problem solving mathematical investigation and modelling module

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Problem Solving, Mathematical Investigation, and Modeling (6081)

This course intends to enhance the students’ knowledge and skills in dealing with real-life and/or non-routine applications of mathematics. Students will have the opportunity to explore the use of problem-solving strategies or heuristics as they engage in mathematical investigations, formulate and justify conjectures, make generalizations, and communicate mathematical ideas.

• Teacher: MELANIE GURAT
• Enrolled students: 2

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Mathematics: Problem Solving and Investigations

A list of resources containing activities which could be integrated into your scheme of work with the purpose of integrating problem solving and investigational maths work into the natural process of learning mathematics and not just as a bolt-on added extra.

The first few resources are aimed at primary mathematics with the remainder aimed at Key Stages 3 & 4.

Making Molecules

Quality Assured Category: Mathematics Publisher: cre8ate maths

This activity asks students to investigate the structure of hydrocarbons.  A printed sheet representing carbon and hydrogen atoms is cut up and used by students to build as many isomers as they can for two chemical formulae.

Students are then challenged to discover a 3-D shape with 60 vertices, made from regular pentagons and hexagons. Teachers may choose to give 12 pentagons and 20 hexagons to groups of students for them to build the model or make up the shape from its net.

Problem Cards

Quality Assured Collection Category: Mathematics Publisher: Nuffield Foundation

This collection contains two packs of problem cards that have been designed for use by students in conjunction with the main work described in the Teachers' Guides. It is intended that the majority of students should at least be able to 'have a go' at most of the questions, but should also be encouraged, to the full extent of their individual abilities, to think around a problem and to devise alternatives and generalisations.

There are two packs of problem cards, purple and red, each accompanied by a teachers' guide.

Starting Investigations

Quality Assured Category: Mathematics Publisher: Collins Educational

A book of mathematical investigations aimed at students working at National Curriculum levels 1 to 3.

Contains forty simple investigations covering topics such as Odds and Evens, Place Value, Number patterns and many more.

Badger Maths problem solving

Quality Assured Category: Mathematics Publisher: Badger

A series of resources aimed at years one through to six aimed at developing problem solving skills. Each resource gives an example of a four step problem solving approach and task cards split into levels.

Problem solving with EYFS, Key Stage One and Key Stage Two children

Quality Assured Category: Computing Publisher: Department for Education

A set of resources from the National Strategies aimed at years one to six designed to help students become proficient problem solvers in mathematics.

Problem Solving Tasks

Quality Assured Collection Category: Mathematics Publisher:

The Spode Group have produced a number of resources to support problem solving in mathematics through real life problems.

The resources contain a wide range of open-ended tasks, practical tasks, investigations and real life problems still useful today to place the mathematics learnt in the classroom into a real world context.

Bowland Maths: Assessment Tasks

Quality Assured Collection Category: Mathematics Publisher: Bowland Charitable Trust

Bowland Maths includes over thirty tasks designed to help assess students’ achievements and progression against key processes. To help with this assessment, each task contains sample work, and a 'progression table' showing how students’ work on the task can provide evidence of their progress with the four key processes: representing, analysing, communicating and reflecting.

These materials are also ideal for formative assessment that concentrates on providing the types of rich feedback that have been proven to help students improve their reasoning.

Graded Assessment in Mathematics (GAIM)

Quality Assured Collection Category: Mathematics Publisher: Nelson Thornes

GAIM is a teacher assessment scheme for Key Stages Three and Four. The scheme is designed to encourage teaching and learning through practical problem solving and investigations,  involve students in all assessment and record keeping and introduce continuous assessment into normal classroom practice.

Investigative and Problem-Solving Approaches to Mathematics and Their Assessment

Quality Assured Category: Mathematics Publisher: Institute of Physics

This resource was written in response to the Cockroft Report to address the recommendation that all mathematics teaching should include opportunities for exposition by the teacher, discussion between teachers and students and between students themselves, practical work, consolidation and practice, problem solving and investigational work. The purpose of the pack was to address these issues and support their introduction and assessment.

