### Teaching Student Centered Mathematics Book Study: Chapter 3-6

Chapter 3- Assessment
Chapter 3 is titled "Assessing for Learning" and discusses methods of assessment and recording which allow assessment to be a tool which informs and creates a path to learning as opposed to purely summative assessment.

When used properly, formative assessment will allow you to determine what your students currently know, will help you to determine where your students need to go and will all give insight into how to go about moving your students to where they need to be. The author laid out 3 types of formative assessment including:

• Observations- Noting a students progress as they work on a given task. Student progress can be recorded in the form of anecdotal notes- short observations focused on a target goal or checklists. Checklists can be created per student with multiple standards or per standard with an entire class list on one page. When choosing either type of checklist you can note whether a student has not yet met, met, or is working above the standard. By leaving the checklist boxes large enough, you can write a date in each box to show growth over time.
• Interviews- An interview may be used when you need additional information on a child so you can learn more about why a child is having difficulty. This will generally be done 1:1 while other students are working to complete a task. The most important tip when conducting a diagnostic interview is to be mindful of the language you use so as to avoid teaching or otherwise evaluating a child's work
• Tasks- The tasks in this chapter reminded me of the "learning through problem solving" in the last chapter. When assigning a high quality task, you will have the opportunity to learn more about what your students understand vs. what they can do by rote as you may observe on a traditional summative assessment.
Chapters 4 & 6- Differentiation
The authors stressed that differentiation does NOT mean planning a separate lesson for each student but using what you know about your students to make tweaks which will allow each student to get the most out of the lessons you teach.

Differentiation may include:
• Parallel Tasks- Parallel tasks include giving multiple tasks that each reach the same end goal but at different levels. When creating parallel tasks, the numbers in a given problem may be adjusted to create a higher level of difficulty or to make a task more accessible. Parallel tasks could also be adjusted in other ways.
• Open Questions- These questions could have more than one correct answer and could be arrived at in a variety of manners. These questions may include situations where you give the answer and ask the students what the question might be, might ask a student to study attributes or may not include enough information for a student to fully answer the question.
• Learning Centers
• Tiered Lessons- Tiered lessons assure that all students will meet the same goals although some students may receive additional assistance, solve a differently structured task or may have a differing level of complexity in the task or process.
• Flexible Grouping- The main point the author made when discussing flexible grouping included being sure to use a mix of homogeneous and heterogeneous groupings and to be sure that all of the "high kids" and "low kids" are not always contained to like ability groupings.
Chapters 5- Cultural and Linguistic Diversity
Math is often referred to as a "universal language" but this chapter made it exceedingly clear that this is not always the case. The way that math is taught, the procedures students are expected to use and the language around mathematics can vary dramatically from country to country.

I was suprised to learn that the "standard algorithm" for subtraction varied so dramatically from country to country as the authors illustrated. I have included a link to a Youtube video which explains the traditional way of teaching subtraction in European countries.

Another consideration when teaching math to an ELL student is around the language involved in mathematics. So many words used in math are used differently than how we traditionally use them in our language. The text points out words such as "foot", "table", and "difference" to name only a few.

If you have not already, be sure to pop over to Adventures In Guided math as they are graciously hosting this blog hop and will have links to additional participants.