Thursday, November 19, 2009

Literacy in Math

Startling Statistics

According to the International Reading Association, in 2003, the United States ranked 15th of 29 OECD countries in reading literacy. In 2006 the United States ranked 21st and 25th of 30 OECD countries in scientific literacy and in math literacy, respectively. These numbers are startling considering this is a global economy. Jobs are not just being competed for in the United States, but overseas and beyond.

With teaching math this year, I decided that I wanted to integrate literacy as much as possible. In order to get myself started on this venture, I purchased a curriculum by Sopris West called Step Up to Math: Writing.

Prior to this book, I had been using some strategies that were in my Language Arts teaching arsenal such as summarizing, finding the main idea, and creating leveled questions for students. However, since reading this book cover to cover, I have found many more ways to integrate reading and writing.

The book has 7 sections: vocabulary, reading and taking notes, summarizing text and writing about graphs, asking and answering questions, writing for assessments, writing for general assignments, and creative/personal writing.

The vocabulary section discusses a variety of ways to include vocabulary in your lesson. They suggest that students keep a notebook with vocabulary words, student friendly definitions and a picture or example to go with it. There is a section within vocabulary that has graphic organizers that outline how to break down definitions so students can retain information better. Additionally, there are organizers for creating concept maps, word maps, and word banks. Of all the vocabulary materials, I have to say that my favorite was the section on riddles. The authors explain that writing and solving riddles is one way to integrate vocabulary and spice up the lessons a bit. Here was a riddle example that I particularly liked: People call me sir for short. I like pie. I hang around circles. Who am I? Isn’t that great? By doing these in class and letting the kids create riddles, this is one of many ways to include vocabulary.

The next section, which was reading and taking notes, discusses just that: how to read and take notes in math. Some of the suggestions include 2 and 3 column note taking, which is very similar to Cornell style notes. There is also some examples that show teachers how to make a framed response, or cloze procedure-like paragraph where students fill in main ideas from that particular lesson.

One of my favorite sections of this book was the section that discusses summarizing. Having been a language arts teacher, I can tell you that this is an area of struggle for a lot of students. I feel that by practicing this skill in math, it should come easier to students as they read across all content areas.

Other areas of inspiration from this resource are the sections on creating questions and writing for assessments. There are examples of what open response questions should look like in math using a holistic rubric. Additionally, rubrics are provided and guidelines are given for how you can utilize writing in lessons as practice before they take an assessment.

http://www.cuesd.tehama.k12.ca.us/woodson/SUW%20math/intermediate.html

The website above comes from a school district and has put up the tools online for this curriculum. These are the same tools that came on my cd. However, I would strongly encourage you to purchase the actual book, as it goes into much more detail.

Thursday, November 12, 2009

How to Close a Lesson

Since I started the blog discussing active learning and opening techniques, I figured it may be nice to comment on some of the ways to close a lesson. Everyone has heard the importance of closing a lesson and it just drives me wild when the bell rings and a teacher hasn't taken the time to re-group and discuss with students what the day/concept was all about. I mean, we want them to walk away with something, right?? I feel with some of the strategies listed below, we can give the kids an opportunity to reflect on their learning that took place.

1. Using the mnemonic S.T.O.P. This is pretty self explanatory. On a notecard, students write:
S- We STARTED the lesson....
T- The TOPIC or(theme) was....
O- Our opportunities to practice were.....
P- The purpose of learning this is.....

2. If you started your lesson with a KWL or anticipation guide, come back to the "L" section and have the kids write everything they learned about that particular lesson. With the anticipation guide, have them refer to the "after" section and re-examine the questions they answered from the beginning of class.

3. Another technique that is similar to S.T.O.P. is 3.2.1. With this strategy, give each kid a post it, notecard, scrap paper, etc. Have them write 3 things they found interesting from the lesson, 2 things they learned and then for one, students will write one question they still have. (You can actually use those questions for a fishbowl activity the following day.)

4. Give each student a sticky note and have them solve an example problem on the lesson and slap the stick on the graffiti wall, if you have one in your classroom. If not, have them place the stickys on the board or the door.

5. Have students find the main idea or summarize the lesson. You can use graphic organizers to do this or create a cloze procedure for the kids to fill in. For example:

In Chapter ________________, on page ____________ we studied ____________. First, you start by _______________________________________________. Then, _____________________________________. Finally, __________________________________________________________________________.

6. Allow students to reflect in journals what they are learning about and what still confuses them.

Saturday, November 7, 2009

Activating Prior Knowledge

David Ausubel said, “The single most important factor influencing learning is what the learner already knows.” It has been said many times before that students learn more effectively when they are able to connect new material with something that they already know. By giving the opportunity for connections to be made in the classroom, this can easily spark the interest of a child and motivate them into the topic you are going to be teaching. So, this week, I would like to discuss ways that teachers can activate prior knowledge in the classroom in hopes that you will be able to utilize these strategies in your classroom.