Design a Board Game

Quality Assured Category: Mathematics Publisher: Shell Centre for Mathematical Education

In this Shell Centre module, groups carefully design and produce their own board games. These games are then played and evaluated by other class members.

Plan a Trip

In this Shell Centre module students plan and undertake a class trip using costings, scheduling, surveys and everyday arithmetic.

Produce a Quiz Show

In this Shell Centre modlue, Produce a Quiz Show, students devise, schedule, run and evaluate their own classroom quizzes.

Pure Investigations

These two books from the Shell centre focus on the pure investigations.

Problem Solving and Mathematical Modelling

• First Online: 14 May 2023

Cite this chapter

• D. N. P. Murthy 3 &
• N. W. Page 4  

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Together with the growth in knowledge over time, there has been a corresponding increase in the complexity of problems that need to be solved. The advances in computational capacity and methodology over recent decades, discussed in Section  8.7 , have provided invaluable tools with which to tackle these problems.

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This is the same for professionals in other linking disciplines as well as for several support disciplines.

From the Greek word problēma meaning, among other things, an obstacle, something that is in the way.

Adapted from Merriam-Webster https://www.merriam-webster.com/dictionary/problem accessed 27June2022.

There can be many other elements such as cost, constraints, impact of solution, risk, etc.

Jonassen ( 2011 ) defined 10 kinds of problems and they vary primarily along related continua of well-structured/ill-structured, simple/complex and static/dynamic. This includes the four kinds of engineering problems discussed in the next section.

Domain knowledge is the knowledge relating to the underlying processes or mechanisms.

System knowledge deals with conceptual models of the system including system components and interactions, fault states (fault characteristics, symptoms, contextual information, and probabilities of occurrence); troubleshooting strategies such as search-and-replace, serial elimination, and fault testing procedures.

Problem solving involves different skills. These are discussed in Chapter 10 .

Facione ( 2016 ).

Mathematical modelling involves different skills. Chapter 10 deals with skills.

This is also referred to as system characterisation.

Most text books on statistics cover these two topics.

Facione, P. A. (2006). Update critical thinking: What it is and why it counts . Insight Assessment, California Academic Press. http://www.insightassessment.com/t.html

Jonassen, D. H. (2011). Learning to solve problems: A handbook for designing problem-solving learning environments . Routledge.

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Murthy, D.N.P., Page, N.W. (2023). Problem Solving and Mathematical Modelling. In: Education and Research for the Future. Springer, Cham. https://doi.org/10.1007/978-3-031-29685-7_9

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The Opening Days of Trump’s First Criminal Trial

Here’s what has happened so far in the unprecedented proceedings against a former u.s. president..

This transcript was created using speech recognition software. While it has been reviewed by human transcribers, it may contain errors. Please review the episode audio before quoting from this transcript and email [email protected] with any questions.

It’s the first day of the Trump trial and just walking out the door in my house. It’s a beautiful day, 6:11 AM. The thing that keeps running through my head is it’s kind of amazing that hundreds of jurors are going to show up at the Manhattan courthouse. And some of them are going to know what they’re there for — probably talking to their friends, their relatives about it.

Some of them are going to learn this morning talking to other jurors in line, asking what all the fuss is about. But I really do imagine that there’s going to be at least one potential juror who, headphones on, getting into court. Here they’re going to be there for the first criminal trial of Donald J. Trump. And just, I mean, how would you react?

[MUSIC PLAYING]

From “The New York Times,” I’m Michael Barbaro. This is “The Daily.” Today, what it’s been like inside the lower Manhattan courtroom, where political and legal history are being made? My colleague, Jonah Bromwich, on the opening days of the first criminal trial of a US President. It’s Thursday, April 18.

Is that his mic? Hi, there.

Hello. How are you?

I’m doing good.

OK. Thank you for coming in, Jonah —

Thank you for having me.

— in the middle of a trial. Can you just explain why you’re able to even be here?

Sure. So we happen to be off on Wednesdays during trial, so.

We being not “The New York Times,” but the courts.

That’s right.

