CHAPTER THREE

Chapter Three

It is clear from Chapter Three that working memory is linked to learning.   The authors state that measures of working memory capacity are excellent predictors of children’s academic attainments, especially in Math.

Let’s devote this chapter’s discussion to Math.   What are we doing that we should continue to do?  What should we change?  What can we do to support low working memory in math class?  Can we make the way we teach math more consistent from teacher to teacher and grade level to grade level?  If we were to support all children’s needs in Math class, what would such a program look like?

You are free to discuss any or all of the questions posed, or even pose one of your own.

Chapter 2

I use touch math to help students with number sense. Each number has "touch Points" that the children use so that they have a visual.
When working with money--- a nickel has one touch point, a dime has 2 and a quarter has 5. The children draw the touch points on their paper and count by 5's. Gradually the visual representation is taken away.

Chapter 2

In 2nd grade we ask students to memorize vocabulary words with our weekly whole class reading selections. To help children with weak verbal short term memory we can teach children use their s tronger visuo-spatial short term memory by teaching hand gestures to go with their vocabulary words. This is an example of one of this week's words, its meaning and its gesture.

Word conservation- Meaning protection of Earth's natural resources, plants and animals- gesture-cup hands as if holding earth

The children are introduced to the vocabulary words and their gestures on the first day and we use the gestures everytime we use the words from the story.

Chapter Two Response

When teaching students to multiply and commit their multipication facts to memory, it is very useful to introduce several visual strategies. One strategy is to have students draw or create arrays for the multiplication facts they are working on. Another strategy is to have students use known facts to solve unknown facts. For example, if a student is having trouble remember 6X8, have the student think of a fact he/she already knows. Most students are familiar with their 5's tables early on, so they may say that they know 5X8=40 and 1X8=8 and then add 40+8 to get 48. Having students draw these arrays and coloring an array for 5X8 in one color and an array for 1X8 right beneath or above it (skip no lines on graph paper) can be a great visual to show that the overall array is 6X8=48. Repeated use of this technique (as well as many others) can help students commit their multiplication facts to memory.

Chapter 2 ?

The visual model that I recently used in Math class seemed quite helpful for many to understand the meaning of division, in a picture. The top area has a large center bubble with an amount written in it such as $100.00 and then you draw lines coming out of it- below it would be the number of bubbles you are dividing that money into or by- such as 5 bubbles and then they can see that if you take the $100. and spilt it or divide it by all 5 people/bubbles, each would get $20.00. This seems so simplistic but we often forget that is exactly what many students need to see.

Chapter 2 ?

Students have difficulty remembering vocabulary words. We have them use index cards. The word is written on the unlined side. The definition is written at the top of the lined side. The student creates their own sentence to show the meaning of the word on one side below the definition, then draws an illustration of their sentence. Having them draw their own illustration helps them to "own" that vocabulary word. In math 4th graders are working on long division & struggle to remember the steps for the process. We use the mnemonic device D -M-S-Ch-B (does McDonalds sell cheese burgers). This is still too much for some students to remember, so I pair the initials w/ the corresponding math signs (+, -, x...) When they see the picture of the sign, they remember what to do next.

Chapter 2

This month in math class we are studying measurement. The amount of vocabulary and information to memorize is staggering for a 9 & 10 year old. Most students do well with the pace at which we revisit and learn new material. However, there are many students who are not developmentally ready to memorize the entire customary conversion table. I use two multiple intelligence strategies to solve this problem. The first is through storytelling and the second is through a hands-on manipulation of the units of measurement.

1.) I created a poster that tells the story of "The Land Of Gallon". The Land of Gallon has Four Queens, each Queen has a Prince and a Princess, each Prince and Princess has two Children each. Students love this story. i see them using it all the time.

2.) Students create "Gallon-Bot Man". Capacity is often a tricky concept for kids to remember. Gallon-Bot Man is a fun way for lids to remember how many cups are in a pint, how many pints are in a quart,etc... We use him as a study guide that is pieced together in sections to learn customary conversion of capacity. Big hit with fifth graders. Also, I tie in a writing assignment as well. They must create a character and story to go along with their figure. It helps to personalize the information and make it easier to remember important information.

chapter 2

In order for students to gain understanding in learning the strategies of multiplication, it requires numerous lessons providing various manipulatives. Students needs to "see" how multiplication works! Drawing arrays and using symbols as the factors to determine the product helps in visualizing this mathematical process. Writing and illustrating multiplication stories, as well as, incorporating the proper vocabulary is also beneficial. Multiplication is a learning process that needs to be taught and not merely introduced. Students will learn the rules and how to take the proper "short cuts" in obtaining the correct results. Understanding and mastering the rules of certain tables is essential. Any number multiplied by 0 is always 0, any number multiplied by 1 is always the other number. Knowing that the 2's table is repeated addition, and knowing how to square a factor helps the learning and understanding process. It is not just memorizing the flashcards. The nines trick is helpful to all learning styles. Using counters and dice is also essential for learners to visualize the outcome. Flashcards are needed, as is, verbal response. Chanting and listing the first 12 multiples of the tables is constant reinforcement and a productive way to open up a math lesson. Constant revisiting and setting up a center for math facts has been successful. There are various picture books to read aloud and for students to enjoy when introducing multiplication and throughout the unit.

Ch. 2 Response
An activity that involves memorization is learning the meaning of vocabulary words. Students w/ weak verbal short term memory would benefit by drawing simple pictures of each vocabulary word. This can be done on index cards or large paper, where students also include definition and a sentence. Students think about the word while they are creating the drawing and also can take a mental snapshop of the picture to help them remember the meaning. Another version is to draw a more detailed scene which includes more than one vocabulary word, then the student w/ a stong visuo-spatial memory is able to recall the picture and in turn, determine the meaning of the word. - Cheryl C.

