Why Are Brain Breaks Important.

How many times, as a student, did you get a bunch of problems to practice the current topic being taught in class?  I remember getting like 30 problems to do and by the time I got to the end of the assignment, I could barely tolerate doing the problems.  I didn't take any breaks because I had to get it all done and my parents believed one needed to start and finish the work in one go.  

What I've noticed over time is that I do much better when I take breaks.  It seems to allow my mind the time it needs to connect pieces so I understand the material better.

By definition, a brain break is a small break to give students a mental break designed for students to focus and get ready to work again. The break can give time so students can get the blood flowing, increase the amount of oxygen going to the brain, and it provides the time students need to reset and get a bit more energy.  A small brain break also gives students a chance to process and think about the material behind the things.

Incorporating regular brain breaks into the schedule can result in students having better behavior, increase their productivity, improve comprehension, have better creative thinking, while spending more time on task.  Time for brain breaks should be regularly scheduled so they are not spending too long on any one task.  When they spend too much time focused on one activity, it can be counter productive. A brain break should include some movement and music and help reduce the level of frustration students experience when working too long on a task.  The length of a brain break depends on the age of the students.  

There was a recent study published which took a look at the brain.  They discovered there was a spike in brain activity during the break where the brain appears to be reviewing the material the student had just been exposed to but it was happening at an extremely high rate of speed. The review of the material went from the neocortex, home to the processing of sensory and motor skills, to the hippocampus which is the center of the brains memory.  This happened at least 24 times within 10 seconds.  So even though the students are taking a physical and mental break, their brains are still processing the material.

When people or students learn a new skill, it has to be connected with prior learning or previous memories.  The process is called binding and it is an important part of learning new skills.  When we learn a new skill, the brain uses the time during a break to review the material, compress  and imprint the new material so it's stored efficiently.

Furthermore, when planning to use brain breaks in class, it is important to schedule them before students become fatigued, bored, or distracted, thus there need to be frequent breaks especially in the longer classes.  It is suggested that elementary students get a 3 to 5 minute break every 10 to 15 minutes while secondary students should have a break every 20 to 30 minutes.

One does not need to plan entertainment for these breaks.  Instead, have the students get up, stretch, move around, or even chat some.  I've found that high school students do not want to exercise or even sing songs but sometimes I've put on music or even math "rap" videos to entertain them. Other times, I have things placed around the room for students to get so they are moving out of their seats.

In fact, there is research to indicate that scheduling brain breaks during tests including standardized tests results in improved test scores. As far as the effectiveness of brain breaks in class, there are indications that student performance increases.  Let me know what you think, I'd love to hear.  Have a great day.

Ways To Activate Prior Knowledge.

 

One of the hardest things I've discovered about teaching math, is getting students to activate prior knowledge associated with the current topic.  Too often, my students have treated each topic and every problem as something new.  It was difficult to get them to connect prior knowledge with the new concept and each problem with the next and with the topic.

Research indicates that when we learn first from our prior knowledge and second from the new material being taught. Thus it is important to take time to find out what students know before introducing the new material because we construct new knowledge from what we already know.

A suggestion has been made that teacher have students take a assessment to determine what prior knowledge and skills they already have so the teacher has a place to start.

It is suggested that we take time to ask students about their prior knowledge, experience, hunches, or ideas with the topic or material, Another possibility is to have students try to relate it to their real lives such as slope can be related to the pitch of a roof or the grade of a road up or down a hill.  There are activities we can integrate into our instruction.

1.  Image Brainstorming.  In this activity, project a picture on the smart board or wall and ask students to tell you everything they see in the picture.  Select pictures that students are familiar with and allows them to connect the picture with the new topic or concept.  

2. K-W-L Chart.  This is a good activity to help activate their prior knowledge but it is easy to overuse to use sparingly.

3. Picture Books.  In recent years, there have been more children picture books written with a math topic.  I've seen a few with Sir Cumference (circumference) or that look at the size of certain numbers etc.  Let students read these picture books before introducing the topic or concept.

4. ABC Brainstorming. Give students a table with 26 boxes with a letter in each box.  Put the students in pairs and have them brainstorm a word or phrase for each letter.  There can be a restriction put on what type of words such as shapes, or solving equations and instead of 26 boxes, have them list as many words as they can starting with a different letter.

5. Class Brainstorming Web.  Place a word in a circle in the center and have students write as many different words as they can associated with the word in the center.  Connect the words to the one in the center so you have a graphic organizer.  Keep the activity visible through the new material so students can refer to it. 