Which is why we’re taping with you. And because we now have two full court days of this history-making trial now under our belts. And the thing about this trial that’s so interesting is that there are no cameras in the courtroom for the wider world.

There’s no audio recordings. So all we really have is and your eyes and your notebook, maybe your laptop. And so we’re hoping you can reconstruct for us the scene of the first two days of this trial and really the highlights.

Yeah, I’d be happy to. So on Monday morning, I left the subway. It’s before 7:00 AM. The sun is just rising over these grandiose court buildings in lower Manhattan.

I’m about to turn left onto Center Street. I’m right in front of the big municipal building.

And I turn onto Center Street. That’s where the courthouses are.

I’m crossing.

And I expected to see a big crowd. And it was even bigger than I had anticipated.

Here we go. Here we go. Here we go. Now, I finally see the crowd.

You have camera banks. You have reporters. You have the beginnings of what will eventually become a protest. And you have this most New York thing, which is just a big crowd of people.

[CHUCKLES]: Who just know something is going on.

That’s right. And what they know is going on is, of course, the first trial of an American president.

All right, I’m passing the camera, folks. Camera, camera, camera, camera. Here we go.

Let’s start with Sharon Crowley live outside the courthouse in Lower Manhattan.

I want to get right to ABC’S Aaron Katersky who’s outside of the courthouse.

Robert Costa is following it outside the courthouse in Lower Manhattan. Bob, I saw the satellite trucks lined up all in a row. Good morning.

Talk to us how we got here exactly.

So this is the case that was brought by the Manhattan district attorney. So prosecutors have accused Donald Trump of covering up the actions of his former fixer, Michael Cohen, after Cohen paid hush money to Stormy Daniels. Stormy Daniels had a story about having had sex with Donald Trump, which Trump has always denied.

Cohen paid her money, and then Trump reimbursed Cohen. And prosecutors say that Trump essentially defrauded the American people because he hid this information that could have been very important for the election from those people when he reimbursed Cohen.

Right. And as I remember it, he also misrepresented what that reimbursement was. Claimed it was a legal fee when, in fact, it was just reimbursing Michael Cohen for a hush money payment.

Exactly, yeah. He definitely didn’t say reimbursement for hush money payment to Stormy Daniels. It’s a cover up case. It’s a case about hiding information you don’t want people to see.

Right. And of course, the context of all this is that it is in the middle of a presidential election. It’s 2016. Trump wants to keep this secret, prosecutors allege, so that the American public doesn’t know about it and potentially hold it against him.

Right. And prosecutors are telling a story about election interference. They’re saying that Trump interfered with an election. And Trump himself is also using the phrase “election interference.” But he’s painting the trial itself as election interference as he now runs again in 2024.

Fascinating.

And because we’re in Manhattan, and because the jury pool is going to be largely Democratic, and the judge is a Democrat, and the district attorney is a Democrat, Trump keeps claiming he cannot get a fair shake. This is democrat central. And in democrat central, Trump doesn’t have a chance.

OK. So, what happens once you actually enter the courthouse?

Outside, there’s all this fanfare. But inside, it’s a little bit business as usual. So I go up to the 15th floor, and I walk into the courtroom, and I sit down, and it’s the same old courtroom. And we’re sitting and waiting for the former president.

Around 9:30, Trump walks in. He looks thin. He looks a little tired, kind of slumping forward, as if to say with his body like let’s get this over with. Here we go.

The judge walks in a little bit after that. And we think we’re all set for the trial to start, but that’s not what happens here. And in fact, there are a series of legal arguments about what the trial is going to look like and what evidence is going to be allowed in.

So, for example, prosecutors ask that they be allowed to admit into evidence headlines from “The National Enquirer” that were attacks on Trump’s 2016 opponents — on Ted Cruz, on Marco Rubio, on Ben Carson.

