Does An App Like Photomath Have A Place In The Classroom?

I know that many students use certain apps like Photomath to help them complete assignments but most of the students I know who have done this?  Well they didn't learn the material.  I can tell who has used it because their homework is 100% but on the assessment, they bomb all the problems.  Fortunately, there are things we can do as teachers to use such apps and help students learn the material at the same time.

In this column, I'll use the Photomath but it is only one of several apps that operate in the same way.  You  use the app to "read" the problem and it provides all the steps to show how it was solved and at the end, you have the correct answer.  It is too easy to just copy the material down without thinking.

I've done some reading up on this topic because I want to allow students this choice but I want to make more of a learning experience, especially as I know certain students will be doing it. It's the old, choose your battles so why not acknowledge some students will resort to apps so they do well and because they struggle. 

When you are ready to introduce a new topic, consider using Photomath instead of the example in the textbook. To prepare for this, select the problems you want to use ahead of time so you can determine where possible misconceptions will happen, where students will have trouble, and places students will need clarification.  The nice thing about having all the students using the same app is that you do not have to write all the steps down on the board, instead you can project the results.  Once you have students all on the same problem, you can walk them through the steps needed to solve the problem, pointing out everything they need to know or think about.  

Another way to use Photomath is to have students work in small groups.  They look at the problem and rather than going straight to the answer, they learn to look at the structure and focus on different ways to solve the problem.  For instance, students might start with a problem like 3(x + 2) = 24. Photomath may start by distributing the 3 across the (x + 2) to get 3x + 6 = 24 and go from there but in this problem, you can also divide both sides by 3 to get x + 2 = 8.  Both methods work for this problem.

Furthermore, some apps allow a person the option of looking at more than one way of solving a specific problem.  For problems that fall into this category, have the students look at each of the methods and then discuss which method they believe is the best choice for this problem.  They can also do a compare and contrast of the different methods to see how they differ.

Furthermore, have the students work on a few practice problems and when everyone has completed the assignments, let them use Photomath to make corrections but they aren't just looking at the answer.  They are looking at the process they used to solve the problem.  They are looking for to identify the missteps the made in solving the problem.  This is a great place for a three column sheet.  The first column is where they do the problem, the second column is for the corrected version and the third column is where students explain what they did incorrectly and what they should have done.

It is fine to let students use Photomath at home to correct their homework but they should always take the time to figure out where they made a mistake and what they should have done to be correct.  These are several ways students can use Photomath or similar app in class to help with their learning. It is important to reassure students that making mistakes is just part of the learning process. If students are willing to do an error analysis for problems they miss, they will learn more.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

 

If a pound of small cucumbers contain 6 cucumbers and each cucumber can be sliced into 23 pieces, how many slices will be in half a pound?

Warm-up

 If takes half a pound of cucumbers to make one pint of pickles, how many pounds of cucumbers will you need to make a gallon of pickles?

Setting Students Up To Do Well.

For many people, school has started and for others, it will be starting soon.  With students already in and out due to COVID, it is important to establish a framework to help students do well in Math.  It is important to set things up at the start of the year.  

Look at doing something a bit different on the first day of school.  Instead of going over the syllabus, assessments, etc, look at laying down a strong support system, listing expectations, and try to get them excited and inspired about math for the year.

Admittedly, many students arrive in class with the attitude that they just can't do math because they aren't good at it, they inherited their parents ability to struggle, or other similar belief and it is important to change their minds.  They need to believe that they and anyone else can do math. In addition, they need to know that it is ok to both struggle and make mistakes.  They should accept that making mistakes is an important part of learning. So start the year with an activity that can help them change that belief.

One should also create a classroom where children feel included. This means that trust should be built between the teacher and students and that you care for them.  They should understand that you are there because you want to be rather than you are there because you have to be and that you want them there in the classroom.  Without trust and the feeling that you want them there, the classroom may not feel as welcoming and inclusive.

On the first day of class, use an activity rather than standing there and talking all period long.  This shows them what will happen instead of just droning on and on. Choose an activity that graph their attention and gets them involved such as the 10 items one. Begin by asking students how good they are at remembering things. Then give them a list of 10 unrelated items to remember and see how well they do.  Once they've done the list, go back over and help them associate items in a way to help them use these visualizations to remember the list of unrelated items.