Letter formation

When young children are learning the proper letter (and number) formation in handwriting, which, in essense is memorizing the motor patterns, there are a few strategies I have used that utilize visuo-spatial short term memory.
1. instructing students to "air write" when introducing the letter
2. repeated writing of letter on chalkboards using colored chalk. After a pre-determined amount of time, students will rotate around a table, to repeat the process using a different color. Monitoring is necessary to ensure proper starting point.
3. tracing the letter in sand or salt
4. with partners, students use their finger make the letter or number on their partner's back
5. using scented markers, students trace the letter in various different scents, creating a rainbow scented effect.

The repetition of these activities help students memorize the proper way to form letter and numbers.

In first grade, students are required to learn/memorize 100 basic sight words. Strategies which I use to help students memorize these words are as follows:

1. Monday - put up 1 new sight word. Read it. Discuss its meaning. Use it in a sentence. Say the word again. Clap 1 time for each letter in the word as you orally spell the word. Air write the word as you orally spell the word. Write the word. Repeat for 4 other sight words. Leave words posted on the whiteboard in front of the classroom for the rest of the week befor moving them to the word wall for the remainder of the year.

2. Tuesday - Thursday - Repeated choral readings of all 5 words. Vary the order of the words.

3. Tuesday - Rainbow Writing - Students choose five crayons and write the sight word 5 times as they say each letter and repeat the whole word. For example, write cat in orange as you say c, write the letter c, say a as you write it, and say t as you write it. Repeat the above steps in 4 separate colors while tracing cat already written in orange.

4. Wednesday - Write each word 3 times each. Use each word in cloze procedure. Supply missing letters to boxes representing size and amount of letters in each word.

Hopefully linking the visuo-spatial short term memory(air writing, repeated crayon writing, clapping) to the verbal act of repeating letters and words will increase long term memorization.

Question # 2

Young children learn the alphabet by memorizing it. Parents and teachers help children learn it by singing alphabet songs, exposing children to alphabet books that display a letter and picture of something that starts with the same letter (for example: "A is for apple") and by writing the letters in the alphabet. In classrooms teachers have charts displaying the alphabet and pictures to go with each letter.
Once children have memorized the alphabet they may not need to rely on picture cues and/or songs.
This may seem like a simplistic example of an activity that involves memorization, but it is an important one.

Chapter 2

I find it easier to pair learning classroom rules with movement or physical cues. For example my student are familiar with "give me 5." I will hold up 5 finger when I say this. From the beginning of the year student have been practicing what the "5" are and display the characteristics with only this verbal cue. Since September we have rehearsed that the Give me 5 are eyes watching, ears listening, voices quiet, bodies still, and raise your hand if you want to share. All of these directions are paired with a physical movement by the student and cues by the teacher. There is also a visual poister with pictures displayed in class. When eyes are watching they point to their eyes, ear listening they cup their ears, voices quiet they put a finger to their lips, bodies still they hug them self, and raise your hand they put their hand in the air. This is rehearsed each time it should be demonstrated in the classroom( such as circle time, story time, or instructional time). The demonstration and physical movements are gradually faded out and the students have now memorized what behavior is expected at particular time. It is also easy to redirect children by simply making the physical movement to remind them of the behavior they should be showing. For example if a student is speaking a teacher can establish eye contact and place their finger over their lip and cup their ear. This will tell the student what they should be doing without having to verbally state it, call the child's name, or disrupt the lesson. With practice and movement it is now easier for the student to remember all 5 steps.

The authors suggest that individuals have a "single limited pool of mental resources that support working memory" and "that working memory activities that include difficult processing leave fewer resources to support memory storage". This is truly evident in math word problems. My child reads each word but cannot ferret out the important details so it seems that after about the first 5 or 6 words he is only speaking the words out loud and not comprehending what he is reading. By the time he gets to the actual question sentence he has forgotten what he just read in the sentences before. As a help, I have him try to look these problems not as math but as a mystery where he can look for clues. Now when he reads aloud a problem, any number he sees he says it louder than the other words, which I imagine would be a form of rehersal. After reading through the problem he then goes back and writes down the numbers (what we call facts) and trys to write out the problem. Hopefully by writing down the information it may free up his "limited working memory storage". Unfortunately this process still requires a few prompts to make it happen and this is only in preparation to do the actual problem. It seems that even a simple math word problem is really quite complicated when you break down into individual processes and can see how it can overload a child's working memory just in the details and how information gets pushed out when they search out what steps to take next.
Back in the 60's we learned the multiplication tables in 4th grade. I vividly remember the flash cards and to this day see the image of the cards in my head. I believe the book calls this semantic or stored memory. I don't remember ever learning why 8X8=64, it just was. What was also good was by having the total image of the each multiplication fact memorized it help in remembering the relationship of the numbers which meant that that learning division wasn't really a learning new process, it was just recalling abd re-using longterm memory.
To the question, would memorizing the multiplication tables inside and out, backwards and forwards, so the information becomes longterm memory in a visuo-spatial way, thereby freeing up the child's working memory for the "deciphering the question" be too much for a third grader who struggles in math? We have worked with the cards but have never pushed too hard.

Chapter Two Question

Short-term memory can be divided into verbal short-term memory and visuo-spatial short-term memory.  Very young children tend to remember through visualizing, but at around 7 years of age, many children begin to remember things by their name instead.  At this point, they can begin to use repetition (what we often call memorization) to move information into long-term memory.  However, not all children develop this ability equally. 

Give a specific example of an activity that involves memorization, and describe how students with weak verbal short-term memory might be helped to memorize through the use of their stronger visuo-spatial short-term memory.