1. KWL- This method has been around since my mom has been teaching, which is about 25+ years. (Maybe it has been around even longer than that!) However, despite its age, KWL organizers are great ways to spark conversation and get a feel for what students actually know about a particular topic. The ‘K’ stands for what students KNOW, the ‘W’ for what they want to know, and the ‘L’ for what they learned. I like this strategy because the ‘W’ should serve as a way to inspire thoughtful, critical thinking. I also think this strategy is beneficial because the “L” serves as a great way to close a lesson or assess what students took from the lesson.

2. Think-Pair-Share- I use this method all of the time in my math class. I think that it is a great way to activate prior knowledge, but it is also a way for students to interact with one another. The way that I use this strategy in my classroom is I will pose a question, in which students will need to think about . I will then have students get with their partner and discuss the question that I asked. Lastly, students from each group share with the class what was discussed in their groups. A few weeks ago, we studied the order of operations. I gave students the following question:

How to Make Cereal

1. Pour milk into bowl

2. Put sugar in bowl

3. Pour cereal into bowl

What is wrong with these directions for how to make cereal? How should they read? Why are following steps important? Where else in our life do we follow sets of rules? Can you provide specific examples?

I chose this because I knew that all students in my class had experience with making cereal, therefore, they would easily connect with this idea. This idea of following rules allowed me to easily transition into my discussion on how the order of operations are specific rules in math we must follow!

3. Real life analogy- I taught a lesson a few weeks ago on prime factorization. The students had to take a number, such as 35, and break it down into its prime factors. (which would be 7 and 5). Anyways, before getting into prime factorization and what the process looked like, I brought in a 10 piece puzzle. I gave each puzzle piece to my students and explained that when we factor a number, it is like breaking the number into pieces, like with the puzzle. Each puzzle piece is a factor. In my analogy, the entire puzzle was like the number 35 and the puzzle pieces represented prime factors.

4. Graphic Organizers- One organizer that I particularly like in math is the T-Chart. As a way to activate prior knowledge on greatest common factor, my class drew a line down the center of their paper. On the left column, they wrote ‘synonyms for the word greatest’ and on the right they wrote, ‘synonyms for the words common’. Then, in groups, students worked together to find the different synonyms and defined GCF on their own!

5. Preview Vocabulary- In my math class, one of the ways that I like to preview vocabulary is by using a semantic map. All you have to do is draw a circle around the vocabulary word you are using and students write all the different words that they associate with that one word. In addition to this, a new curriculum that I purchased, Step Up to Writing: Math, has different graphic organizers and suggestions on how to preview vocabulary. I will post more as I continue to explore this wonderful resource.

6. Link to personal experience- Like the example in the Think-Pair-Share strategy with cereal, I chose this because I knew the kids had personal experience with making cereal. Any time you are able to find that hook or question that most kids have experience with, this is a great way to get the lesson going. Asking questions such as ‘Have you ever…..” is just one way I start lessons and try to link to personal experience.

7. Anticipation Guide- This strategy is used all the time in reading, but it can be used in math, too! Check “Agree” or “Disagree” beside each statement prior to the lesson. Then, students compare their choice and explanation with a partner. After the lesson is over, they revisit their choices and check “Agree” or “Disagree” on the opposite side. Students are then encouraged to compare their answers with the answers noted prior to the lesson.

8. Graffiti Wall- Cover one spot on your wall with butcher paper and invite students to write down their comments about the topic you are studying.

9. Video Clip, Music, Art- Using visual/auditory aids are great ways to activating prior knowledge. Last year when my students were studying theme in my University Prep class, I played the song ‘Umbrella’ by Rhianna for them. They were instructed to listen to the song and then with a partner, explain what they thought the song was about. This introductory activity was a great segue way into a discussion on theme in literature.

Sunday, November 1, 2009

Active Learning Strategies

Confucius said, “I hear and I forget. I see and I remember. I do and I understand.” This quote really is applicable to a concept that is gaining more and more attention: active learning in the classroom. In the past, the traditional teaching model has been that the student listens, while the teacher presents material. This inactive model of teaching has prompted many researchers, such as C. Bonwell and J. Eison, to examine how students really learn best.

So, what does research have to say about some of those traditional modes of teaching? Currently, there is confirmation that students do best when they are involved in their own learning. It has been said that when students learn actively, they are able to remember content for longer periods of time and more readily apply it.

With that being said, I guess this begs the question of what is active learning? Active learning involves providing opportunities for students to meaningfully talk and listen, write, read, and reflect on the content, ideas, issues, and concerns of an academic subject” (Meyers and Jones, 1993, p6).

In this first post on my blog, I want to present some learning strategies that would help teachers promote active learning in their classroom.

Jigsaw- this is a strategy that involves cooperative learning and gets students to be involved in their own learning. The way that it works is that students are divided into groups of 3 or 4. Each member in the group is numbered (1,2,3, or 4) and that is their home base team. Each person in this group is responsible for different subtopics of content. Then, what happens is the ones get with the ones, twos get with the twos, etc and they work to investigate their one subtopic. Once research has been conducted, the home base groups get back together and take turns teaching students in their home base group. While each member in the home base group is teaching to the other members, you can have members record key information in graphic organizers. You can also have the person who is teaching make up their own story problems and have the other students practice the concept.

