill a 16 ounce jar?

Warm-up

 

If a peanut plant produces on average 42 peanuts per plant, how many peanuts would you have if you grew 1538 plants?

Is Online Instruction Effective?

 Many teachers are on their second year of virtual instruction being alternated with in person as the number of COVID cases increase and decrease.  Most of us were thrown into the deep end back in the spring of 2020, without any training, any direction. We are on the second year after that are we are still bouncing back and forth.  

In the meantime, people has had a chance to conduct research on this topic.  It is obvious that when class has to go virtual, students miss out on the interpersonal interactions they normally experience in person.  

In regard to most online courses for high/middle school, and elementary are designed to resemble the in class structure. The teacher usually has a warm-up, the lesson, and offers chances to interact virtually before homework is assigned.  The teacher tries to include time to work with individual students. Unfortunately, online classes are not as effective as in-person classes for most students.

In one study, students were placed in either online or in person classes when they had to repeat the second semester of Algebra I.  The results indicated that the students who took the class in person did much better than those in the online version. In addition, those who took the online class felt it was more difficult than taking the same class in person.

Although some students do well in virtual or online classes, the majority do not. Students who have a weaker academic background tend to so much worse in online classes. There is evidence to support the idea that students who do really well in person will do well online but for those who struggle to learn math in person will so significantly worse when enrolled in an online class.

It is possible to design an online class to help lower performing students.  An online class needs to have a strong curriculum with strong teaching practices in place. It needs to have activities and teaching methods designed to engage students because they face more distractions with less oversight so they may not have the same motivation. Teachers need to set expectations such as responding to a specific number of questions or interacting with other students during class time. 

Unfortunately, students who have fewer resources at home, tend to learn less than they do when they are in school In addition, research shows that giving students access to virtual classes is better than nothing.  The biggest point of virtual classes is that it does provide a chance for teachers to interact with students but there needs to be improvements made to online classes to improve student learning.

I don't know if many students struggle with online because of the way the classes are organized due to districts trying to make it so virtual classes mimic in person classes or if it's just the distractions.  I'll be investigating that next.  Let me know what you think, I'd love to hear.  Have a great weekend.

The Mathematics Of Knitting

I am one of those knitters who does it when I have a bit of time or when I'm watching a video and need to keep from phasing out.  I was thrilled when I found an article about a physicist who was working on unraveling the mathematics of knitting.  

If you look, you'll notice there are at about 100 basic knots, which if you vary the combinations, you  alter elasticity, strength, and the three dimensional structure of the finished product.  

One of the first steps in this process was to sit down and list all the possible stitches before figuring out how to classify them. 

Although yarn by itself is not very elastic, the elasticity doubles when it is made into a knitted fabric. Elisabetta Matsumoto is researching this topic.  She hopes to create a dictionary of stitch types, the various combinations of stitches, and the resulting fabric.  She is basing her research on knot theory which says that a knot is a tangled circle, or a circle embedded with crossings that cannot be undone. 

 Knot theory is what explains how knots are formed and is used to explain how DNA folds and unfolds and much more. She uses knot theory to explain how each stitch entangles with each of it's neighbors. She has discovered that when small changes are made such as moving how the yarn crosses in a knot, can influence the mechanics of the finished fabric. 

Knitting is actually a series of slipknots in a row. These slipknots when placed rows and columns form a lattice similar to a crystalline structure. When a knitter uses one stitch such as all knitting or all purls, the edge of the fabric curls where as if these two are combined by alternating rows or columns, the fabric lies much flatter. Although the two fabrics may look the same, the amount of elasticity is different. 

She argues that knitting is a type of coding while the yarn is the programable material. For a presentation, she knitted a swatch that illustrated a type of plastic surgery called Z-plasty.  Z-plasty is a plastic surgery technique which can improve both the functional and cosmetic appearance of scars.  

Matsumoto is working with several programmers to get the computer to think like a knitter by teaching it about the properties of yarn, the mathematics of each stitch, any intentional stitch defects, constraints, the twists and compresses of yarn blends, the number of plies, its thickness, and how floofy it is. Floofy is a term that refers to the location of the fuzzy fibers that stick out. 

Eventually, they hope the program will be able to predict the properties of the finished fabric.  They hope this information can be used for growing human tissue or used in wearable electronics.  Let me know what you think, I'd love to hear.  Have a great day.

Improving On-line Teaching.

 

I know of at least two districts here in Alaska who have had to move to online teaching due to the number of Covid cases locally.  I know that the numbers are running between 800 and 1,100 per day which is higher than it was back in the spring.  The districts that shift to online teaching, usually have students who have decent access to the internet or the district has set up some sort of intranet for the town to use.

It is important to plan ahead to create an online class that is engaging and allows for student choice, proper feedback while covering the content and providing students with opportunities to master the material. 

First thing is to identify what must be covered, essential contact. Teachers need to think about what concepts need to be covered, which can be touched on, and which ones can be eliminated totally.  For instance, one might briefly review solving multiple step equations in one class period in Algebra 2 but totally eliminate matrices and Cramer's rule.  Which topics are the most important?

If possible, move instruction to asynchronous by offering videos either remade or self-made on demand and save the synchronous for going over example problems, work with students and correct misconceptions.  When you provide videos on demand, they should identify key objectives and include a way for students to check and monitor their own understanding.  This helps make it so students can work more at their own pace.

Instead of looking at homework, look at student learning. Rather than grading the work they turn in, look at evaluating them on their reflections and revisions.  Provide the final answers so students can check their work but give them the opportunity to revise their work so they can be graded on that. 

Take time to intentionally design opportunities for interacting with students. One possible way is for students to pretend that they have a partner who does not understand how to do the current topic and have them make a video in which they explain how to do it. In other words, let students make a peer tutoring video since they can't do it in person. When a student creates a video to explain things, they develop a deeper understanding and these video can be viewed by students who struggle with said topic.  Don't be afraid to assign collaborative tasks using multimedia or storyboarding and let students work together in breakout rooms.

Consider rethinking assessment by using three different ways.  First, think about using automated assessments such as quizzes that use multiple choice questions and can be completed within 15 minutes.  Second, use oral exams by having students spend 5 to 10 minutes to explain how to do a problem, and finally, let students create a culminating project at the end of the unit.  Allow students to have a choice in the final unit project which can enrich both understanding and experiences.  

Think about changing up the way you create lessons when you switch to online.  Let me know what you think, I'd love to hear.  Have a great day.