Look at selecting another activity to help students explore their mindset using either a 3 act play or even something from Jo Boaler but it needs to be one that will spark curiosity. The activity should leave students feeling as if this year might be fun or interesting.  Then take time to let your students know how you've set the class up to support your expectations and their success.  

In fact, the first day of class is great for a collaborative activity because you are showing them that collaboration is an important part of the learning process.  For the first collaborative activity, consider using random grouping as a way of breaking the ice and having students work with people they would not normally choose to work with.

In a way, this is the teachers way of hooking students so they want to keep trying through the year.  Next time, I'll be looking at the why the first 30 days of class is important.  Let me know what you think, I'd love to hear.  Have a great day. 

How To Turn A Word Problem Into A Rich Math Task.

 

As we all know, most textbooks have a section of word problems at the end of each lesson but these word problems are designed specifically to be done in the same way as the other problems.  They lead to only one answer and rely on students identifying specific key terms to set up the equation.  Rich tasks are much better because are more open ended with multiple possible answers and multiple paths that can be used to solve the problems.

It is quite easy to transform a word problem into a rich math task by following six steps.  Begin with selecting a visual problem.  In other words, choose a word problem that can easily be pictured both in the mind and in the answer.  The answer needs to be expressed visually through a drawing, or by using manipulatives.  In addition, a student should be able to visualize several different ways to solve the question.

Next get rid of all those key words such as "in all", "total", "less than", and all the other words we teach students to look for. Now you have a word problem that has had all the key words removed but whose meaning is still the same. When the key words are removed, students are forced to think about the operation that must be used rather than relying on underlying certain words.

Now rewrite the problem again except this time you are adding in extra details and information that do not contribute to the solution of the problem.  If a student has. been trained to look only for key words, the additional information will confuse students but the reason or doing this is to help students learn to sort through information to decide which is important and which isn't.

Then personalize the problem by adding names to it.  You might choose the name of a student to make it more relatable by everyone.  At this point you've added enough details and names to turn the word problem into a story.  Remember, students relate to stories better than word problems.  You might start with a generalized problem on the specific number of apples needed for a pie and change it into a problem dealing with apple pies for thanksgiving. 

Turn any single step problem into a multiple steps tome it more challenging.  A one step problem might ask how long will it take to peel 30 apples if it takes 2 minutes to peel an apple.  To change this, you might tell someone that it took Sam 5 minutes to peel 2 apples and how long might it take the same person to peel 14 apples.

The final step is to change the numbers to make it more challenging and do not be afraid to end up with fractional answers.  The real world is more likely to end up with fractional answers so it is important for students to get used to working with them.  

So if you want to turn a word problem into a rich math task, just follow these steps to do it rather than searching the internet looking for the perfect topic.  Let me know what you think, I'd love to hear. Have a great day.

4 Steps You Can Do To Help Students Learn Math

 

The new school year is starting and I know of some school districts in the state who have already had to switch to distance due to an outbreak of Covid cases.  Once all the students have been tested, they'll move to a structure where half the students attend school each day but the four steps I'll be sharing with you today.

First off, ask students why at least once a day.  Ask they why the strategy worked?,  Why does it work in all these other cases?,  Why do you have to do this step?.  We know that students who memorize material do not perform as well as those who understand the concept.

When we ask students why, we are letting students know that what they are learning is contributing to their overall understanding of mathematics and overall ability to do it.  It also helps students see the overall bigger picture better. In a sense, it is showing students the tools and helping them understand how to use those tools while seeing that not all tools are used all the time or might be used in a slightly different way. It helps them understand the math rather than just learning to solve problems by rote.  It opens the door for deeper understanding.

Second, rather than focusing on the answer being correct or incorrect, take time to identify what the student did correctly.  This helps the teacher understand what they've gotten and what they didn't so the teacher is able to identify what the student needs scaffolding in.  It also helps the teacher build on what the student understands to take them to the next level.

When teachers analyze where the student got off when trying to solve a problem, it helps pinpoint where student understanding stops.  Furthermore, if enough students stray at the same place in a problem, it tells the teacher that they should either reteach the material or provide scaffolding so the students can move on while learning the material.  

Thirdly, consider using the textbook as a tool rather than as a major part of the instruction.  Find meaningful tasks in the textbook or change a problem into a meaningful task with a small change in numbers or contexts.  Unfortunately, most problems, even word problems in the textbook, are set up so they can be solved in exactly the same way as the numerical problems.  