Because prosecutors are in some sense putting Trump’s 2016 campaign on trial. These headlines are a big part of that because what prosecutors say they show is that Trump had this ongoing deal with “The National Enquirer.” And the publisher would promote him, and it would publish damaging stories about his opponents. And then crucially, it would protect Trump from negative stories. And that’s exactly what prosecutors say happened with Stormy Daniels. That “The National Enquirer” tipped Cohen off about Stormy Daniels trying to sell her story of having had sex with Donald Trump, which he denies. And that led to the hush money payment to her. So what prosecutors are doing overall with these headlines is establishing a pattern of conduct. And that conduct, they say, was an attempt to influence the election in Trump’s favor.

And the judge agrees. He’s going to admit this evidence. And this is a pretty big win for the prosecution. But even though they win that one, they’re not winning everything.

They lose some important arguments here. One of them was that after the Access Hollywood tape came out, there were allegations of sexual assault against Donald Trump. And you know this, Michael, because you reported two of them — two of the three in question at this very trial.

Prosecutors had hoped to talk about those during trial in front of the jury to show the jurors that the Trump campaign was really, really focused on pushing back against bad press in the wake of the Access Hollywood tape in which Trump seemed to describe sexual assault. That was a big problem for the campaign. Campaign did everything it could to push back, including against these allegations that surfaced in the wake of the tape.

But the judge, saying that the allegations are hearsay — that they’re based on the women’s stories — says absolutely not. That is incredibly prejudicial to the defendant.

Interesting.

And that Donald Trump would actually not get a fair trial were those allegations to be mentioned. And so he will not let those in. The jurors will not hear about them.

So this is a setback, of course, for the prosecution, a victory for Trump’s legal team.

It’s a setback. And it also just shows you how these pre-trial motions shape the context of the trial. Think of the trial as a venue like a theater or an athletic contest of some sort. And these pre-trial motions are about what gets led into the arena and what stays out. The sexual assault allegations — out. “The National Enquirer” headlines — in.

OK. And how is Trump sitting there at the defense table reacting to these pre-trial motion rulings from the judge?

Well, as I’ve just said, this is very important stuff for his trial.

Right. Hugely important.

But it’s all happening in legal language, and I’m decoding it for you. But if you were sitting there listening to it, you might get a little lost, and you might get a little bored. And Trump, who is not involved in these arguments, seems to fall asleep.

Seems to fall asleep — you’re seeing this with your own eyes.

What we’re seeing, overall, including our colleague, Maggie Haberman, who’s in the overflow room and has a direct view of Trump’s face — I’m sitting behind him in the courtroom, so I can’t see his face that well.

You guys are double teaming this.

That’s right. I’m sitting behind him, but Maggie is sitting in front of him. And what she sees is not only that his eyes are closed. That wouldn’t get you to he is asleep.

And we have to be really careful about reporting that he’s asleep, even if it seems like a frivolous thing. But what happens is that his head is dropping down to his chest, and then it’s snapping back up. So you’ve seen that, when a student —

I’ve done that.

(CHUCKLES) Yeah. We all kind of know that feeling of snapping awake suddenly. And we see the head motion, and it happens several times.

Lawyers kind of bothering him, not quite shaking him, but certainly trying to get his attention. And that head snapping motion, we felt confident enough to report that Trump fell asleep.

During his own criminal trial’s opening day.

Does someone eventually wake him up?

He wakes up. He wakes up. And in fact, in the afternoon, he’s much more animated. It’s almost as if he wants to be seen being very much awake.

Right. So once these pre-trial motions are ruled on and Trump is snapped back to attention, what happens?

Well, what happens in the courtroom is that the trial begins. The first trial of an American president is now in session. And what marks that beginning is jurors walking into the room one by one — many of them kind of craning their necks over at Donald Trump, giggling, raising their eyebrows at each other, filing into the room, and being sworn in by the judge. And that swearing in marks the official beginning of the trial.

The beginning is jury selection, and it’s often overlooked. It’s not dramatized in our kind of courtroom dramas in the same way. But it’s so important. It’s one of the most important parts of the case. Because whoever sits on the jury, these are the 12 people who are going to decide whether Trump is guilty or whether Trump is innocent.

So how does jury selection actually look and feel and go?

So, jury selection is a winnowing process. And in order to do that, you have to have these people go through a bunch of different hurdles. So the first hurdle is, after the judge describes the case, he asks the group — and there are just short of 100 of them — whether they can be fair and impartial. And says that if they can’t, they should leave. And more than half the group is instantly gone.

