Making connections: Learning math using concrete examples

Like in most classroom these days, in my classroom I have students of varying needs and abilities. This means that I need to plan my lessons and find ways to motivate and engage everyone, as well as reach the greatest number of students, in order to have the majority of my students understand the concepts being taught.

There are many ways of doing this, such as by playing games, by role playing and by providing manipulatives to students. By providing concrete examples, students are more likely to remember the lessons because they will have learned them through visual (eyes), auditory (ears) and kinesthetic (through motion or touch) experiences. Even if students don’t understand everything, they are more likely to get the gist of it and catch on during follow-up lessons and activities.

An example of an activity I did involving this type of learning was when my fourth grade class was learning about the Cartesian plane.

I started by using the tiles on my floor to create a gigantic Cartesian plane. I used circular stickers by Avery to mark the coordinates on the plane and Post-its to identify the vertical and horizontal axes. 

We talked about maps and how we use them to find destinations.

We then compared the Cartesian plane to a Battleship board game, where players must sink battleships that are on hidden coordinates. We looked at how the vertical axis on a Cartesian plane is identified with numbers rather than letters. We discussed how in the Cartesian plane there are zeros, while in Battleship there aren’t any.

We then moved on to talk about another difference between Battleship and Cartesian planes. When we give coordinates in Battleship, it doesn’t matter which order you say the letter or number in, because there is only one row or column labelled C, for example, and one column or row labelled 2. However, the Cartesian plane can be tricky because you need to know the order in which to read the ordered pair describing coordinates. 

I needed to provide visual cues and reminders to my students. I used some Scholastic book display boards and stuck some signs onto them to make them visible to all students.

The next step was to provide ordered pairs on construction paper strips to my students, so that they could work with partners and figure out where to plot their points.

Once their points were plotted, we checked with the entire group to see if they were plotted correctly. We discussed which were correct and why, and figured out why the incorrectly plotted points were in the wrong position and made adjustments to plot them correctly.

I made sure that every students had a turn plotting points on the Cartesian plane before trying to translate what they’d learned to apply it to a 2-dimensional example within their workbooks. More than 90% of my students were able to complete the tasks on their own, without further explanation, because we has explored Cartesian planes in a concrete, hands-on way, while making connections to their prior experiences. 

If you have used similar means to teach math concepts with your students, please share them in the comment section below, or on my Facebook page, by clicking here.

Until my next blog post, don't forget to be the change.

Chantal

Journal writing with a purpose

I absolutely love doing journal writing with my students.

I do journal writing for several reasons.

The first is because my students and I get to know each other well and it helps us build a relationship. Students can express their thoughts and opinions without being interrupted. They enjoy communicating directly with me and I enjoy responding to them.

The second reason I love journal writing with students is because journals provide insight to me about what students need to learn, either having to do with grammar, spelling, sentence structure, content organization or other language arts related concepts. I know from their journals what to base my next writing lessons on.

The third reason I like journal writing is because I can see students’ progress as I flip through the pages of their books. I can see how well they apply my lessons into their writing. I get a good sense if students have assimilated the information from my lessons properly or if we need additional practice.

A student's journal from my fifth grade class

When I do journal writing with students, these are the guidelines I like to follow:

1 1)   Have several topics for students to choose from.

I want for my students to have a lot to write. When I choose topics, I think it is important to spark the desire to express themselves and share their thoughts, their opinions or everything they know about a topic. When I provide only one choice, I cannot be certain to inspire a student to write about a topic. It is better to provide options.

Topics in all grades should be open ended questions. With younger students, they can be expected to respond to journal prompts with complete sentences. With older students like those whom I currently teach, I expect them to provide explanations, justifications and details in their writing.

Examples of prompts for journal writing could be:

What can you, a fourth grader, do to make the world a better place?

Why do you think someone would steal a book from class?

Why should you be allowed to take the class pet home?

Explain why winter could be someone’s favorite season.

   2)   Make expectations clear.

My students know that when I will be reading their journals, I will be checking their work for correct use of grammar concepts that we’ve learned, such as possessives and correct use of apostrophes. They know that I expect students to skip lines to make it easier to read their work and to edit and revise it. Students know that I expect them to provide explanations and details in their writing. Students know that I expect them to check their work.

   3)   Make time for students to share their journals with their classmates.