We as teachers need to learn to change word problems into meaningful task problems.  A word problem generally has a specific set of numbers, one or more operations that the student uses to arrive at a single answer while a meaningful task often has less information with the possibility of multiple correct answers. Furthermore, they don't have key words to tell you the operation so you can't underline them. 

Finally, allow students to have the opportunity to solve a problem mentally before explaining how they solved it at least once a day. This means they don't use any pencils, paper, or digital device so as to improve their sense making, creativity while helping them feel as if they are mathematicians.

In addition, mental math helps students become more accurate with their calculations, it helps students develop a deeper conceptual understanding, it helps improve student memory, and helps increase SAT and ACT scores.

Making just these four changes will help students understand concepts better so they can improve their ability to do math and raise their grades.  Let me know what you think, I'd love to hear.  I'm going to be traveling to Sweden and Iceland over the next couple of weeks but I'll still be posting.  Have a great day.

Warm-up

 

What if each leaf weighs .32 ounces?  How many leaves are in a pound?

Warmup

 

If a pound of leaves contains 360 leaves, how much does each leaf weigh?

How To Use The Word Wall Effectively

 

So far this week, we've look at why one should use a word wall in math, how to create one and today we're going to learn to use one effectively to help increase student knowledge.  Unfortunately, it is extremely easy to go through the effort of putting up a word wall and then not do anything with it. When I first started using word walls in math, I only put up the word and it's definition but over time, I learned more about using the word walls properly.

Once you have everything associated with the concept or word posted, it is important to introduce the material in context since the definition of many terms is based on it's context.  Make sure to discuss any real world applications, diagrams, and equations. In addition, use the terms in a variety of situations so students see they apply to our lives.

One activity is to play "I'm thinking of a word wall word that means..........." for about 5 to 10 minutes a day.  The teacher says the phrase and has students write down the word on an iPad or paper and hold it up so the teacher can see their responses.  This is repeated again for two to three more words.  You can have students raise their hands so you can call on them but I prefer using white boards so more students can participate.

Another activity is to divide the students up into groups of two.  Each student chooses one word from the word wall and they have to decide how the two words go together. For instance, one student chooses equation while the other selects variable so the two go together because the variable represents the unknown quantity in the equation.  This activity encourages students to think about relationships and how these concepts and words go together.

To make sure you involve all students, try playing a game called link doodles.  In this game, the teacher decides which words are going to be used that day.  Students need a pencil or pen and a paper.  The teacher calls out a word and the students doodle something to represent the word for about 30 seconds before the teacher calls out the next word that they doodle something visual for about 30 seconds.  Repeat the process until the teacher has completed the words.  At the end, students will draw lines between the doodles, linking them together.

Take time to redo the word wall.  Take down all of the words and associated material, mix them up and have the students sort through the cards to hang them up again on the wall in the proper grouping.  This forces students to think about which items are grouped together as they are reassembling the wall.

In addition, have students create their own vocabulary cards using the Frayer model so they have the material close at hand and have had a chance to practice the vocabulary.  This also offers the opportunity to integrate some English activities by having students create a short story using some of the vocabulary, create sentences using the vocabulary, or create graphic organizers for each concept.

Another activity to help students review the material is to type up the words in one column, the definitions in another column and if there are formulas associated with the word, put them in a third column.  You can have students draw lines connecting the word with the definition and formula or you can have students cut all the words, definitions, and formulas out before gluing them in groups on a different page.

There are more activities but these are some suggestions to help students use the word walls more effectively and pay attention to them rather than treating them as just something on the board.  Let me know what you think, I'd love to hear.  Have a great day.

Creating A Word Wall

I've used word walls for years but I haven't always created them properly.  When I first began creating the word wall, I only had the words with definitions but over time, as I learned more about making them, I had to add to them.  Unfortunately, using only definitions do not help students connect everything associated with the concept.  

In mathematics, it is important to do more than tack the word and it's definition on the wall.  One needs to include the formula associated with the word and define all variables contained in the equation.  It is also important to create a visual of the word so students have a way of remembering it and for many students it is much easier to remember a picture.

It is recommended that each item posted be done in a clean and easy manner so it's easily readable, includes some sort of visual, be colorful if possible because the mind remembers color, have a concise definition, and allow the words to present the visual for terms like fractions, percentage, etc.

So let's start at the very beginning.  I recommend that each math class have one area dedicated to it such as Algebra I, Trades Math, Algebra II, etc.  Although many terms are found repeatedly throughout the different classes, the depth of coverage may vary.  I've set aside bulletin boards for this but I've also hung everything on a school wall using tape or the squishy stuff.  It depended on how the room was arranged.

