How to help your children with homework

In the NCTM “Mathematics Teaching in the Middle School” journal article “Homework: How Much Help is Enough“, suggestions are given to parents with regard to homework help that benefits students, and that that does not.

As a message to teachers, the article points out that while their role is to provide practice opportunity so students can build understandings and make connections, not providing adequately structured homework experiences can set students (and parents) up for failure. To structure positive experiences, teachers should
* assign homework based on previously taught material or material from upcoming lessons to give parents an idea of what their children have accomplished and what is to come.
* assign questions that require higher-order thinking skills
* give students time to read through homework expectations and discuss them with a peer to ensure that they understand what is expected of them
* provide parents with a list of questions they can use to help their child instead of supplying answers. Ex. Would it help to make a list/draw a diagram/break the question into parts.
* provide information to students/parents on how homework is to be assessed and policies for lates/incompletes
* provide parents with resources to help their children Ex. web-based tutorials

As for parents or teachers battling with the question as to whether parents should help their middle school children with homework, the article answers YES. But the authors are quick to point out that the help provided should evolve as children move from elementary to middle years. Middle years students need to develop independence, responsibility and confidence in their abilities and so, need support in getting their homework done and not support in actually doing the homework. The article even goes so far as to suggest that correcting your child’s mistakes, directing them on what to do or saving them from consequences can inhibit their development of independence, responsibility and confidence.

The article suggests that parents can help by:
* providing students with adequate work space, supplies, and time to complete homework
* being informed about the school’s expectations for their child and their child’s progress and achievement

Math 6 – Outcome #1

N6.1 Demonstrate understanding of place value including:

  • greater than one million
  • less than one thousandth
  • solving situational questions using technology.

a. Explain, concretely, pictorially, or orally, how numbers larger than one million found in mass media and other contexts are related to one million by referencing place value and/or extending concrete or pictorial representations.
What are the students interested in? If they are interested in sports, have them research salaries or costs of race horses. If they are interested in health, they could research how many litres of pop are consumed each year in the world.
Use authentic sources such as Tobacco article or Energy_Revenue_Deficit and have children organize numbers found within in place-value charts.
Contrast the way the numbers in above article are written with the way the numbers in Tomato Article are written. Why?
Use visualizations such as Planet Distances to examine large values. Have students use authentic data like http://www.allsands.com/science/planetsdistanc_aju_gn.htm (convert to metric) to create scale representations.

b. Change the representation of numbers larger than one million given in decimal and word form to place value form (e.g., $1.8 billion would be changed to $1 800 000 000) and vice versa.
Have students create popular media using authentic, large-number data. For example, they could write a newspaper article using planet distances, internet hits, or whatever data they researched in step a.
c. Explain, concretely, pictorially, or orally, how numbers smaller than one thousandth found in mass media and other contexts are related to one thousandth by referencing place value and/or extending concrete or pictorial representations.
To bridge from large to small, use visualization like Cells Alive to see what the common rhinovirus looks like when magnified one million times.

If one rhinovirus is 1/1000 000 of the size of a pin head, how big is it in terms of a square mm?
d. Explain how the pattern of the place value system (e.g., the repetition of ones, tens, and hundreds), makes it possible to read and write numerals for numbers of any magnitude.
Use Place Value Tents (template example ) to help students break up numbers and represent them in expanded form.

e. Solve situational questions involving operations on quantities larger than one million or smaller than one thousandth (with the use of technology).
f. Estimate the solution to a situational question, without the use of technology, involving operations on quantities larger than one million or smaller than one thousandth and explain the strategies used to determine the estimate.

Web resources – http://www.emints.org/ethemes/resources/S00001120.shtml

Differentiating Instruction – Betty Hollas – August 24, 25 – Weyburn

Betty Hollas is an engaging speaker who presents useful, applicable activities to complement differentiated instruction. Some of my favourite examples include:

1. Show, Don’t Tell
This is a general vocabulary activity which would work very well with math terms.

Give the students the words to learn and their definitions (on a handout or projected). Working in small groups, students are to DRAW a representation of their term then come up with a GESTURE that represents the term.

Taking turns, the group members present their picture and gesture both before others are allowed to guess at the term being illustrated. Once it has been correctly identified, ALL students repeat the gesture together.

Imagine the ease with which you could review these terms – show the picture and ask for the gesture, gesture and ask for the word,…

2. R.A.F.T.
This activity has been well-used in ELA classrooms for quite a while. But let’s think about applying it to the Math classroom.

R – Role of the writer –

A – Audience for the writer –

F – Format of the writing –

T – Topic of the writing –

• Have a circle write to his polygon friends about how lucky he is to have no straight sides.
• Have an improper fraction write to the textbook company complaining that his name is unfair.
• Have the variable x write to a psychiatrist to get help with his identity crisis

3. Cubing
This activity consists of rolling a die with different choices/activities on each of its six faces. This activity can be made much more fun using the SMART Notebook software’s interactive cubes.

 

4. We Have, Who Has?

I have a triangle, who has two sets of parallel sides?
I have a parallelogram, who has a set of points equidistant from a central point?
I have a circle, who has three sides?