Reciprocal Learning- this is a strategy that works to promote student partnerships where two different roles are taking place. One student acts as a player, while the other acts as a coach. The way that this strategy works is that you create a set of reciprocal learning sheets to give to each student. The students are working in groups of two and Player A has a copy of Player B’s problems with hints and coaching tips. Player B has a copy of Player A’s problems with hints and coach tips. Together, one acts as a coach and one acts as a player. At the end of this task, there is some sort of cooperative challenge for the students to solve together after they both took their turns acting as a coach and player.

Active learning during lecture- some strategies to use during lecture are as follows:
1.) Give students a set of questions to answer during the lecture.
2.) Take periodic breaks during lecture and ask students to jot down questions they are having.
3.) Give powerpoint notes that have some blanks missing where students are forced to fill in the blanks.
4.) When one student answers a question in class, ask another student to summarize the first students’ response.
5.) Give students a chance to turn to their partner and restate what they heard in their own words to their partner.
6.) Give students a chance to pair up and have one student explain a concept to their partner. Then, have the other student paraphrase (What you’re saying is….)what their partner said.
7.) In the middle of the lecture, stop and ask students to write a short list of everything they know/learned about the topic at hand.
8.) Give students questions to answer as they watch the powerpoint, video, or other multimedia.
9.) Place questions in a paper bag and give the bag to a group of students. One student picks a strip with a question on it and the group must answer the question together. If a question is pulled that you have not covered, put it back and grab a different strip. Then, the group reports their answer to the class.

Write Around- Students are asked place their initials on their paper and answer the question that is posed to them. This question may ask for students to summarize the lesson, it may have students respond with what they learned or wondered about, etc. Then, the teacher tells the students to respond and when time is up, their paper is passed to another student in class. That new student initials their paper and responds to what the first person wrote on their paper. This transfer of paper takes place a few times and then the paper is passed back to its original owner.

Writing a ‘How to’ piece- in math, I have students write complete instructions on how to solve problems all the time. Then, we give the instructions to a different student and ask him/her to follow the directions. If he/she can get through them, then the directions worked out. If not, the student goes back to revise them.

Peer teaching/tutoring- students get in small groups and teach other students about a topic. Make sure to give the kids a heads up on different activities and active learning techniques they can do in their “lessons.”

Transfer of Control- this allows for the students to take on the role as the teacher and serve as the facilitator. One easy way to do this is by giving the students the pen to the overhead and have them come up individually or in groups and present how to do something to the class.

Brainstorm/Factstorm- this can be used as an activity to activate prior knowledge as you begin a new unit. It works by asking a multiple response question and kids brainstorm on large sheets of paper everything they can think of in regards to the question being asked.

Think-Pair-Share- the way that I like to run this activity is that I devise a sheet that says THINK on the top and the question I am posing is written there. I provide blanks for students to write down any thought that they may need to jot down. Below that is a section titled PAIR and it explicitly states that the students must turn to their partner and explain what he/she feels the answer is to the question and vice versa. Then, students take time to SHARE this information aloud with the rest of the class.

Leveled Questions- teach students question answer relationships and the types of leveled questions available. Then have students create leveled questions and have them swap papers with their partners to answer their questions.

Journals- as a starter, students can respond to questions in journals and use those as a segue way to the lesson being presented. You can also use journals in the middle of a lesson or at the closing, where students must summarize what they learned.

Posters- students can work in groups or individually to design posters where kids respond to questions, illustrate how to do a problem, etc.

Comparing notes- this is when you ask kids to exchange notes and others are able to jot down anything that they see could aid in helping understand the concept.

Intentional Errors- give students an example of a problem done incorrectly and have them work through it to try and explain what the error is.

Gallery Walk- this technique actually gets the kids out of their chairs! Using higher leveled thinking questions, you post more than one piece of chart paper around the room with a question on it. Students are then assigned to groups of three and each person has a role. One person is the leader, who keeps the group on task. The other is the recorder who will write out the group's answer on a sticky note and place it on the poster. Another member is a reporter, who will present the group’s thoughts to the class. Give students a rubric that explains how they will be assessed on answering the questions, their behavior, and presentation to the class.

Ticket out the door- this is a summative technique that allows use as a teacher to ask a question of higher order to the students. In order to leave the room, students must answer this question. Another technique that could be used in place of this is posting a large sheet of paper on the door and students can write what they learned for the day on the paper.

Wipe boards- present a problem on the board for the students to solve. Give them a certain number of minutes and when you say, ‘BOARDS UP’, students show their work on their wipeboard with the answer to your problem.

Choral Responding- pose a question to the students and in unison, they respond with the answer.

Students make up their own problem/quiz problem- in math, I often have students make up their own problem and give it to another student or group to solve after I have looked it over.

Numbered Heads- ask students to number off in their teams from one to four. Give a question and set the timer for x minutes. In groups, students work to solve the problem and together come up with an answer. Then, when the timer goes off, call a number and each person with that number from the group has to stand and answer the question.