What Is Or Isn’t Growth Mindset.

 I was on a tour yesterday and ran into a young lady whose pre-algebra teacher did the growth mindset videos from Jo Boaler, I know that some people are confused about the term growth mindset as defined by Carol Dweck. In a nutshell, a growth mindset is one where the person believes that their talents can be developed through hard work, feedback, and the use of good strategies while some with a fixed mindset believe that only someone with innate gifts.

Unfortunately, the basic idea has been taken by the general public, twisted, adjusted, and changed it. So today, we’ll look at how people have begun interpreting growth mindset since the term has become such a buzz word in education and industry

Some people believe they have always had a growth mindset because they have always been flexible and / or have a positive outlook. This is referred to as a false growth mindset because they do not understand what a true growth mindset is. In addition, most people are a combination of fixed and growth mindset simply because a pure growth mindset does not exist. The mixture changes over time based on experiences.

Other people believe a growth mindset involves praising and rewarding effort but it does not work in school, nor does o]it work in industry.  Unfortunately, outcomes matter in both situations. If we are going to reward people, we need to reward them for effort, learning and process because unproductive effort is not a good thing. It does not produce a desired outcome. It is important for people to understand that the process which includes asking for help, trying something new, analyzing set backs to move forward effectively.

Espousing growth mindset is not enough to change anything. Most places have mission statements describing what they want to do in wonderful terminology but they have not implemented any policies to help folks attain those goals. They encourage risk taking knowing people might not reach the goals and they also reward people when they learn something even though the project goals were not met. They are willing to support collaboration throughout the organization instead of encouraging competition. They want every member of the organization to grow by providing opportunities.

These are the three area where misconceptions abound but even if all of these misconceptions are cleared away, it does not pave the way for growth mindset. This is because of a persons fixed mindset triggers such as received criticism, comparing ourselves poorly to others, or certain challenges. 

This is a general overall look at the topic. Monday, I will look at growth mindset and what can be done from the start of the year to encourage it.  Let me know what you think, I’d love to hear.

Covering As Much Material As Possible. - Pacing

 

We all know that every math book comes with a suggested pacing guide designed to get through just about every topic in the time available. The problem is that most students are not ready to move at that pace. If you have students who struggle, or have certain limitations, you just cannot teach at the pace suggested. I once had a principal who could not understand why my class ( filled with special ed students, students who were not up to grade level, etc) could not keep pace with the other class filled with gifted students. The other teacher had to explain why I couldn’t match her pace. No matter what, we want to teach students as much as possible, so today we are looking at ways to do that.

One of the first things to do is administer a protest to students. Most books have a pretest associated with the chapter. The results of the pretest give you an idea of which parts you can teach, which you can touch on, and which ones you can skip. The results also give you an idea of which students need scaffolding, or need to be challenged. 

As you teach the material, you might notice that some students did not fully get the material, look at the material in the rest of the book to see if there exists the opportunity to reinforce their learning by reteaching the topic in the future. If the opportunity does exist, then you can move on, revisiting the topic as needed.

Periodically sit down and see how far your pacing has taken you eithr]er individually or as a department. If you have not covered as much as you hoped, sit down and determine if there are concepts or topics that can be cut out. Sometimes, it is possible to combine material rather than teaching them individually. This should be done a couple times throughout the school year.

Another thing to look at is the structure of the lesson itself. Are you spending a third of the period going over questions, is the lecture taking up most of the class, or do they have enough time to work on the assignment. In this vein there are a few things one can do. It is important to know how much to]ime you actually have to do the lesson. Pacing with in the lesson is just as important as pacing through the year. When pacing is good, students are more likely to be engaged.

It is said that a well paced lesson leads to increased instructional time. In addition it is important to identify the specific learning target so you know what they need to know already and what they should have learned by the end of the lesson. In addition, plan the questions you want to ask ahead of time so the questions are specific to the learning goals. Also plan your teaching points so you stay on topic.

Finally, make sure the planned activities are ones that meet the time scheduled, help students learn the concepts. So pacing is both through the year and through the lessons. Let me know what you think, I’d love to hear. Have a great day.

More First Day Of School Activities.

 Today, we will be looking at more activities that can be done on the first day or two of school. I do not like starting immediately with the syllabus and regular class because students seem to take a day or two to transition back into tzhe swing of things. I addressed this last week and today, we will look at a few more activities. Although, these activities may not contain direct instruction, they will be mathematically based.

Maybe start with the odd one out game. In this game, you give students a card with numbers on it but one number is not part of the pattern. The student has to identify the odd one out and they have to explain what makes it the odd one out. An example might be, 1, 4, 9,16, 25, 35, 49. The odd one out is 35 because it is not a square number.

Another activity is to have students create three dimensional shapes from colored paper and tape. The shapes students can make might be cubes, prisms, cones, cylinders, or rectangular prisms. The students have to figure out how to create the shapes rather than giving them pre-done nets. Some students might get a bit frustrated but others will have a great time. This is an activity that can provide a situation for students to collaborate.

Another activity is designed to review fractions. The idea is to pass out different shapes and then ask students to color in a potion of it to illustrate a fraction. For instance, you pass out triangles and ask students to fill in 1/3rd of it. This is a good way to figure out if students understand that all parts need to be the same size. When you have students work with different shapes, they have to think about it. Most fractions are illustrated using circles or rectangles so when you give them a trapezoid, triangle, diamond, etc, they have to figure out how to subdivide it into equal parts. 