6. Making Connections.  In this activity, students work in pairs to look at, analyze, and determine relationships between pre-selected topics such as tools, vocabulary, types of problems, or even math they've already learned. This activity helps students build connections between  concepts or terms and prior knowledge. It also helps students find connections and learn more about relationships they might not see otherwise.

7. Modeling and Coaching.  In this activity, students are coached into breaking down solving the problem into steps while using guiding questions to help students use self-questioning to activate prior knowledge. Sometimes, it might be having students begin with a less complex problem, identifying steps before having them solve the actual problem.

These are just a few ways to help students address prior knowledge since prior knowledge is extremely important in learning the new material.  Next column, I'll address connecting prior knowledge with the current material.  Let me know what you think, I'd love to hear.  Have a great day.

Warmup.

 If the average number of mangoes produced by one tree is 232 fruits in a year, how many mangoes will an orchard of 187 tree produce?

Warmup

 If one large mango gives one cup of pulp, how many mangoes will you need to make twelve gallons of pulp?

Geek Out On A Show

Ok, I discovered a show on Netflix that I absolutely love because it combine two interesting and rather different activities into one.  The show, "Baking Impossible" pairs bakers up with engineers and each week they are given an assignment to complete.  One pair wins and one pair goes home.

Although it does not directly "show" math, one can see it being used in every single show.  I love the combination of engineering with baking because it shows some unique problem solving.  Yes, problem solving in that if one thing doesn't work, they'll try something else. There were some spectacular loses and some equally spectacular wins.  

The first week started with something fairly simple but each week, the show raised the bar and the challenges became more and more complicated.  The show began with nine pairs and then by the eighth week, only two couples were left.  

The projects were judged on the engineering aspect, the flavor of the cake that had to be moved or protected, and a couple of other things.  Usually the frame of the product is made of wood, electronics, or other nonedible material but the rest of it had to be made of any edible product and there was a cake involved that had to be transported, protected, or presented and the judges tried and enjoyed. For every project, competitors were given parameters including size, any special electronics. 

The first episode had the collaborators create an edible boat that would travel a specific distance in water. Only three boats actually floated and two made it all the way to the end within the time limit.  The majority of boats were too top heavy and just flipped on their sides as soon as they ended up in the water but they all had a second cake for the judges just in case something messed up.  

The second episode brought us a robot that had to navigate an obstacle course included foods such as marshmallows. It was interesting in that only two robots managed to get through the whole course.  All the rest either couldn't turn left or right so they got stuck at the slalom, or they got bogged down in the marshmallow pit.  It was interesting to watch the engineers try to create a robot that could be covered in edible foods.  One failure ended up too wide and heavy so it couldn't even move.  

The third episode had each team create a run with three simple machines to create a Rube Goldberg type machine so if everything worked well, the cake hidden inside a container would be exposed.  The majority of teams started the ball at the top and worked their way down but one team started the energy at the bottom and it went upwards.  Of course some had paths that went directly to the end and others got super creative so they had higher chances of failure.

In the fourth episode, the competitors had the assignment to create mini-golf courses. This episode differed in that the competitors were divided into two teams to create three putt putt golf holes with some sort of theme.  The winning pair came from the winning team and the pair chosen to leave came from the loosing team.  The size was predetermined by the size of the wooden base. 

The fifth episode differed from all the other episodes because the pairs were required to create fashion from edible materials to walk down a runway.  Some of the designs were disjointed while others got so creative and I was impressed by the results.  The models came from previous competitors who had been eliminated.  One group made a cyborg samurai  out of pineapple skins, watermelons, chocolate, pasta and a few other things.

Then the sixth episode required pairs to create a city block with one tall building, a couple of small buildings, surrounding countryside and it had to survive on a shaking table.  The same kind of table that is used in real life to test scale models to see how well they would survive an earthquake.  The cooking competition provided gingerbread for the highest building so the competitors used the same basic building material

By the seventh episode, they were down to three pairs who had to build a car that was five feet wide by eight feet long.  It had to be able to survive a crash going 25 miles per hour.  This meant they had to build the bumper with edible materials so that it would absorb the energy to protect the car.  It was fascinating to see the three different styles of vehicles. Rather than mess with an engine, they hooked the car/truck up to a tow rope.