When I first began, I would create the words and definitions by hand.  I'd write it all out but that took so much time so I switched to using other programs.  I've used MS word, Pages, or sites such as school express or Canva but I like the school express because it is basic, allows me to type everything in and it will create pages with the terms I need.

Once you have the word, definition, visual, forumla, definition of variables, and any thing else you want associated with the word, place them all together on the wall so students see them connected.  If you are focusing on  words that all mean the same thing such as increased by, added to, together because they are all words that refer to addition.  

As a way of helping students take ownership of the new vocabulary, you might divide the class up into small groups and assign one vocabulary word to each group.  Let the individual groups create the material for the word wall by supplying cards, colored pencils.  Be available to guide students if they have questions.  I usually save this activity for the end of a section so they've had time to learn more about the vocabulary.

If you'd like a word wall but do not have time to create the word wall cards yourself, you should check out the Virginia State Department of Education. They have a set of words already done for Kindergarten through Algebra II, functions, and data analysis.  You have your choice of word or pdf format and the cards come with examples and have color.  

On Friday, we'll look at ways to use the word walls effectively to help students learn more.  Let me know what you think, I'd love to hear.  Have a great day.

Word Walls

Since mathematics is considered another language because it has terms that have specific meanings, I've always had a word wall for every class.   Unfortunately, too many people do not think about using a word wall in mathematics since it is normally associated with English. 

A word wall in mathematics is a good way to identify the words and their meanings that are important for students to know and learn.  It is the vocabulary they need to have so they can discuss mathematics.  

The words that are posted are the ones associated with the current section.  A teacher should introduce the words with meanings in class before they are posted on the wall.  The words posted should include a visual clue to trigger the memory such as in the photo to the left.

The wall might is a great way to incorporate scaffolding for all students by creating context for much of the vocabulary.  For instance, if you are teaching about simple interest, you can have the words simple interest, the formula for simple interest with each variable identified as to it's meaning, with an example at the end.  Most teachers have students who are English Language Learners, who have always struggled with math, or who end up needing extra assistance in class.

A word wall in mathematics should include more information because so many words are associated with a formula.  For instance, we talk about the Pythagorean theorem and assume students should know the formula of a^2 + b^2 = c^2 is one definition of it.  They also need the visual so they know what a, b, and c represent.  So instead of just listing the words "Pythagorean theorem", they need everything associated with it so they understand the context.  

If word walls are set up with as much information as possible associated with each word, it provides an immediate reference for students so they become more important.  If you are using the Pythagorean theorem to solve a ladder against the wall problems and a student doesn't remember it, they can look over at the word wall, read up on it quickly without having to ask the teacher.  

Furthermore, it allows the teacher to point to the material rather than falling back on the "You should have learned it three years ago." comment.  Sometimes students didn't learn it the first time, or the second time and by having everything on the wall, they have immediately scaffolding and support available.  If a student asks about something, the teacher can refer to the material on the word wall. 

In addition, maintaining a word wall shows students that the teacher cares about the students and their learning. When parents come in for teacher-parent meetings, the parents see that you care since they can see the word wall.  The word wall also provides automatic connections to previous topics.  A student might night always remember how to set up a coordinate grid and having it on the wall allows students to do a quick check and it exposes students to the topic another time thus helping them learn it better.

A math word wall is also considered a low floor, high ceiling activity allowing students different entry points depending on their need.  By providing visual information with more limited verbal explanations, students with learning disabilities, who are English Language Learners, or are afraid of math, are all able to access the material.

On Wednesday, we'll explore different ways to create a word wall in your math class.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

If you have two pizza's.  One has a radius of 6 inches and the other has a radius of 7 inches, how much more area does the second one have compared to the first one.  Express the answer in percentages and in square inches.

Warm-up

If the radius of this pizza is 4 inches, what is the perimeter of the pizza?

Hooks To Start The Day With.

I'm always hearing that I need to hook students at the beginning of the period but I don't always know what to do.  I've used games such as Bingo, Kahoot, Estimysteries,  and I've even created short movie trailers to introduce the next concept but I know there are more things I can do to capture their interest. My goal is to have a months worth of hooks available to start class with.

There are several "hooks" teachers can use to engage students in the class. Once you capture their attention, it is easier to keep their focus through the rest of class and that is important.  

