Teaching Walls: App-Friendly?

Many educators face challenges when it comes to technology since they are unable to easily access apps and programs that they learn of. This lack of ready access prevents the good teaching possible. For example if an educator has access to technology in fluid, workable ways, he/she can test apps and other programs with regularity and student input. However, if the systems for tech access are cumbersome, lengthy, and inaccessible, then educators will quickly lose interest and the needed timeliness to try out new apps and programs and employ them for best student learning.

For teachers to do their work well they need ready, regular access to the best tools, supports, and programs. Teachers do their best work also when they have voice and choice with regard to what they use and how they use it to teach well. When others, distanced from the learning, hold the reigns of teacher tools and programs, voice and choice is diminished and children don't get the deep and dynamic programming possible.

In light of this, systems need to think carefully about the following questions:

• How are curriculum decisions made? Do teachers have voice and choice?
• Are the people choosing the technology distanced from the daily classroom efforts and work?
• Are teachers and administrators asking the right questions when it comes to quality teaching and learning?
• Is there a good synergy between and amongst administration and educators when it comes to curriculum design and implementation?
• How is the entire learning community including students and parents involved in this decision making?
• Do we make decisions based on good informal and formal data analysis, discussion, and debate?

Teach Math Well: Are We Asking the Right Questions?

Emails circulated about the value of using an online unit assessment versus the paper/pencil unit assessments of the past. It's a good question, and one that should be posed and discussed. Personally, I'm a fan of using multiple formal and informal formative and summative assessments, and I support the use of online assessments as part of that overall assessment approach.

I also believe that we have to be mindful to have a good assessment balance and not make teaching and learning all about the test--we have to make space for children to enjoy their learning. While it's important to discuss assessment types and the role of assessment when teaching math, there are also many more questions that beg our attention and discussion.

For example, one of the greatest math question that we face in our standards-based school communities, and how do we continually uplift and teach the students who are one or more years behind the expectations. Of course, I believe that math education should be progressive where every child is moving ahead from where he/she is and that the focus should be on that movement rather than if everyone is at the same level. For example if I have students at fifth grade who are testing at a second grade level and others who are testing at a seventh grade level, they all should be working to move up. I don't want those "seventh grade level" fifth graders to think they've achieved all there is to know in math and sail along without a good challenge, and I also don't want those "second grade level" fifth graders to get discouraged and always feel behind. So the question, How do we challenge all in positive, proactive ways resulting in good math growth, engagement, and knowledge?, is a great question to ask and discuss amongst peers.

Another good question to discuss in math is what are the best ways for specialists, assistants, coaches, and classroom educators to work together to maximize math teaching and learning for all. We have instituted Responsive to Intervention in creative ways that help in this regard. We also differentiate during core instructional times. The way we collaborate matters when it comes to uplifting children's skills, knowledge, and concept.

Further we can ask questions about content specific teaching and learning. For example, at a recent meeting, it was acknowledged that teaching the "behavior" of the base ten place value system is challenging. Students at fifth grade find it difficult to grasp that numbers increase by X10 as they move up each place in the place value system and decrease by 1/10 as they move down in value place by place. Fluency with that concept takes time.

Time is an important consideration. Many on the outside would like teachers to work like soldiers and be at the same place in teaching at the same time. This, in many ways, negates the where students are at and what they need. It also disregards the need for educators to make the curriculum their own and teach it with the artistry, experience, and analysis needed. Good teaching is not a robotic function, and good teaching makes good use of time. Unlike a robotic response, good teaching analyzes deeply and maximizes the use of time to teach all well.

Too often we spend time talking about questions that don't matter that much in education. Instead we should dig a little deeper and spend time discussing what matters--the big, deep questions that truly impact what we can do to better teach all children.

Introduction to Math Workshop

Tomorrow I'll introduce students to Math Workshop.

First, I'll restate why were learning what we're learning, and the many ways students can effectively support their own learning in school and outside of school.

Then I'll say that Math Workshop is a time for you to practice what we're learning in ways that help you learn best.

I'll ask students to practice the place value skills and knowledge we studied yesterday by completing the following tasks:

• Complete the worksheet
• Check in with a teacher anytime you have questions or upon completion
• If done, practice more using Khan Academy Place Value practice, and again when you have questions ask a teacher.

There's no simple way to learn tomorrow's focus skills and knowledge without simply practicing. Students can aid their practice by making the following steps:

• Work alone or with a friend
• Focus on the task
• Use a sharpened pencil or pen that you enjoy writing with
• Take your time and work with precision
• Work quietly so others can concentrate too

I'll set up shop at the big table so that I'm accessible and available to those that need me and for those when they complete the task. Also when students pass in their assignments I'll ask them to read a number of numbers to assess their ability to read numbers. 

The following day students will complete more practice items, then next week we'll focus on the "behavior" of the base ten place value system as we look closely at the ways number increase and decrease as you move up and down the place value system. 

Mathematical Reasoning: Number Sense

How many people live in Massachusetts?

We used five population statistics today as part of the place value unit students are studying.

Early in the day, I asked students how many students they thought were in the school. They made fairly good guesses that were close to our approximately 400 students.

Then I asked how many people live in the town where our school is located. Their guesses were about 100 or 200 more. Later when discussing this more they added rationale that increased the estimate with points such as the fact that there is more than one school, some students don't go to public schools, students have siblings who aren't in school, students have parents, and there are older citizens too. A few came close to 13,000 which is close to the exact number of people.