The last episode had the couples building bridges that would raise for a ship to pass under, allow a weighed car to drive over, and be able to survive having 160 pounds placed on it.  The bridges were over some sort of body of water with the surrounding area decorated.  It was fascinating to see the two different bridges they came up with.  One group basically lost because the road leading up to their bridge was a bit too steep and the car couldn't go up it.

Although they didn't show much direct math, you'd see the engineers sketching out ideas, see people measuring, the bakers determining how much they needed for everything and problem solving.  You could see problem solving being used from start to finish.

I can see this showing students when I had to be out of the classroom.  It is entertaining and if you watch ahead of time, you could easily create a list of questions for students to answer.  I admit much of the obvious things are science based but the math is there.  Let me know what you think, I'd love to hear.  Have a great day.

 

Word Games

An important component involved in having students learn vocabulary is to get them to use it.  As teachers it is good if we can integrate games and activities to help students.  We don't want to just have them define the words and quit or have them write the words multiple times like elementary teachers have their students do to learn spelling words.  We want to get students involved. 

There are three digital places I enjoy using to help students with their vocabulary.  The first one is Kahoot because I can make games using the vocabulary for each section.  I can have questions that are definitions and four choices for the word it is associated or the word with four possible definitions.  Most of the students I've worked with love playing Kahoot.  The second is jeopardy which can be done with either the vocabulary word and have the students give the definition or give them the definition and ask them to come up with the word.  This is good for vocabulary from one chapter or multiple chapters or it could be one of the category choices for a review.  The final is the Quizizz which can be done independently. Students can choose the correct definition of the word or vice versa.

Sometimes, you want students to play vocabulary games that get them up and moving around a bit or give them a break from their digital devices. Last time, I discussed matching games like concentration but today, we'll look at other ones that can easily be used in the classroom.  

One game is a variation of Tic-Tac-Toe. You set up the Tic-Tac-Toe grid with vocabulary words which you've made with the word wall.  Then divide students into teams.  One team chooses a vocabulary word and define it.  If they define it properly, remove the word and replace it with either a O or an X, otherwise leave the vocabulary word there if the definition is incorrect.  Then let the other team choose a vocabulary word to define.  If they are correct, they get the other letter, otherwise the word is let there.  Repeat until there is a winner or no winner.  This can be done with two teams for whole class or with multiple teams so smaller groups can play together at once.

An activity is to use a Cloze activity where the teacher writes two or three sentences with blanks so the students can fill in the blank with the appropriate word.  A variation on this is to call out a word and students write a sentence go express a connection between that math word and another term, situation, concept, or real world application. 

Then we can integrate some art into the study of vocabulary by giving students a blank sheet of paper and a pencil.  The teacher calls out a vocabulary word and lets students draw or doodle a picture representing the word for about 15 to 20 seconds before calling out the next word.  After calling out 5 words, have the students connect their drawings or doodles with a simple line from one to the next till all 5 are connected.  The next step is to have students label their drawings without looking at their vocabulary list or the word wall.  Finally, have the students check their work. 

Here is another use for the vocabulary cards.  Divide students into groups of two or three and make sure each group has a stack of words.  Then have students sort words into groups in as many ways as they can. For instance for geometric shapes they might divide them into quadrilaterals and not quadrilaterals, angles versus sides, shape properties and names of shapes.  This encourages critical thinking and thinking of math in different ways.

Now for some poetry.  Have students choose one word from the word wall and write it on the first line.  They choose two words that are synonyms for the first word and write them on the second line.  The third line is composed of three words that describe the word on the first line.  The fourth and final line is where they write a fact about the first line.  

Most of these activities are short and can be done to support vocabulary learning.  Let me know what you think, I'd love to hear.  Have a great day.

Ways To Help Students Use Math Vocabulary Resources.

 

No matter how many ways we use to help students learn vocabulary, we have to teach them how to use the resources available to them. We can't just have them define vocabulary or throw the words on a word wall without having students use the vocabulary so they can learn it.  Without knowing the vocabulary, students will struggle in the math class.  If they don't understand terms like evaluate, justify, or simplify, they'll have trouble completing the assignment.  So today, we'll look at some ways to help students use the vocabulary resources available to them.

First introduce new vocabulary during the lesson as you normally do but do not put all the words on the word wall at once.  Place the words on the word wall as you introduce students to them.  When you've placed the word on the wall, take time to discuss it and come up with a class agreed upon definition that students can use in their dictionary, graphic, or dictionary.  If you do not discuss the word, students will just copy the definition out of the textbook verbatim or will change one or two words.