First show a list of words associated with the next topic to the students. After a moment or two, have students guess the topic they are going to learn about.  For instance, you are getting ready to introduce algebraic fractions so you could use words like part, whole, variables, common denominators to peak their interest. 

Or one can start with a short game such as Kahoot, bingo, a web based game, a dice or card game, or even a team building game.  I've used bingo before to cover many concepts. I pass out an empty bingo card so students can fill it out based on a list of possible answers.  I pull out questions which students have to workout to find the solution.  I've done it with fractions, binomial multiplication, trinomial factoring, geometric shapes, angles, and more.  

I've done relays where I divide the students up into teams, pass out a sheet with say 5 problems. The first person completes the first problem, the second person solves the second problem etc till all the problems are done. The first team with all the problems done correctly wins.  If they get done and I check the problems, they have to check their work if I find one wrong answer. 

I ran across a suggestion for the teacher to show a short video clip.  The video clip is shown in class and then students are asked to share "what they notice?", "what they wonder?" and what type of math do they see in the video.  You can also use a 3 act task that begins with a video or you can use iMovie to create a trailer that introduces the next topic.  I've made a couple that were a mission impossible type and another one that was a romantic type trailer to introduce complementary and supplementary angles.  

Incorporate activities that ask them to think about real world situations such as in Estimation 180, Would you rather, or Which one doesn't belong.  I've used all of them before and they were a great way to have students explain their thinking while using math to justify their answers.  The nice think about the Which one doesn't belong is that there are multiple answers so every student can be "right". 

There is always the Notice and wonder activities one can begin with.  You find an interesting picture, show it to the students so they can communicate what they notice about the picture and what they wonder about the situation.  

None of these activities should take more than 10 minutes.  They get the students into the right mood and allow students to practice their mathematical communications while hooking them so they are engaged in the lesson.  Let me know what you think, I'd love to hear.  Have a great day.

Making Your Own 3 Act Tasks

The nice thing is that all 3 act tasks follow a very specific pattern which makes it easy to create your own if you like.  The opening act where you grab student attention must have a picture or video which does not contain all the information.  The video might be one you create yourself by filming you doing something or it might be a photo.   I found this photo which is from a coffee shop.  It lists prices, extras, and sizes but it does not list the number of ounces in the regular or large sizes.  This menu is something most students would connect with since many high school students enjoy a cup of coffee.

This picture allows for quite a few notice and wonder comments.  This is also one that a teacher might have a question chosen or they might use a question the class comes up with. When choosing the question, it is important to know what information is visible and what information would be needed.  For this type of photo, I'd call or visit a few shops that sell coffee or tea and find out if the regular and large sizes are standard, how many ounces are generally in the espresso and other drinks so you can answer questions and ask students questions that touch on their prior knowledge in Act 2.  

Act 2 is where the students try to figure out what information they have and what they still need in order to answer the question.  It is important to have the additional information ready for students who need additional information. This is also where students use the information to come up with an answer to the question.  Act 3 is where the teacher has the answer prepared for the question that was chosen ahead of time or the teacher can work it out at the time.  I usually go with the preselected question so I can have it finished ahead of time. 

This site has the information from a two day workshop on creating a three act play.  If you go about half way down the page to the section labeled documents and click on the one that says Lesson Plan Template under day 2, it will provide a chart with questions to help you plan the 3 act task.  For act 1, it asks what question will you use and what responses are you expecting from the students. For act 2, it asks you what information is needed, where will they get the answer, what solutions are you expecting, and what are the different entry points.  For act 3, it asks you to determine the possible errors, and how the discussion will help enhance the learning.  It also asks about sequels, and to think about the title.  To the right side is a set of links to already done 3 act tasks you can use if you'd prefer.

If you prefer using a templets, Desmos offers a nice three act templet where one can insert the picture or video, insert the question for the Act 1 of the activity, making an estimation, sketch the estimation, going back to the estimation, class answers .  For act 2, it asks students to remember the question asked before asking what information is needed to answer the question, asks if there is enough information to answer the question after identifying what information is provided in the picture or video, before asking for their solutions,  The last slide is the reveal.  It asks students if their answers are the same and to share their thinking.  In addition, Desmos has a collection of 3 act tasks done for you using Desmos. 

Now you have everything you need to make your own 3 act tasks.  Let me know what you think, I'd love to hear.  Have a great day.

