Scaffolding and Justifications.

  As you know most of my students are classified ELL (English Language Learners) who often have trouble explaining their thinking process in regard to answering questions.

For the majority of students, we have to teach them how to solve performance tasks.  Unfortunately, it is a fine line between telling them every step vs scaffolding the process so they learn to do it on their own.

It is also important to provide opportunities for students to justify their thinking when solving an open ended performance task. The idea is to have students do the same task but focusing on a different aspect so they learn to justify at each step.

The task in this case might be exploring how scaling the sides of a two dimensional figure changes the area of the new figure.  The first time through, students should focus on patterns between the scaling sides and the resulting area.  They are expected to explore the relationship using numerical observations.  it is important to ask for justification at this point so students can express their thoughts and understanding of the patterns.  Setting up a table for students to record their findings like they do in science provides a way to organize the data.

If they start with a square and move on to doing the same activity with rectangles, circles, triangles and trapezoids it allows students to generalize their findings to other figures. The next time through, students are expected to explain why the relationship is true using algebraic and geometric representations rather than the numerical. The students are again asked to justify what they discovered.

The things to keep in mind when scaffolding a task includes designing it so students focus on one facet of it in detail before connecting it to a more generalized view.  Next its important to ask students to justify their reasoning early and often.  Furthermore, students should be prompted to create multiple representations of their thinking. 

In addition, it is important to show how to use different strategies because the use of different strategies can increase student understanding. Take time to help students understand that there is a difference between identifying a pattern and understanding why it works.

This meets the idea that as students learn to explain and justify their thinking, they have taken steps towards being in charge of their own learning.  In addition, it is necessary to create learning activities based on prior knowledge or adjust help tailored to student need as expressed above by focusing on one aspect, then moving towards the more generalized math.

These two activities show the  interrelations  between concepts  and it is something that should be done when scaffolding learning. It is important to do this so students can see that all of mathematics is related.

Let me know what you are thinking.  I'd love to hear.  Have a great weekend.