Next, model, model, model.  When you run across the word in class or in the textbook later on, refer to the word wall or ask students to check their personal dictionaries so they get used to using the resources, otherwise students won't take the time to learn the vocabulary.  It is important to review the words on a regular basis.

Instead of stapling or pinning your words to the word wall, make sure you have a second set of words in a pocket at the bottom of the word wall.  This way you can take the cards out for games, or activities designed to help students learn the vocabulary better.  If you make several sets of cards with the word on one card and definition on another card, students can play games like concentration or matching words with the definition.

In addition, you only want the words from the current unit.  Do not start putting words from chapter one and keep adding to them as students continue with new units otherwise you'll have too many words on the wall and it will end up being too confusing. If you don't want to make multiple sets of cards, have students create their own vocabulary cards so they can play games.  In addition to matching and concentration, they could play go fish with previous vocabulary words.  Go fish would sound something like "Who has a five sided figure?" and someone would reply "I have a pentagon."  So it could be either the definition or the word.

Integrate more writing into your class. First set expectations that you expect them to use precision when using the words.  You might also tell them what you expect such as  "Use three of the vocabulary words when explaining how to solve one step equations".  It is important to create opportunities for students to use the vocabulary words. So many workbooks only have a list of vocabulary for students to define but never have the students use the words again.  Have students write in their math journals so you can check their work once a week.  

On Wednesday, I'll be talking about a variety of games that can be used in the class to help students learn their vocabulary. Some of the games will be digitally based while others are print or verbal based.  Although most of us have so much to cover in class, it is important to review vocabulary over and over no matter whether we are talking third or ninth grade.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

 

If the weeping willow grows 5.5 feet per year, how long will it take to reach it's full height of 40 feet?  What if it grew 3 feet a year?  Or 8 feet a year?

Warm-up

 The hybrid poplar tree is considered the fastest growing tree.  It grows between 3 and 8 feet per year. How long will it take if it grows 3 feet per year to reach 50 feet?  How long will it take to reach 50 feet if it grows 8 feet per year?

Student Created Math Dictionary.

 In language arts, students are exposed to dictionaries beginning in early elementary but in math, we kind of expect students to "get" vocabulary without the use of dictionaries but what if we made math dictionaries a part of our regular instruction. 

Dictionaries are important for students to develop their vocabulary and connect the word to multiple meanings. Mathematical vocabulary consisting or words and/or symbols. Math has words that may be general words, multiple meaning words, or words that are specific to math.  An example of a general word might be car which appears in word problems but it means the same thing in English that it does in Math.  Product has multiple meanings such as the result of a multiplication problem, something that is made and sold in a store or the result of a situation such as a child in a marriage. The word "Torus" is a math specific word referring to a shape like the doughnut. It is important to know mathematical vocabulary to unlock the meaning of any problem.  A dictionary helps students learn the vocabulary while providing a personalized reference.

I know many teachers teach vocabulary, have students fill out some sort of graphic organizer as a word but not enough teachers have students create their own dictionaries so today we'll look at how to do this.  The nice thing about creating a student dictionary is that it can be done in a composition note book or a spiral book with tabs, or a digital notebook program. 

When students make their own personal dictionary, they are more likely to take ownership because they created it. Since it is their own personal dictionary, they are the only ones using it so they can tailor it to their needs. When they come across a new word, they learn more about it as they enter the information into their dictionaries so they are more likely to remember the term. It is portable so they can take it home and use it at school. 

There is no one way to do a dictionary so it is up to the teacher to set up how they want the word done.  One way is write the word down, define it, and then use it in a sentence.  Another choice is to write down the date, the page the word is found on, the word, and it's definition.  Then there is dividing the dictionary into sections for the various letters.  When students enter the word, they might put the word, it's definition, a visual drawing, and an example of what it isn't.  

Of course, you can just use Frayer-model graphic pages with two to six per page.  You punch holes in the pages and place them in a binder with tabs to mark the different letters.  If chose this method, it is helpful to provide students with an alphabetical list of all the vocabulary words they will run into throughout the year so they know what word goes where and the words remain in alphabetical order.  As they fill in the word, they check it off the main list. A variation is to fill out the graphic pages, cut them out once they've been filled out before folding them in half and glueing them to a blank page in a notebook.

Although this can take time, it is worth the time so students are exposed to vocabulary and are able to create their own personalized dictionary.  On Monday, I'll look at more ways to expose students to vocabulary.  Let me know what you think I'd love to hear.  Have a great day.