Pass out the dice and have students calculate probabilities. Start with one dice before moving to two dice. Of course, one can also calculate the probabilities for various cards in a card deck. On the other hand, pull out the fun data so students can practice bar graphs, pie charts, line graphs, etc. it is easy to find these types of activities online. I had my students do one on blueberry production in the United States and then world wide. 

In the past, I have passed out packets of M & M’s or skittles to the students. I had them sort them into colors , create a bar graph of all the colors before asking them to figure out the percentage each color is of the whole bag. I finished off by asking them to create a pie chart.  Another activity is to pass out a candy bar to each child and ask them to calculate its volume.  I am aware one has to be aware of allergies so it might not work at your school.

Finally, bingo. It might be a mean, median, or mode version, order of operations, fractions, decimals, percent conversion, or whatever topic you want. It is easy to do. Simply, pass out empty bingo cards, give a long list of possible answers, and let the students fill out their own cards, then it’s time for the equations or data so students find the answer. This activity has always generated lots of discussion 

So with this many suggestions, you have some great choices available to make the first day of school enjoyable. Let me know what you think, I’d love to hear, have a great week.

Warm-up

On average, a bee hive contains 50,000 bees. If they weigh a total of 12 pounds, how much does each bee weigh? 

Warmup

 If one bee collects 0.0288 ounce of honey, how many bees are needed to collect one pound of honey?

Geometry Of Bees.

 

Yes, we know that bees like to use the hexagonal shape due to its stability and strength but scientists have discovered another facet of bees and how they build their hives. In fact, both bees and wasps have managed to solve an architectural problem using geometry. The problem boils down to figuring out how to  increase the size of each cell and being able to combine the cells effectively. Nest building material is expensive and one cannot combine different sized hexagons into a single array.

So both bees and wasps came up with a unique solution. They produce both five and seven sided cells to fill in the blank areas created by using different sized hexagons. Being able to combine different sized hexagons is difficult but these creatures figured out a solution.  

Many of the colonies are run by female workers who raise the offspring of the queen in hexagonal shaped cells. At a certain point, the focus of the hive is to switch from raising offspring to raising new males and new queens. Since these bees are larger than workers, the hive needs larger cells. 

Scientists analyzed 115 images of various colonies by using an automated image analysis tool but the also verified all results by hand to double check everything. They counted the sides of the irregularly shaped cells that filled in the region between the smaller worker cells and the newer cells for male offspring and new queens.

The scientists discovered that the bees paired one 5 sided cell with a seven sided cell, repeating the pairing again and again to fill in the area. This pairing has the same number of open sides as pairings of hexagons. In fact the five side is made first and then the seven sided shape is created. Then a mathematician created a mathematical model for this and the results of the model indicate this is close to the optimal geometric solution. Thus, these creatures discovered s solution that is great. Let me know what you think, I’d love to hear. Have a great weekend.

Activities For The Beginning Of School In Math,

 

The summer is rapidly speeding by and the first day of school is not too far off. Often on the first day or two of class, I provide a few activities to get them back into school rather than diving straight in. I find it takes a couple days for students to transition into the right mind set.

One activity I enjoy having my students do is to think of something mathematical for each letter of the alphabet. I pass out a sheet of paper with instructions at the top and the alphabet down the side. They have say 10 minutes to come up with something math for each letter. For instance they might say add for A, or base for B. The time could be longer or shorter depending on your students. 

When the time is up, have students leave their answers on their desk and get up and look at other peoples answers. At the end of a minute (again, the time is up to you) they go back to their desks and fill out any missing letters. Then go through all the letters, having students share out answers that you write on the board. 

Want to get to know your students? Ask them to complete a more about me math activity. In this activity, students tell you all about themselves and their family but via mathematical equations. Instead of giving their age as 16, they might say my age is 4^2 or sqrt 64 x 2. They might tell you they have ( 5-4) brothers and 24/8 sisters. All numerical info must be conveyed using mathematical equations.

Set up a “which would you rather?” School based activity that has a bit of silly. A question might be “which would you rather”….. wear a superhero outfit to school or wear a cowboy hat with a fake mustache. It is not a serious game, just something to break the ice and add a twist of fun to the class.

Another fun activity is to create equation puzzles where each puzzle piece has equations or answers along the sides that match up. In groups students are expected to match up the equation with the correct answer without using a calculator or pen and paper. They are only allowed to talk about it. You can make puzzles out of a large triangle divided into smaller triangles or a large square or rectangle subdivided into smaller quadrilaterals. If you make them out of paper and laminate the pieces, you can use them every year.

Start the year off with writing prompts such as “I want to become better at math so I can ……” or “people who are good at math …..” or “ I used math this summer when I ……….”. Writing is an important way to communicate and it doesn’t hurt to begin having them do a night of writing on the first day.

Finally, think about emoji logic puzzles. The ones that have three lines of math but instead of numbers, there are emojis or other characters. An example might be:

😀 + 😀 + 😀 = 45

👀 + 👀 + 😀 = 35

👀 + 😀 + 🙈 = 30

Find the value for each character.

I will be back with some more activities you can use the first day of school. Let me know what you think, I’d love to hear. Have a great day.