Working Memory and Math Word Problems

 

A recent study from the University of Kansas sheds light on a critical cognitive function impacting math word problem-solving: working memory. The research, involving 207 third-grade students with and without math difficulties, underscores the significant role working memory plays in tackling these multi-step problems and suggests that targeted interventions can lead to improvements, particularly for struggling learners.

Working memory, as defined in the study, is the limited capacity our brains have to hold and manipulate information concurrently while performing other tasks. In the context of math word problems, this "mental chalkboard," as described by lead author Michael Orosco, is where students temporarily store the numbers, the question being asked, and the steps needed to arrive at a solution. The study aimed to investigate how working memory influences word problem-solving abilities and whether specific instructional strategies could mediate this relationship.

The researchers randomly assigned students to one of four intervention conditions over an eight-week period: a verbal emphasis strategy (underlining questions, circling numbers, crossing out irrelevant information), a visual emphasis strategy (using diagrams to represent relationships), a combined verbal and visual strategy, and a materials-only strategy (using the same materials without the overt motor activities). Before and after the intervention, students were tested on their working memory capacity and their ability to solve word problems.

The results revealed a strong correlation between working memory and word problem-solving success. Students with higher working memory scores consistently performed better on the word problem post-tests. Importantly, the study found that the implemented strategies, especially those incorporating overt cues like underlining and diagramming, helped to improve students' word problem-solving skills by reducing the strain on their working memory as they gained experience. As Orosco explained, these strategies effectively "free up space in the working memory to learn more information while working to solve problems" by offloading some of the cognitive load.

Furthermore, the interventions showed promise in improving the working memory of students with math difficulties, particularly strategies that progressively increased the complexity of the problems. This suggests that targeted instruction can not only help students utilize their existing working memory more efficiently but also potentially enhance its capacity within the context of problem-solving. However, it's important to note that despite the benefits of the interventions, students without math difficulties continued to outperform their struggling peers.

The study highlights the critical role of working memory in mathematical problem-solving and provides evidence that instructional strategies designed to reduce cognitive load can be beneficial. The authors suggest that future research should further explore the interplay between other executive functions and word problem-solving, as well as the potential of artificial intelligence in understanding these cognitive processes and developing even more effective interventions.

Orosco emphasizes the importance of bridging the gap between educational neuroscience and teacher training, as understanding the cognitive underpinnings of learning difficulties can empower educators with better tools to support all students, including those who don't respond to general instruction. This research contributes to the growing body of knowledge in the science of math, ultimately aiming to improve instruction and outcomes for both students who excel and those who struggle with mathematics. By acknowledging and addressing the limitations of working memory, educators can create more effective learning environments that enable all students to succeed in tackling the complexities of math word problems.  Let me know what you think, I'd love to hear.  Have a great weekend.

Worksheets To Help Master Word Problems

In the world of math education, worksheets packed with word problems often get a bad rap. Some see them as monotonous drill exercises. However, well-designed worksheets can be a powerful tool for developing students' understanding and problem-solving skills, particularly when it comes to tackling word problems. Worksheets also reinforce the ability to read and find important information in different situations.

Worksheets offer a structured platform for practicing key math concepts. They allow students to see problems presented in various formats, reinforcing their grasp of addition, subtraction, multiplication, and division in real-world contexts. This repetition helps solidify the foundation needed to approach more complex word problems later on.

Word problems can be daunting for students. Worksheets, with their step-by-step approach, can act as a scaffold. By providing a series of problems with increasing difficulty, they guide students through the process of identifying relevant information, choosing the appropriate operation, and applying it to solve the problem.

Effective worksheets incorporate varied word problems that require different approaches. This encourages students to develop a toolbox of problem-solving strategies. Some problems might require visualization through drawing a diagram,while others might benefit from creating a table to organize data. This exposure to various approaches helps students become more flexible and adaptable when tackling new challenges.

Successfully solving problems on worksheets builds confidence in students' mathematical abilities. As they progress through the worksheet, they gain a sense of accomplishment and the belief that they can tackle even more complex problems.

Of course, not all worksheets are created equal. Here's what makes a good worksheet.  There should be a variety of problems ranging from easy to hard. The worksheet should offer a mix of problems, starting with easy ones to build confidence and gradually increasing complexity. Problems should contain real world connections.  In other words, problems should be relatable to students' experiences, making them more engaging and helping them see the importance of math in everyday life. Furthermore, one should incorporate diagrams, charts, or illustrations that can help students visualize the problem and approach it strategically.

While worksheets offer a valuable resource, they should not be the sole focus of math instruction. Interactive activities, group discussions, and technology integration can all enrich the learning experience. Worksheets, when used strategically, are a valuable tool for helping students master word problems. By providing a structured platform for practice, building problem-solving strategies, and promoting confidence, they can empower students to approach even the most challenging word problems with a sense of capability. Let me know what you think, I'd love to hear. 

Sparking Ideas

Today I received notification from Next Lesson about two new math lessons that are available at their web site for a small fee.  It was the titles and descriptions that sent my mind scrambling to figure out how to use these ideas in class.