Using Apps To Supplement Instructions

 

Back in 2019, there was a study published in the Journal of Educational Psychology which looked at raising mathematical achievement in early elementary using interactive apps.  The study looked at a randomized control trial carried out in the United Kingdom that focused on the use of interactive math apps that focused on early education for children aged 4 to 5.

They felt that interactive math apps used in addition to regular instruction or instead of small group activities would help scores increase.  The study lasted 12 weeks and at the end, student scores for those who used interactive math apps, did indeed increase. The apps selected focused on basic facts and concepts, higher level mathematical reasoning, and skills needed to solve problems.

They defined interactive apps as apps that use educational psychology to combine direct instruction with play.  The results suggest that this type of app is a good vehicle for high quality instruction in the classroom resulting in raised achievement.  It is well known that students who have a strong mathematical foundation in their early years do better in middle and high school.  

It is well known that developing mathematical skills happens in four general areas - factual knowledge and conceptual knowledge which covers basic math skills and mathematical reasoning and problem solving which covers higher level mathematics. Students should be able to attack problems of different levels of difficulty from all four areas.  It has also been shown that students who are able to automate their basic number skills do better in higher level math while those who had poor fluency in basic math skills find math difficult.

The best apps combine feedback, repetition, and rewards associated with direct instruction with the features of free play such as self-regulation and control. It is best to have students use the apps on a touch screen because young children find it motivating and easy to use.  The reason for tablets is they are light weight and mobile but do not rely on the same dexterity skills needed to use a computer. 

As for the apps, they need to include active learning such as manipulating of virtual objects, verbal labels, and numerical representations.  There should also be a simultaneous use of audio and visual parts to create a multi sensory experience that helps stimulate learning.  The apps should also provide immediate feedback both positive and negative immediately after every interaction. Learning is promoted through a curriculum that builds on their previous knowledge while guiding students to work beyond their current abilities.  Furthermore, the apps need to include some sort of continuous assessment of knowledge learned through various topics such as retrieval based learning.

The best use of apps is to use them as interventions to support standard math instruction.  The two apps used for this study were "Maths 3-5" and "Maths 4-6" by onebillion (a not-for-profit educational organization).In addition the apps match the requirements for instruction of the UK and meet what is needed for early elementary learners. These apps target factual knowledge and basic conceptual knowledge through the use of child centered tuition.  Children, wearing headphones,  work through the apps at their own pace and can repeat any instruction or activity as needed.  After they work their way through the lessons, they take a quiz at the end of the topic and if they pass, they receive a certificate and are allowed to move on.

These apps can be used instead of small group instruction or to supplement whole group instruction. When this type of app is integrated into the classroom in the first year of school, it provides a good way of promoting development of early math skills.  I liked this study because it gave me a better idea of what to look for in apps for early elementary students.  Let me know what you think, I'd love to hear.  Have a great day.

 

Are The Top Rated Math Apps For Early Childhood Research Based?

Most of us have to find apps designed to reinforce or teach skills to students.  I know from personal experience, I had to try different apps in the hopes they'd do what I need but what about math based apps designed for children around the age of five. There was some research done to see if the top 25 math apps are based on research.

The study was done by the University College London and they concluded that these 25 apps are not based on best practices and do not develop their early math skills. As a matter of fact, there are few regulations or rules for educational apps. Only one of the apps in the top 25 list has actually been evaluated to see if they had any impact on a child's learning.

They based their research on synthesizing 50 research studies from 18 countries that looked at 77 apps used in the first three years of school.  They concluded that 90 percent of these studies revealed that math apps did provide some benefits for children's mathematical learning and development.  The apps that worked best provided a personalized learning situation with immediate feedback on why their answers were right or wrong. It was noted that few if any apps in the top 25 list have this feature.

It was calculated that 66 percent of the top rated 25 math apps focus on number skills while 64% on counting but these skills were being introduced in isolation away from other math skills and concepts. Furthermore, skills such as basic arithmetic, basic shapes, patterns, and measurement were not covered nearly as often. 

This is important because many parents will put math apps on their children's digital devices to give them a head start but if most of the education apps are not based on best practices,  students will not have the instruction they need.  In addition, with the pandemic interrupting instruction, many teachers and parents may have used apps to keep students moving but they may not have gotten the best instruction possible.

The authors of the study concluded that there are limited ways for parents and teachers to tell if the app is high quality. There needs to be a better way of categorizing apps so parents and teachers know if the app is based on research or best practices. To choose apps, one needs to consider design features, the learning experience, and how it fits into your classroom. 