So after we do this big mass excusal, we’re left with the smaller group. And so now, jurors are getting called in smaller groups to the jury box. And what they’re going to do there is they’re going to answer this questionnaire.

And this part of the process is really conducted by the judge. The lawyers are involved. They’re listening, but they’re not yet asking questions of the jurors themselves.

And what’s on the questionnaire?

Well, it’s 42 questions. And the questions include, their education, their professional histories, their hobbies, what they like to do whether you’re a member of QAnon or Antifa.

Whether you’re far left or far right.

That’s right. Whether you’ve read “The Art of the Deal,” Trump’s book, which some prospective jurors had.

Right. It was a bestseller in its time.

That’s right. And some of it can be answered in yes/no questions, but some of it can be answered more at length. So some of the prospective jurors are going very, very fast. Yes, no, no, no, yes.

Right. Because this is an oral questionnaire.

That’s right. But some of them are taking their time. They’re expanding on their hobbies. So the potential juror in seat 3, for example, is talking about her hobbies. And she says some running, hiking. And then she said, I like to go to the club, and it got a huge laugh. And you get that kind of thing in jury selection, which is one of the reasons it’s so fun. It’s the height of normality in this situation that is anything but normal.

Right. The most banal answer possible delivered in front of the former president And current Republican nominee for president.

Well, that’s one of the fascinating parts about all this, right? is that they’re answering in front of Trump. And they’re answering questions about Trump in front of Trump. He doesn’t react all that much. But whenever someone says they’ve read “The Art of the Deal —” and there are a few of those — he kind of nods appreciatively, smiles. He likes that. It’s very clear. But because there are so many questions, this is taking forever, especially when people are choosing to answer and elaborate and digress.

This is when you fall asleep.

This Is. When I would have fallen asleep if I were a normal person.

And by the end of the day. Where does jury selection stand?

Well, the questionnaire is another device for shrinking that jury pool. And so the questionnaire has almost these little obstacles or roadblocks, including, in fact, a question that jurors have seen before — whether they would have any problem being fair and impartial?

Hmm. And they ask it again.

They’re asked it again. And they’re asked in this more individualized way. The judge is questioning them. They’re responding.

So, remember that woman who said she liked to go to the club got a big laugh. She reaches question 34. And question 34 reads, “Do you have any strong opinions or firmly-held beliefs about former President Donald Trump or the fact that he is a current candidate for president that would interfere with your ability to be a fair and impartial juror?” She said, yes, she does have an opinion that would prevent her from being fair and impartial. And she, too, is excused.

So that’s how it works. People answer the questionnaire, and they get excused in that way, or they have a scheduling conflict once they reach the jury box. And so to answer your question, Michael. At the end of day one, given all these problems with the questionnaire and the length of time it’s taken to respond to and people getting dismissed based on their answers, there is not a single juror seated for this trial.

And it’s starting to look like this is going to be a really hard case for which to find an impartial jury.

That’s the feeling in the room, yeah.

We’ll be right back.

So Jonah, let’s turn to day 2. What does jury selection look like on Tuesday?

So when the day begins, it looks almost exactly like it looked when the day ended on Monday. We’re still with the questionnaire, getting some interesting answers. But even though it feels like we’re going slow, we are going.

And so we’ve gone from about 100 people to now there’s about 24 the room there’s 18 the jury box. And by the time we hit lunch, all those people have answered all those questions, and we are ready for the next step in the process.

Voir dire. And what it is the heart of jury selection. This is the point where the lawyers themselves finally get to interview the jurors. And we get so much information from this moment because the lawyers ask questions based on what they want out of the jurors.

So the prosecution is asking all these different kinds of questions. The first round of wajir is done by a guy named Joshua Steinglass, a very experienced trial lawyer with the Manhattan District Attorney’s Office. And he’s providing all these hypotheticals. I’ll give you one example because I found this one really, really interesting. He provides a hypothetical about a man who wants his wife killed and essentially hires a hitman to do it. And what he asked the jurors is, if that case were before you, would you be able to see that the man who hired the hitman was a part of this crime?