After that we estimated the amount of people that live in Boston. Students knew it was bigger than our town with more people and most made guesses that doubled, tripled, and quadrupled the town's population. Only a few used more reasoning and experience to compare Boston with cities they had visited or knew about thus guessing larger numbers. As for the United States and world population similarly only a few could come close to the actual number.

When watching the Presidential election debates, I was struck by the large amount of numbers thrown about--numbers that were difficult to imagine and compare when sharing with just language. I found myself wishing there were reliable infographics to help me understand the comparisons, proposals, and critique. I think the Presidential elections of the future will be blended presentations as the information is simply too sophisticated for words alone, thus the back and forth jabs.

Too often too many of us can't quickly make a numerical comparison or imagine a measurement or value. Yet, it's a very important critical thinking and decision making skill.

Working with numbers that relate to students' lives is a first step towards helping to build number sense, and then allowing students to estimate "how many" and explain their rationale for their estimations is a good way to share and develop mathematical reasoning and explanation.

Tomorrow we'll continue working with these numbers as students learn to write and think about numbers in many ways. Onward

Place Value: Population

Tomorrow students will consider the population of the small town where they learn, the state's capital city, the state, the country, and the world.

Using numbers that pique students' interest help them to learn
math with greater depth, interest, and skill. 

Town Population: 13,294 (2014)
Capital City (Boston): 667,137 (2015)
State: Massachusetts: 6,794,422 (v2015)
Country: USA: 324,718,574 (Census Clock)
World: 7,346,044,7784 (Census Clock)

First, I'll hang up the maps of the US, town, Boston, and State around our white board.  Next, I'll simply list the numbers on the board like this:

324,718,574       6,794,422         13,294      667,137   7,346,044,7784

Then I'll say what do you notice about these numbers?

I'll listen carefully to their responses as their observations will inform me about their number knowledge.

After that I'll ask students to order the numbers. I'll mention that mathematicians typically put numbers in order to help their analysis and number work.

I'll then tell them that these numbers represent the population, number of people, that live in the town, capital city, state, country, and world. I'll ask them to guess which number belongs to which location.

Once we have that information we'll focus on the population of Boston.

I'll suggest that we can write that number in many ways, and we'll practice writing the number in the many ways shown below. After that I'll say that it's difficult to remember that number and that's why people often use estimates instead. A ballpark number is easier to remember. We'll round the number to its nearest 100,000.

We'll then round the numbers of the other locations to the nearest highest value the number represents. Finally students will have a chance to write the other numbers in many ways to practice.

Why Math? Looking at Base Ten Place Value with a Systems Lens

We started today's lesson talking about the marriage between math and medicine. That was to provide some rationale for the importance of learning the early math skills we're focused on. Students understood the relationship and were interested in the related story.

Then we thought about the categories that belong to systems think including the parts, structure, function, purpose, and environmental affects.

We then used a systems' lens to begin to study the Base Ten Place Value System also referred to as the Base Ten Numeral System, Base Ten System, and Base Ten Number System.

We discussed the purpose with the question, Why would someone choose to spend their time inventing this system? Students had great ideas about this including communication, common understanding, making life better and easier, and more.

Then we looked at a model of its structure--on paper it looks a bit like a sports field. After that we started looking at the parts beginning with the decimal point which could be known as "The Separator" if it were a super hero since it separates whole numbers from parts or decimal numbers or fractions. We talked about the 10 digits that make up all the numbers in the Base-Ten System, numbers that go to infinity "large in value" and infinity "small in value." We'll watch the famous Eames Power of Ten video to make that more understandable tomorrow.

After that we began inserting powers numbers, words, exponents and expanded form to demonstrate the value of numbers from the ones place to 100,000's place. Tomorrow we'll complete the model by labeling up to the billion's place for the whole numbers and down to the thousandths place for decimal numbers.

Then we'll begin looking at the patterns that exist within the system. I'll have students work with each other to discuss what they notice and then we'll share.

It's a deep introduction to the the base ten system, one that will be followed by the study of how to write numbers in number name and expanded forms, rounding and its rules, and the "behavior" of the base ten system as we move up and down in value. We'll likely weave in the study of the metric system here too since it's directly related.

It's a lot of fun to reveal math concepts, knowledge, and skill with and for students--they're incredibly bright and curious especially when you match math with their lives, interests, and questions.

Fifth Grade: Systems Think

The overall focus of the fifth grade science curriculum is systems think. How might educators thread that theme throughout the math teaching/learning year too?

First, define systems with students.

I like to begin with more sophisticated definitions such as the one I found on Wikimedia.

Then I like to pull the definition apart with main words:

• interacting or interdependent parts forming a complex/intricate whole.
• surrounded and influenced by its environment
• described by its structure and purpose
• expressed in its functioning or behavior
• also refers to a set of rules that governs structure or behavior

After that I put together a fifth grade friendly and memorable definition, one we can return to each time we discuss a new system in math. For example, we can describe systems in this way:

A system is parts that work together with with structure(s), purpose, and behavior to create specific function(s) or result(s). 

With that definition students can study each math unit with a "systems lens" that focuses on the following questions:

• What is the title(s) of this system?
• What are the parts of this system?
• What is the structure (framework) of this system? How can we model and describe this?
• Why was this system created? What is its purpose?
• How does this system work, act, or behave? 
• What is the result or function of this system? What does this system help us to do?

As we study the base-ten place value system, we'll answer these questions.

How do you help fifth grade students to learn math with a systems lens? Why is this important? How will it affect their learning and understanding? What would you add to this approach?