On Wednesday, I'll be looking at a study that looked at using mathematical apps to supplement the normal programs for those children in the 4 to 5 year old range.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

 If it takes 208 cranberries to make one can of cranberry sauce, how many cans of cranberry sauce can be made with 522 pounds of cranberries. (remember 440 cranberries in one pound).

Warm-up

 If there are on average, 440 cranberries in a pound, how many cranberries are in a cup?

What Happens When We Don't Understand Fractions.

There have been events throughout recent years that show most people do not have a good unstanding of fractions.  By that I mean that they do not grasp the differences between one-third and one-fourth or five eights and six ninths.  Many ended up with the idea that the larger the number in the denominator, the larger the number which as we know is not really true.

If you look back to when the A & W restaurants tried to take on McDonalds by offering their own burger deal.  They decided to offer a larger one-third pound burger which was bigger, tasted so much better in blind taste tests,  and cost less.  In other words, they offered a better deal than McDonalds but people didn't go for it because they didn't understand that one-third is bigger than one-fourth. People thought that one-third was less than one-fourth because three is less than four.

Another example comes from the 1980's when the game Dungeons and Dragons became popular.  A they spread across the country that players of Dungeons and Dragons were more likely to commit murder or suicide due to a few cases.  This happened during the time when the United States was undergoing a panic about Satan and his influence and it even made the news show "60 minutes". Unfortunately, no one took the time to actually look at the numbers of players who committed murder or suicide versus the total number of people who played the game.

One person researched the numbers and over a five year period, only about 28 players either committed murder or suicide out of the 3 million or more teenagers who played the game.  In order for the fear to be true, the numerator should have been at 360. or more based on the normal number of teen suicides back in the 1980's.  So in reality, the people who played Dungeons and Dragons were less likely to commit suicide than the regular teen age population.

Now if you look at a test given to more than 20,000 eighth graders about 40 years ago, only about 24 percent were able to answer questions on fractions correctly.  Since then, the number of students who showed they understood fractions only increased to 27 percent.  Not much of an increase.  It has been discovered that how well a fifth grader understands fractions and can use them can be used to predict how well they will learn algebra and what they achieve in high school mathematics.  By the time a student gets into high school math, they will be facing more problems and formulas containing fractions. In fact, a lack of knowledge of fractions can impede students learning high school math and can make it difficult to do certain jobs once they are out of high school.

Furthermore, when students learn fractions in elementary school, they often have trouble intrinsically with being about to use what they've learned.  For instance, when they multiply fractions, they have to multiply the numerators and then the denominators but in adding or subtracting fractions, they cannot do that. This and other things makes it difficult for students to learn to use fractions challenging.  

The second thing that makes it more difficult is that teachers often find it difficult to explain why problems are done a certain way.  For instance, many teachers are unable to provide an explanation for why we turn a fraction division problem into a multiplication problem with the reciprocal. It's even difficult to provide a visual to show fractional division.

So when these same students become adults, they carry the same lack of understanding with them so when they see things like the A & W third pounder, they have no idea it is a bigger hamburger.  Humans have a tendency to not look at the full picture when deciding if a situation is really bad or good. Instead, humans rely on a cognitive framework to make quick decisions.  This process is called heuristics and for the most part it works but when it fails, it fails horribly. 

Let me know what you think, I'd love to hear.  Have a great weekend. 

Student Created Math Handbooks.

Most students do no want to take their textbooks home and notebooks just contain notes based on what the teacher has provided.  There is something between the two that can help students organize the information into a usable form. 

Instead of giving note after note, have students create their own personal math handbook.  A handbook is a portable reference guide while the textbook is the course book filled with everything and is often quite thick and heavy. The handbook is different than the regular notes in that the handbook is more organized with proper examples and is easier to use because the topics are together.

Often, students are introduced to equivalent fractions before learning how to compare the fractions and a bit later they are introduced to making sure denominators are the same when adding and subtracting fractions.  Many times, they have notes on other things scattered between the topics so by creating a handbook, the student organizes the information into a more cohesive unit.  When they redo the material as they organize the handbook, they are reviewing the information so their brains have another chance of learning the material.

A student created handbook can be made using a composition notebook or an app on the iPad or computer.  The way a student puts the handbook together is the same for either the hard or digital copy.   The first page or two is always going to be the table of contents.  The listing will not be every single topic covered in their notes but will be grouped according to topics such as fractions, decimals, volume, quadrilaterals, etc.  The page number is the page number the section starts.  So it might say Fractions.          7-12 letting the reader know that all the material between page 7 and 12 is information on fractions.