Journal sharing has many benefits. However, I feel that it is important to agree on guidelines and expectations about respect before the first journal is shared in the classroom. 

Knowing that students might be asked to share their work with their classmates motivates them to be more careful when checking their work. They are more likely to catch mistakes before reading their work aloud. Also, when students read their work out loud, I find that they are more likely to catch their own mistakes and make the appropriate corrections to their work.

In my class, when it is time to share our journals, we sit in a circle to be able to face one another.

When students share their work and hear each other’s comments, they are all more likely to try to make the same improvements to their journals the next time they write.

When students listen to their peers share their journals in class, they are asked to:

-        Think of something positive the writer did, such as the way they used a certain adjectives to describe something.

-        Share constructive criticism on how the writer can improve to their work. For example, a classmate could suggest a synonym for a word that was repeated often in the journal entry.

    When students share their work and hear each other’s comments, they are all more likely to try to make the same improvements to their journals the next time they write.

    4)   Respond to your students’ work appropriately.

     If I want students to feel comfortable pouring their thoughts and hearts out onto their paper, I do not correct their work.

     I’ve learned that if students find their work covered in ink when it is returned to them, they are less likely to take risks and to write all of their thoughts. They are more likely to stick to writing what they are sure they can spell correctly and to topics that are familiar with.  

     Instead, I choose the most repeated or important mistake from their writing and model the correct spelling or use of grammar so that they can then go back and make the corrections themselves.  I use the information acquired from the journal entry to direct my next lessons.

The words two, chicken and vegetables were misspelled.
I made sure to include these words in my response to my student. 

   5)   Expect students to make improvements to their work.

     I expect my students to go back and check their work. If I have completed a grammar lesson about the proper use of possessives, then I will expect my students to go back and check their work. 

     If there were some recommendations made by a classmate to improve a journal entry, I expect all of my students to go back and see if they could make the same adjustments to improve their writing. 

    

     I also expect my students to read my comments and check their work if they noticed the correct spelling I may have used for a word they had misspelled in their text. 

Note the editing in the journal entry, with inserts and eraser marks, from peer review and noticing ways that the text could be improved and clarified. 

    

    Please share in the comment section below, what you like or dislike about journal writing with students and the ways you use journals to teach your students about writing. 

Engaging students with the Plickers app

For those of you who aren’t familiar with the Plickers, it is an app that allows teachers to project multiple choice questions on their Smartboards through a live feed and for students to answer the questions them by holding up their Plickers card, a QR code card, upright in the position that represents their answers for their teachers to scan with the app on an iPhone or iPad.

Are you confused?

That’s okay.

Here’s what a Plickers card looks like.

In my class, I have written each student’s name on their cards and have had my students color code the possible responses.

In order to prevent students from losing their cards, I have made simple tuck in pockets inside students’ desks to ensure that the cards all have a safe place to land. I just took a strip of construction paper and taped in on three sides to slide the Plickers cards into. 

When I start using Plickers with a new group of students, I initiate them by asking general questions, such as "What is your favorite colors? Favorite seasons? Favorite school subject?", etc.

I project the questions and the possible answers on the Smartboard for all students to see, with the Live Feed view. For the purpose of the exercise, I choose the option to display student names and their responses on the screen. Students practice holding up their cards and holding them in the right direction.

With the teacher’s device (my iPad or iPhone), I could see which cards had been scanned, as well as the answers they provided.

Meanwhile, on the Live Feed screen on the Smartboard, students can verify if their card has been scanned properly and if the response matches what they intended to display.

Now that students are familiar with Plickers, I use it to have students inform me of their Daily 5 choices, to do anonymous (to students) class surveys about the amount of time they studied for a test and I can quiz my students on any topic or concept that I choose to get immediate feedback of their understanding.

Plickers keeps a log (archive) of answers that were provided so I can check the answers in the future for reporting purposes.

I can also keep different folders for different groups containing different questions. It is really simple and quick to use.

Students love using Plickers. They like that everyone has a voice and can share their opinions and their answers with the group. 

Plickers also provides an anonymous way of providing answers and prevents students from influencing each other’s responses (no more students looking around the classroom to see who has their hand up before deciding whether or not to raise his or her hand up as well).

I especially like that now I can be spontaneous in asking student questions because they are organized and always have their Plickers cards handy! 

Try using Plickers if you haven't yet and let me know what you think in the comment section below. 

Enjoy!