Why Use A Three Act Task

A three act task is an activity designed to engage the whole class while challenging them because these are open ended.  The three act task is made up of part one which captures their attention and hooks them, part two has them finding out more and working towards a solution while the third part has them share their answers, their thoughts, and the way they found their solutions.

We know that the three act task provides an engaging situation for students to use the math while developing better understanding.  These tasks are set up so the student wonders what comes next.  The nice thing about three act tasks is that they provide few barriers to students trying them and the teacher can implement scaffolding as needed.  This activity also provides opportunities for students to discuss and communicate their mathematical thoughts, reflect, and refine.

The three act task is a nice way to help students build new knowledge from prior knowledge, allows students to attack the problems using multiple approaches, creates situations for students to practice mathematical modeling, and helps students develop their mathematical thinking.  Not all three acts are done in the same exact way.

The three act task is designed so each task fulfills certain skills.  In the first act, the students are shown a video, a picture, or other presentation to set up the problem.  For instance, the teacher shows the students a picture found at a coffee shop where the size and prices of coffee are listed for both cold and hot coffee.  The teacher projects the photo and students talk about what they notice and what they wonder.  They brainstorm questions they could ask about the photo and together they might decide what the question is the class should answer.  Sometimes, the first act may have a specific question for students to explore. It depends on the type of three act task.

For the second act, students work on finding the solution to the question asked.  They use the information they have from the photo or video.  If they need additional information, they can ask the teacher for it.  They might have to adjust their questions as they work through the problem.  

In the final act, students share their work, their thinking, and their justifications. The teacher then reveals possible solutions to the question and has students discuss their answer as compared with the solution provided by the teacher or solutions provided by other students.  They can discuss the assumptions they made as they worked on the solution and how their assumptions compared to the ones the teacher or others used.  The teacher can also ask students what other questions they might have answered with the setup.

These are great activities to do and they can be done in one day or each part can be done over a period of three days depending on the time available in class.  On Wednesday, I'll be talking about creating your own three act tasks.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

If this pearl ring costs $12,500, how many pearl rings of this type could you purchase for a half a million dollars?

Warm-up

Estimate the value of this broach if each black pearl costs $225 each while the white pearls average $60 each?

Reading A Math Textbook

I would love to take the time to have students read the math textbook but I've found few students who arrive in high school knowing how to do it.  In fact, most students try to read the math textbook the same way they do an English or Social Studies textbook.  I suspect that is because they are not taught how to do it.  The school I've been working at uses a set of textbooks in Elementary that are more a book full of worksheet so they never really learn so when they get to middle school, they don't have that skill.

Unfortunately, the skills needed to read a math textbook are different than those used for English or Social Studies. Although in a math textbook, it combines passages of English explanations are combined with examples, diagrams, and drawings.  This means the student cannot scan the text the way they do in English, or History.  It is necessary to read every single word in order.

In addition, it is important to pause to make sense of the material in small chunks.  Instead of reading the section straight through, it is important to read a paragraph, pause to think about it, then take time to understand exactly what it is saying.  If a student does not understand it, they may need to break it down into smaller units, or they might need to look up the mathematical vocabulary.  The student may need ro reread the passage multiple times to get the meaning and once they understand it, they may move on.

When they hit any examples, they need to read each step and the associated explanation. They need to see why each step is there and what is happening during each step.  It is important that they do not skip any steps or explanations because what follows the skipped material makes it harder to understand what is going on. 

Furthermore, they should work each example out on their own beginning with having the book open so they can refer to the example if they get stuck.  Once they are comfortable working the problem, close the book and try the problem. When they can work the example problem through with the book closed, they are ready to move on to the next example.  

This is important because the problems at the end of the section, on quizzes, and in exams, are going to be similar to the problems the author worked out.  If a student can work out all the examples on their own, they will do well with homework assignments, quizzes, and exams.  

Students need to read all the notes contained in the margins of the section. Often these notes offer additional information to clarify or remind students of things.  Too often, students ignore these pieces of information and it may be exactly what they need to piece all the pieces together.

Finally, students need to carefully study each and every picture, diagram, or drawing in the section.  They need to read all the written titles and explanations associated with them so they know what is going on.  It is important to understand the information being conveyed by any and all illustrations since many help clarify the concept.

In other years, I took time to teach students how to read a math textbook on the days we had really short classes such as on Fridays after lunch.  The 20 minute class was great for practicing one of the skills they needed to learn so they could effectively read a math textbook. Let me know what you think, I'd love to hear.  Have a great day.  Enjoy your weekend.