The information written in the handbook may answer the what is it, how is it used, or why is it done this way. It doesn't have to include everything, just the information needed to do it.  For instance, when placing information on fractions, it might include the vocabulary for the numerator and denominator, finding equivalent fractions and why they are needed, how to make fractions equivalent with one or two examples, adding and subtracting, multiplying or dividing fractions, and improper and mixed fractions. This section could cover regular fractions or algebraic fractions.

In addition, each section should have several extra pages so the student can go back and add additional information and examples as needed.  The organization makes it easier for students to use the material and they can identify relationships between topics and concepts.  Yes, this might be adding another level of work but it allows students to look at the most important concepts and ideas.  The student might show solving one step equations with fractions and decimals in their notes but they would show the general formula in their handbook with short notes on what to do if the problem has fractions or decimals.  The student can also include a short note about referring to page 27 in their notes for more in-depth information and examples. 

So handbooks provide a quick organized way for notes so they are in a more cohesive form.  It also allows teachers to help students learn what is the most important information out of their notes and what isn't but is still good to have.  Let me know what you think, I'd love to hear.  Have a great day.

Digital Task Cards

Most teachers end up being out of the classroom at some point.  It's always hard to set up something for students to do when you are out but I've used a learning platform to leave the lesson for the day so I don't have to make tons of copies of make-work for my sub.  Having students use task cards is one option and they can be done digitally. 

Task cards are cards with problems for students to do.  Although most schools are back in session, some students are out due to covid so by having digital cards, all students can participate even though they are not at school.  They can also be a part of the lesson used by a sub when the teacher is out.

Digital task cards can be set up so students can either scroll through the choices or work their way through the cards so the teacher becomes the facilitator. In this case the facilitator can walk among the students, encourage them to work together, edit each others work, explore, analyze, while providing a choice.  Furthermore, the tasks can be differentiated from relatively simple to much harder so students can find something they can do. Digital Task cards allow students to work at their own pace or the teacher can set a deadline.  There can be choices for students who finish early or need something more challenging. 

There are a couple ways to create and use digital task cards.  One way is to create the cards in Google Slides. Open google slides and set up a new presentation.  Place a different task on each slide. One can create four answers on each slide with one correct and three incorrect answers.  Link the correct answer to a slide telling them it is correct and when they click the next button, they go to the next question while the incorrect answers are linked to slides that say incorrect and back.  The other possibility is to create a open ended task that students answer using a google doc where they explain their thinking. Once they have their answer down, they move to the next slide.

If you prefer, you can set up a google form for students to place their answers.  Each slide lists a different task and each task should be numbered.  Then set up a google form so it's set up as a self-grading quiz.  If you go with tasks that have absolute answers, set up google forms with the correct answer so students type in their answers and they find out immediately if their answers are correct.  Otherwise, if the tasks are open ended, set the form to short answers so students can place their answers in the form and you can provide feedback.

Another way to create digital task cards is to take a pdf of all the task cards and capture a picture of each task card.  Then import one task card per google slide so you have a slide presentation filled with the cards so they can choose one or work their way through.  This can also be done in google forms so that one picture of a task card is imported for each question.  In the question box, you type the number of the task card and import the task card image for the question.  Click short answer and required, then done. 

If your questions have a single answer, you can click multiple choice and list four answers for students to select from.  The correct answer is identified and inputed so when students chose the correct answer they get immediate feedback.

If you use keynote or power point, you can set it up as a presentation and import pictures or type out the questions and follow the directions for google slides with the appropriate links.  You can have students type the answers into pages or Microsoft word.  So now you know how to create digital task cards.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

 

If there are 1100 cinnamon flavored candy hearts in a pound, how many would be found in a 12 ounce bag?

Warm-up

 If there are 137 hearts in a 12 ounce container of jelly hearts, how many are there per ounce?

Ways To Use Task Cards

Task cards are a great activity to use in the classroom as it encourages independence, critical thinking, used for review, assessment, and can replace worksheets.  Task cards can be either in hard copy or digital form. Today I'm just exploring ways to use them in class and on Monday, we'll look at how to create digital versions that can be assigned via a learning platform.

A task card is a card with a question or task students are asked to do or answer.  These are great for reviewing a topic or concept and they are not a good activity for introducing something new. 