1. Block Buster Movies.  Students could research the top 10 blockbuster movies for the past three months, for the summer, for the year. It all depends on how you want to set it up.  As they research the movies, they could find information on how much did it cost to make vs the amount of profits.  How many theaters did it show in.  What was the average amount per theater.  What is the average cost of a movie ticket?  How many people saw this movie?  Create a chart, an infographic, or a report. 

2.  What about Gross National products, etc.  Students could look up values for economic indicators for 2015, 2010, 2005, and 2000 to show how these indicators have changed over the past 15 years.  Find the economic indicators for several other countries such as Iraq, England, Japan, Korea, Brazil, or Mexico.  Students could prepare charts, compare and contrasts, infographics, etc. 

The above two ideas require the internet to find the information.  They require students to create a compilation of the information, turn it into a readable form, interpret the data, and present it.  All skills that are required in jobs and in college now a days. 

Increasing reading and writing using the iPad.

Wednesday is the day I work with my students on learning to solve word problems.  Since so many are classified as ELL, I make them write down the answers to the following questions:
1. What do I know?
2. What do I need to find?
3.  What things do I need to consider such as special formulas, the operation, additional information to keep in mind or other things.
4. The work.

I need to start using something like Showbie so they can annotate, underline, etc any information in the word problem before writing the information on their worksheet.  I think taking the time to underline, identify and comment on things before writing the information down will help increase their English, cut down on guessing and get them to slow down and really check out the information. I am hopeful this skill will transfer to the mandated testing.

Flash cards

I am having my students do word problems today and it became apparent that my students have issues with some of the vocabulary in terms of operations. 
I introduced students to the KFCW chart which is a math version of KWL.  They have to list what they know or information they are given.  F is used for the part of What do you want to find?  C is what do you need to consider?  This is where they write down what operation do they need to use? Is there some formula they will need to use?  How are you going to solve the problem?  Finally is W which stands for Work. This is where the student shows their work and the solution.  I showed it to the new Science teacher and she is making her students use the same form for science word problems.  I like the consistency between the two classes.
As my students are working the problems they get to the words telling them what operation to apply and they don't really know those words.  I have the SAS flash card app on their iPads, so I think beginning tomorrow, I will have students create flash cards for operation vocabulary so they can test themselves and learn the vocabulary.  I like the SAS flash card app because they can make either text based cards with the word, a picture, a voice over and the answer or an actual math problem. 
Yesterday, I managed to update the OS on all the ipads and downloaded a few different notebook type programs so I can use a different one in each period.  I am hoping that this will eliminate the issue of one student messing with another student's work.  I am hoping to begin the notebooks around mid October.

Using Word salad and other apps in Math.

I saw someone recommend Word Salad as a good app for the classroom.  Since it resembles Wordle, the first thing that entered my mind was simply "Can I use it effectively so the students learn?"  This was followed by "Can it be used to help build higher order thinking skills."  So while looking up more information I stumbled across this column in which the author suggested using word salad in combination with fotobabble to explain their their word salad.  Nice idea.  The other thing about this column was the author gave ways of using the iPads for think, pair, share and jigsaw.  This gives me a starting point on integrating technology into these activities.
As a side note.  I teach mathematics to students who are either ELL or who do not have a huge vocabulary and they have difficulty solving word problems. They grab numbers and try anything till they get the answer. So today I had them do Think, Pair, Share to find the information they are given (Know), Identify what they have to find, and to consider how they will solve the problems.  Since it was the first time I've done this it went a bit roughly but the students did actually talk.  I'll find out what they found when I grade papers a bit later.

Infographics + finding information.

Most of my students are below proficient in writing.  That is the last part of the state test they tend to pass.  I was playing with infographics yesterday and had a great time.  In the process I decided that I am going to see about importing infographics into a program such as subtext and adding some questions so that my students have to find the information and reply using complete sentences.  I can also add in some compare and contrast activities.  Since many infographics have actual stats, it falls neatly into math.  Right now, the students get out early on Wednesdays so teachers can have their weekly meetings.  The length of the classes on Wednesdays are perfect for this activity.  I think I will also do one word problem on Wednesdays using the KWC process. They need to work on taking the time to find information rather than asking me immediately for help.
Tomorrow and Friday, my ebook on Amazon is available free. 

Neat app for word problems.

Found a new app called Subtext.  It allows you to take a book or web page or document and layer things like questions, quizzes, assignments, etc to make it more educational than just reading.  Right now they do not do PDF's but they are working on it and hope to have that facet available by next school year.  I've heard great things about it and it seems to be mostly used for literature or reading.  I tried to think of where I could use this actual application in my math classroom and at first thought about worksheets.  Once they get the PDF feature up and running that would be a possibility but this morning, it hit me.  Word Problems.  Most of my students take the numbers provided in the word problem and guess the operation, hoping for the correct answer.  If I used word problems with this application I could incorporate the KWC  (What do I want to know, what do I need to find and what considerations or special conditions do I need to keep track of).  This is something I could easily layer into the material.   Honestly I do not do enough on word problems and this could give me a tool to help them practice doing word problems.