I have 12, who has the square root of 400?
I have 1 ½, who has ¾ + ½ ?

DI – Is not a YES or NO proposition. We do not have a choice about whether or not we should differentiate – we must!

DI – Is not a program, a resource, a new bandwagon. It is a way of thinking.

DI – Strengthens shift from the teacher-centred “I taught it – they should have learned it” focus on how hard we are teaching to the more student-centred focus on how well students are learning.

DI – can help students who need differentiation because of varied interests, abilities or readiness levels.

THE MORE WAYS WE TEACH, THE MORE STUDENTS WE REACH!

PBL

What does PBL look like with technology integration? 

Here is a problem involving permutations and combinations that was designed for a grade 12 (Math B30) audience.  I have used it with grade 9 and grade 11 students as well. The feedback?  Why can’t we do more like this!

A good way to encourage collaboration is to display the problem on the SMARTboard and let the class work through it as a large group.


 

Inquiry Learning

Last week I attended an SPDU session on Inquiry Learning. It was interesting, applicable, but really nothing new. What defines the difference between inquiry, PBL, situated learning,… Or are they all simply slightly different applications of constructivism?

In ETEC 512 we created a concept map of learning theories and in ETEC 530 we created one just on constructivism.  Reviewing the important concepts and how I linked them together and organised them, I realize that the term INQUIRY LEARNING is nowhere to be found.

 

So what is Inquiry Learning anyway?  And how is it different?

 

In my opinion, Inquiry Learning is the practice of asking students questions instead of giving them information.  Feedback tends to turn the assessment back onto the student, asking them to evaluate their performance and suggest areas for improvement.

I think that I have taught using the inquiry approach for many years.  I just didn’t know what it was called!

Math lends itself very well to inquiry processes.  Experienced math teachers can develop progressions of questions that will enable students to apply possessed knowledge, construct new knowledge, and transfer knowledge to new and different problems.

Here is a sequence that exemplifies my understanding of inquiry learning:

2/7 + 3/7

2/x + 3/x

 

2/7 + 3/14

2/x + 3/xy

 

2/7 + 3/5

2/x + 3/y

What are we preparing them for?

As a wrap-up to my ETEC 533 e-folio, I am required to consider the theme of my blog and put together a final consensus of what I have learned over the course of my class experiences. Well, if there is anything that I know with utmost confidence, it is that the more you learn, the more you realize how little you know.

I am a good math teacher. I was a good math teacher when I followed strict behaviourist practices and lead remarkable, linear, lessons. I was a better math teacher when I realized that children’s understanding and retention were not being well served by my practices and I began to use more constructivist methodologies. I believe that I am a better math teacher now because I have added Physics to my teaching assignment. Application, to me, is the point of learning skills.

I have long agreed with technology integration. I have seen children blossom once released from the tedium or extreme frustration with having to perform pencil and paper calculations. I am also adamant that children know the capabilities and limitations of the tools they use, as well as be skilled in many of the processes that they ask technology to perform for them.

But I am not a good teacher because I don’t know what I am preparing my kids for. I don’t know if I am encouraging them to be the creative problem-solvers who will be able to adapt to whatever environment their future affords. Am I knowledgeable enough about what they will face?

I cannot summarize my learning at this point because I have more questions than answers. I know that technology can help me prepare my students. But more than that, I think that creating my own individual Personal Learning Network will help me guide my students into creating one of their own. It is in fostering a natural curiosity, an internal motivation, a love of learning more that I will help to prepare my students for their future.

This class has opened my eyes to programs attempting to help educators step away from the texts, step away from the chalkboard, and step away from pre-determined curriculums. This is liberating and dangerous at the same time.

Technology makes math come alive and makes science real. Technology brings application to the classroom in an authentic way – not like a text-book word problem designed to replicate a real-world situation. Technology affords collaboration, creativity, engagement, learning. Technology connects us and we learn through our connections to the knowledge of others. To finish, I will connect to a presentation made by Wesley Fryer on the need to foster creativity.

Designing the Perfect Learning Experience…

What aspects of the following math and science learning environments would be useful in the design of my perfect learning experience? 

As I navigate the various math and science learning venues, I am aware of two important similarities; interaction and authenticity.  I think that most of the software options attempt to include both, but I am not sure of the degree to which they have succeeded. 

Model-It  

 

I can see limited benefit in the Model-It  visual modeling and simulation tool. The information on the website claims that students can build, test, and evaluate qualitative models without needing to know the underlying calculus driving these models, but I wonder at the reason for doing this.  I created a few models that were not based on any scientific knowledge whatsoever.

 

I believe that the addition of parameters or criteria is missing from this design.  I think that creating a tool that would allow students to model their knowledge and extrapolate from that model would be incredibly beneficial.  In my opinion, the design process used for Model-It did not rely enough on the need for authenticity.

 

NetLogo

 

NetLogo affords design of authentic modelling applets and use of effective models that have been created be skilled designers.  I have used NetLogo in my classroom, specifically the Climate Change model.  Like the Model-It, there is no intrinsic interactive component, but teachers would be free to set up interactive activities within their own classroom.