And of course, what he’s really getting at is, can you accept that even though Michael Cohen, Trump’s fixer, made this payment, Trump is the guy who hired him to do it?

That’s right. If there are other people involved, will jurors still be able to see Donald Trump’s hands behind it all?

Fascinating. And what were some of the responses?

People mostly said, yes, we accept that. So that’s how the prosecution did it.

But the defense had a totally different method of voir dire. They were very focused on their client and people’s opinions about their client.

So what kind of questions do we get from them?

So the lawyer, Todd Blanche, is asking people, what do you make of President Trump? What do you think of President Trump?

And what are some of the responses to that?

Well, there’s this incredible exchange with one of the jurors who absolutely refuses to give his opinion of Donald Trump. They go back and forth and back and forth. And the juror keeps insisting you don’t need to know my opinion of him. All you need to know is that I’m going to be fair and impartial, like I said. And Blanch pushes, and the guy pushes back. And the only way the guy budges is he finally kind of confesses almost at the end that, yes, I am a Democrat, and that’s all we get.

And what ends up happening to this potential juror?

Believe it or not, he got dismissed.

[LAUGHS]: I can believe it. And of course, it’s worth saying that this guy and everybody else is being asked that question just feet from Trump himself.

That’s right. And you might think you were going to get a really kind of spicy, like, popcorn emoji-type exchange from that. But because these are now jurors who have said they can be fair and impartial, who, to some extent, want to be on this jury or at least wouldn’t mind being on this jury, they’re being very restrained.

Mostly, what they are emphasizing — much like that guy just described dis — is that they can be fair. They can be impartial. There’s one woman who gives this really remarkable answer.

She says, I thought about this last night. I stayed up all night. I couldn’t sleep, thinking about whether I could be fair. It’s really important to me, and I can.

What ends up happening to that particular juror?

She’s also dismissed. And she’s dismissed without any reason at all. The defense decides it doesn’t like her. It doesn’t want her on the jury. And they have a certain number of chances to just get rid of jurors — no questions asked.

Other jurors are getting dismissed for cause — I’m doing air quotes with my hands — which means that the lawyers have argued they actually revealed themselves through their answers or through old social media posts, which are brought up in the courtroom, to be either non-credible, meaning they’ve said they can be fair and they can’t, or somehow too biased to be on the jury.

Wait, can I just dial into that for a second? Are lawyers researching the jurors in real time going online and saying — I’m making this up — but Jonah Bromwich is a potential juror, and I’m going to go off into my little corner of the courtroom and Google everything you’ve ever said? Is that what’s happening in the room?

Yeah, there’s a whole profession dedicated to that. It’s called jury consultant, and they’re very good at finding information on people in a hurry. And it certainly looked as if they were in play.

Did a social media post end up getting anybody kicked off this jury?

Yes, there were posts from 2016 era internet. You’ll remember that time as a very heated one on the internet, Facebook memes are a big thing. And so there’s all kinds of lock him up type memes and rhetoric. And some of the potential jurors here have used those. And those jurors are dismissed for a reason.

So we have these two types of dismissals, right? We have these peremptory dismissals — no reason at all given. And we have for cause dismissals.

And the process is called jury selection. But you don’t actually get selected for a jury. The thing is to make it through all these obstacles.

You’re left over.

Right. And so when certain jurors are not dismissed, and they’ve made it through all these stages, by the end of the day, we have gone from zero juror seated to seven jurors who will be participating in Donald Trump’s trial.

Got it. And without going through all seven, just give us a little bit of a sketch of who so far is on this jury. What stands out?

Well, not that much stands out. So we’ve got four men. We’ve got three women. One lives on the Upper East Side. One lives in Chelsea. Obviously, they’re from all over Manhattan.

They have these kind of very normal hobbies like spending time with family and friends. They have somewhat anonymous jobs. We’ve got two lawyers. We’ve got someone who’s worked in sales.