Task cards can be used in so many different ways in the classroom.  Rather than seeing them as "tasks", see them as a versatile element of instructional activities. It is important to know what process students are using the cards for.  It is a review, additional practice, or assessment so you know what the expected result is.

Task cards can be used with individual students to reinforce their learning of a specific concept or topic if they need a bit more time to master it.  In addition, a teacher can use the student's answer to assess their understanding of the material. Students can do a many as needed for them to learn the topic so if they just need one more time, they do one task card, if they need several more tries, they will do those.

Instead of sending home a worksheet or book assignment, use task cards so they an work on the skill outside of the classroom.  This is a perfect situation for either a physical or digital task card.  The advantage to using a digital task card is that the student cannot forget or lose it.

For students who are ahead of everyone else, create more challenging task cards so these students are not bored. These can be available to those students who always finish early or need enrichment.  Task cards can be created for students of different ability levels.

In addition, physical task cards can be used to create movement within the classroom.  It often helps students focus better if they can move around the classroom. Just make sure students know what you expect when they move around.  One way to do this is to place task cards around the room like you do in search and rescue and have students work their way through the cards.  They write their answers on an answer sheet where they can show their work.  At the end of the period or time, they turn in answers to the teacher.

Task cards can also be used in small groups by passing out one card at a time to each group and have all the members of the group write their answers on white boards so they can compare answers.  If any of the answers are different, it opens up the group for a dialog so they can work on determining which answers are correct or reasonable.

Turn the use of task cards into a game such as "Scoot".  In this game, students each get a stack of task cards. They need to answer as many as they can within two to three minutes. They can write answers in their notebook, on a whiteboard, or in a journal.  When time is up, the teacher calls "Scoot" and the students either move to the next stack to the right, or they pass the stack of cards to the right and they do it again.   Another possible game is to have two students, standing back to back,  in the middle of the room.  They are each given the same task card that the teacher reads the card so the class knows what they are doing.  Students write the answers on a whiteboard and when they are both done, they compare answers and then two new students are chosen.  

It is possible to turn the material on task cards into a board game that students play.  Task cards are ideal for interventions.  Use them when working with students who need additional help.  So many ways to use task cards instead of worksheets.  Let me know what you think, I'd love to hear.  Check back on Monday to learn how to make digital task cards.   

Adaptive Learning Software.

I'm sure by now, most teachers have used adaptive technology in their classrooms.  This past semester, I had students working on a program that used adaptive technology but they didn't understand that when they used calculators to do the arithmetic, it would give them harder problems because they gave correct answers.

Adaptive learning software is software that is used to teach and help the student learn via personalized lessons, practices, and assessments. It does this by using artificial learning and machine learning techniques to "adapt" a learning plan for individual students.  It also provides data for instructors and the administration to analyze so they can provide instruction to meet the needs of the students.  Usually, adaptive learning software is web-based and contains all the information necessary for the class so it can direct students along their journey of learning.

Adaptive learning software works by assessing what skills or concepts students have mastered before adjusting lessons or activities so students learn.  So this software begins with an evaluation to determine which skills or concepts the student needs to work on, creates an individualized pathway, and monitors and assesses their progress.  Some programs can distinguish between performance data and engagement data.  In other words, are they really engaged in their learning or just there going through it.

Adaptive learning software is able to provide a plan for personalized learning for every student with scaffolding, flexibility, targeted learning lessons, and any resources needed. In addition, they provide immediate feedback on practices, clear learning objectives, determine what is needed to improve, and low stakes assessment.

Furthermore, the software allows students to monitor their progress so they are more self-directed, work at their own pace by skipping skills and concepts they've already mastered while reviewing and practicing new concepts and skills more slowly than with direct instruction. It provides lessons that match their needs and readiness, can be used to replace textbooks, provides a framework of lessons, activities, instruction, and assessments that meet their needs while allowing instructors to provide additional instruction to students for areas they struggle.

Since the software contains all materials needed for the class, it is able to break down the concepts and skills into properly sequenced and manageable chunks leading students to mastering the learning goal. The software works on providing instruction and activities between the students comfort area and the zone where they get frustrated which is known as the zone of Proximal Development. This zone is the area between what students have already mastered and the material that is too challenging so they get frustrated.

Many schools are relying on adaptive learning software to help fill in gaps of student knowledge gained during the pandemic. Based on my personal experience, the students who really work through the material and try, tend to learn but those who didn't try, didn't accomplish much.  Let me know what you think, I'd love to hear.  Have a great day.