 

I can see models like those created using NetLogo being of great use in educational settings.  But one danger of the authentic-looking models is to make sure students realize that these models were created to show hypothesized information.  Just as we know that science is always changing, we cannot be completely sure of the science that has gone into the creation of the model.  As educators, we must encourage our students to ask important questions about the source of the underlying data and identify possible biases in the model.

 

Using a combination of activities from Model-It and NetLogo would be beneficial in that it would teach students that models are designed by individuals to represent their knowledge.  When we use a model created by another, it is important to understand their knowledge base.

 

Geometer’s Sketchpad

 

In my resource sharing, I referred others to Geogebra, which is, in my opinion an excellent resource for knowledge visualization and representation.  Geometer’s Sketchpad kicks things up a notch by integrating the Java Sketchpad!

I think that geometric construction software is ideal for math and science education.  The ability to make the sketches interactive adds to the educational value.  The ability of Geometer’s Sketchpad to make the interactions fluid and vibrant using Java adds to the student engagement.  But there is still the question of authenticity.  The question is not with the authenticity of the geometric constructions created in Sketchpad, it is with the students’ understanding that authenticity is required.

 

Imagine having a student create a parallelogram.  Think of the requirements using a compass and a straightedge, or even using a MIRA.  Will students understand that they are constructing parallel sides, congruent angles, congruent sides,… if they use a geometry sketching program without having learned to construct manually?

 

As with Geogebra, I can see value in Geometer’s Sketchpad as a teaching tool, a learning tool, and an assessment tool.  I would forgo all the bells and whistles and stick with the free Geogebra though!

 

Wisweb

 

Wiseweb is an excellent site full of interesting math-based applets that would provide great activities for students using an interactive whiteboard.  There are getting to be a great many of these type of learning object repositories; Illuminations, Interactivate, National Library of Virtual Manipulatives among others.

 

I think that there is definitely a place to integrate these learning objects into our classrooms, but I would caution over-use.  Important discussion about the theory behind the activity must be included and reflected upon before use, during use and after use.

 

Graphing Claculators

 

In my opinion, the use of graphing calculators takes knowledge building in mathematics to a higher level.  But, as with any tool, they must be used responsibly.  Learning how to check pencil and paper graphs of circular functions is an excellent reinforcement of graphing concepts.  Applying transformations to functions to understand change without the tedium of multiple pencil and paper graphs is liberating.  Using calculate functions to determine points of intersection and lines of best fit encourages accuracy. 

 

Imagine the interactive activities one could design using a graphing calculator emulator projected on an interactive whiteboard!

 

However, the Texas Instruments graphing calculators afford much more than graphing capabilities.  The financial and statistical applications of the calculators enable students to calculate monthly payments, future value of investments, and standard deviations at the touch of a button.  It is easy to forgo the complex formulae and rely on the calculator to find the answers.

 

Globe

 

In my opinion, science teachers should use Globe!  Combining interaction with authentic data collected to answer authentic problems is the epitome of ICT use in education.

 

Similar to Journey North  where students around the world are asked to help forward scientific efforts of real scientists, Globe engages students to take part in helping solve real-world problems affecting them and the world around them.

 

Students can learn from the experiences of others, or they can get involved as data collectors, following the data interpretation and use.  Those that are actually charged with collecting the data must follow strict processes, reinforcing important scientific principles.

 

 

 

 

 

 

Geogebra

Geogebra  is an excellent tool for knowledge representation and information visualization.  I see the software having a variety of uses:

 

1.  Allows users to generate accurate diagrams that can be used in quality documents to aid student learning and understanding.  

 

2.  Allows users to create interactive learning objects that can be used to

 

            a. Create interactive worksheets – Pythagorean Theorem

 

            b. Model transformations – Sine Function

            c. Understand Relationships – Relationship between a circle and its equation.

 

3.  Allows students to explore geometric and algebraic relationships by creating constructions of their own.  Try it out!  Go to the Geogebra Webstart and construct a right-angled triangle, an equilateral triangle then an isosceles trapezoid.

            – Use the HELP resources!

 

I shared this math resource with my peers through the ETEC 533 discussion forum.  Honestly, it did not generate any discussion except for a comment about the learning curve for students.  If I look at the uses identified above, the only time that users would need to learn how to use the software would be for the third option where they generate their own applets.  This would, of course, require learning on the part of the students and many would find it frustrating.  However, this would be an excellent activity in terms of knowledge representation as students would need to understand not only how to interact with the software, but also fundamental geometric properties.  

 

The GeogebraWiki is an excellent place for users to go for examples, tutorials, and support.  Many developers have created interactive applets, some integrated with java for exceptional graphics and interactivity, and have offered their products freely to those interested.

If you don’t find what you need on the wiki site, there is a Geogebra user forum that will connect you with users from around the world.  If you have a question about the program affordances or a more specific “how-to” problem, post it to the forum for other Geobebra users to ponder.  Those who have taken advantage of the support find that the service surpasses much of what is available in commercial applications.  Browsing through the Wiki and the forum, one can see knowledge diffusion in action.