So there’s not that much identifying information. And that’s not an accident . One of the things that often happens with jury selection, whether it be for Donald Trump or for anyone else, is the most interesting jurors — the jurors that kind of catch your attention during the process — they get picked off because they are being so interesting that they interest one or the other side in a negative way. And soon they’re excused. So most of the jurors who are actually seated —

Are not memorable.

Are not that memorable, save one particular juror.

OK. All right, I’ll bite. What do I need to know about that one particular juror?

So let me tell you about a prospective juror who we knew as 374, who will now be juror number five. She’s a middle school teacher from Harlem. And she said that she has friends who have really strong opinions about Trump, but she herself does not. And she insisted several times, I am not a political person.

And then she said this thing that made me quite surprised that the prosecution was fine with having her on the jury. She said, quote, “President Trump speaks his mind, and I’d rather that than someone who’s in office who you don’t know what they’re thinking.”

Hmm. So she expressed approval of President Trump.

Yeah, it was mild approval. But the thing is, especially for the defense in this trial, all you need is one juror. One juror can tie up deliberations in knots, and you can end with a hung jury. And this is actually something that I saw firsthand. In 2019, I was the foreperson on a jury.

How you like that?

Yeah. And the trial was really complicated, but I had thought while we were doing the trial, oh, this is going to be a really easy decision. I thought the defendant in that case was guilty. So we get into deliberations, but there’s this one juror who keeps gumming up the works every time we seem to be making progress, getting a conversation started.

This juror proverbially throws up his hands and says, I am not convicting. This man is innocent. And we talked and we talked. And as the foreperson, I was trying to use all my skills to mediate.

But any time we made any progress, this guy would blow it up. And long story short, hung jury — big victory for the defense lawyer. And we come out of the room. And she points at this juror. The guy —

The defense lawyer.

The defense lawyer points at this juror who blew everything up. And she said, I knew it. I knew I had my guy.

OK. I don’t want to read too much into what you said about that one juror. But should I read between the lines to think that if there’s a hung jury, you wonder if it might be that juror?

That’s what everyone in the courtroom is wondering not just about this juror, but about every single person who was selected. Is this the person who swings the case for me? Is this the person who swings the case against me?

These juries are so complex. It’s 12 people who don’t know each other at the start of the trial and, by the end of the trial, have seen each other every morning and are experiencing the same things, but are not allowed to have talked about the case until deliberations start. In that moment when deliberations start —

You’re going to learn a whole lot about each other.

That’s right. There’s this alchemical moment where suddenly, it all matters. Every personality selected matters. And that’s why jury selection is so important. And that’s why these last two days are actually one of the most important parts of this trial.

OK. So by my math, this trial will require five more jurors to get to 12. I know also they’re going to need to be alternates. But from what you’re saying what looked like a really uphill battle to get an impartial jury or a jury that said it could be impartial — and Trump was very doubtful one could be found — has turned out to not be so hard to find.

That’s right. And in fact, we went from thinking, oh, boy, this is going awfully slowly, to the judge himself saying we could be doing opening arguments as soon as Monday morning. And I think that highlights something that’s really fascinating both about this trial and about the jury selection process overall.

One of the things that lawyers have been arguing about is whether or not it’s important to figure out what jurors’ opinions about Donald Trump are. And the prosecution and, I think, the judge have really said, no, that’s not the key issue here. The key issue is not whether or not people have opinions about Donald Trump.

Right. Who doesn’t have an opinion about Donald Trump?

Exactly. They’re going to. Automatically, they’re going to. The question is whether or not they can be fair and impartial. And the seven people we already have seated, and presumably the five people that we’re going to get over the next few days and however many alternates — we expect six — are all going to have answered that question, not I hate Trump; I love Trump, but I can weigh in on the former president’s innocence or guilt, and I can do it as fairly as humanly possible.

Now, Trump is not happy about this. He said after court yesterday, quote, We have a highly conflicted judge, and he’s rushing this trial.” And I think that he is going to see these beats of the system the criminal justice system as it works on him as he is experiencing it as unfair. That is typically how he talks about it and how he views it.