Using Math Journals To Assess Students.

 

If you have students use math journals, at some point you'll have to read through them. Do you need to grade them regularly?  How do you use the material contained in the journals to help assess student understanding?  

Use the journals to help you, the teacher, determine more about your students and their understanding.  When you read the entries think about these things such as is the answer correct?, Does the students thought process support the solution they obtained?, If they have to come up with a numerical solution, did they show all their work or did they rely on "mental math"?, Is there something more you want to know about the student's thinking and process?

It is not necessary to comment on every entry, every day.  The only time a teacher really needs to leave feedback is when assessing for personal progress, otherwise a checkmark works fine.  When you leave feedback, do not use the general "Good job" type comments.  You should leave more specific comments that are in response to what they wrote.  Focus on the mathematics used in the problem, their reasoning, or  make suggestion on their thinking.  Take this one step further by meeting one on one with each student for a more personalized interaction.

Since journal entries often require students to show their thinking or reasoning, teachers can use the information to understand their thinking and progress.  In addition, the information can be used to plan the next lessons based on their understanding or misunderstanding of the material.  It allows the teacher to provide extra support to students who need additional scaffolding and providing extensions for those who have mastered the topic.

Furthermore, there has been at least one study done showing that when math journals are used for assessment, the entries actually show the level of student understanding for a specific topic whereas problems on a test can be done without full understanding of the concept. When students use math journals, they've showed an improvement mathematical thinking, vocabulary, and student showing improved understanding of the concept.

If you want to do some sort of daily assessment, you can do the assessment based on did they complete the assignment? Or did they use some sort of diagram or drawing to visualize it?  Students are not being graded on the correctness of the solution so they are more willing to try and it allows teachers to see where any misunderstandings lay.

Therefore, math journals are a great way to see where the students are at and what is needed to correct misconceptions.  They provide ongoing evidence and data for the teacher to plan lessons that meet their needs so much better.  Let me know what you think, I'd love to hear.  Have a great day.

Math Journaling

 

I have not used math journals in the last couple of years for several reasons. One reason is simply that the district I worked for was very much into following the pacing guide and it didn't have this activity incorporated into the textbook experience.  The second reason is that once the pandemic hit, it was hard enough teaching students with all the restrictions going on.  

Using math journals in the math class room help the student boost their learning.  It is also a great way to introduce writing into the classroom.  It has been shown that when students use a math journal, it helps them expand their thinking, and make sense of the problems that they might find confusing.

In addition, students are able to express their thoughts, and examine and monitor their thinking. It also provides a record of their thinking for the teacher to monitor their progress, understanding, and areas of misunderstanding.  A journal can be used in so many different ways in the classroom.  Some teachers have students record all their notes and sample problems in a journal.  Other times, students are asked to record entries at the end of class so they can discuss what they learned, what questions they still have, what they still don't understand, or reflect on their understanding.

A math journal can also be used with math prompts.  A math prompt is usually a beginning sentence, or question that requires students to finish it. It might ask them to compare and contrast two topics such as squares and rectangles, one and two step equations, etc.  It might be more general like "What I know about  __________ so far is ________.  The prompt might ask students to discuss why they are sure they got the right answer, or explain another strategy they could have used to solve the problem.  A math prompt is great for giving students a starting point otherwise they might just copy half their notes to show what they learned or they might not know what to write.

A journal can also be used to help students learn to explain their thinking.  A good way to help students is to work one on one by having them explain their reasoning. Let them begin the explanation verbally and then after one or two sentences, ask them to write it down.  Have them read back what they wrote and explain them to continue telling you more about their thinking, then have them write down what they just explained verbally.  Let them read it back and have them explain more.  Continue the read, explain, write down until they've finished the explanation.

Use the math journal as a starting point for a class discussion.  Assign the same activity to all your students.  When they are done, ask them to record how they carried out the assignment in their journals.  Collect the journals.  Overnight, read through the entries and select a few to read out to the classroom without mentioning who wrote them.  The next day, read out each one to the class while having students "see" what the writer had done.  If they couldn't, have students suggest what additional details are needed to make it clearer.  When done, ask the students to go back, review what they wrote, and make changes to improve their explanations. 

Next time, I'll explore how teachers can use math journals as effectively as possible in class.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

Create a key to go with this pie chart.  List what each color represents and it's approximate percentage.