But what he’s getting is what defendants get. This is the system in New York, in the United States. This is its answer to how do you pick a fair jury? Well, you ask people can you be fair? And you put them through this process, and the outcome is 12 people.

And so I think we’re going to see this over and over again in this trial. We’re going to see Trump experience the criminal justice system.

And its routines.

Yeah, openings, witnesses, evidence, closings. He’s going to go through all of it. And I think, at every turn, it makes sense to expect him to say, well, this is not fair. Well, the judge is doing something wrong. Well, the prosecutors are doing something wrong. Well, the jury is doing something wrong.

But at the end of the day, he’s going to be a defendant, and he’s going to sit, mostly silently if his lawyers can make him do that, and watch this process play itself out. So the system is going to try and treat him like any other defendant, even though, of course —

— he’s not. And he is going to fight back like no other defendant would, like no other defendant could. And that tension, him pushing against the criminal justice system as it strives to treat him, as it would anyone else, is going to be a defining quality of this trial.

Well, Jonah, thank you very much. We appreciate it.

Of course. Thanks so much for having me. [MUSIC PLAYING]

PS, have you ever fallen asleep in a trial?

I have not.

[CHUCKLES]:

Here’s what else you need to know today.

It’s clear the Israelis are making a decision to act. We hope they do so in a way that does as little to escalate this as possible and in a way that, as I said —

During a visit to Jerusalem on Wednesday, Britain’s foreign Secretary left little doubt that Israel would retaliate against Iran for last weekend’s aerial attack, despite pressure from the United States and Britain to stand down. The question now is what form that retaliation will take? “The Times” reports that Israel is weighing several options, including a direct strike on Iran, a cyber attack, or targeted assassinations. And —

Look, history judges us for what we do. This is a critical time right now, critical time on the world stage.

In a plan that could threaten his job, Republican House Speaker Mike Johnson will put a series of foreign aid bills up for a vote this weekend. The bills, especially for aid to Ukraine, are strongly opposed by far-right House Republicans, at least two of whom have threatened to try to oust Johnson over the plan.

I can make a selfish decision and do something that’s different, but I’m doing here what I believe to be the right thing. I think providing lethal aid to Ukraine right now is critically important. I really do. I really — [MUSIC PLAYING]

Today’s episode was produced by Rikki Novetsky, Will Reid, Lynsea Garrison, and Rob Zubko. It was edited by Paige Cowett, contains original music by Marion Lozano, Elisheba Ittoop, and Dan Powell, and was engineered by Chris Wood. Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly Lake.

That’s it for “The Daily.” I’m Michael Barbaro. See you tomorrow.

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• April 16, 2024   •   29:29 A.I.’s Original Sin
• April 15, 2024   •   24:07 Iran’s Unprecedented Attack on Israel
• April 14, 2024   •   46:17 The Sunday Read: ‘What I Saw Working at The National Enquirer During Donald Trump’s Rise’
• April 12, 2024   •   34:23 How One Family Lost $900,000 in a Timeshare Scam
• April 11, 2024   •   28:39 The Staggering Success of Trump’s Trial Delay Tactics
• April 10, 2024   •   22:49 Trump’s Abortion Dilemma
• April 9, 2024   •   30:48 How Tesla Planted the Seeds for Its Own Potential Downfall
• April 8, 2024   •   30:28 The Eclipse Chaser
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Hosted by Michael Barbaro

Featuring Jonah E. Bromwich

Produced by Rikki Novetsky ,  Will Reid ,  Lynsea Garrison and Rob Szypko

Edited by Paige Cowett

Original music by Dan Powell ,  Marion Lozano and Elisheba Ittoop

Engineered by Chris Wood

Listen and follow The Daily Apple Podcasts | Spotify | Amazon Music

Political and legal history are being made in a Lower Manhattan courtroom as Donald J. Trump becomes the first former U.S. president to undergo a criminal trial.

Jonah Bromwich, who covers criminal justice in New York, explains what happened during the opening days of the trial, which is tied to Mr. Trump’s role in a hush-money payment to a porn star.

On today’s episode

Jonah E. Bromwich , who covers criminal justice in New York for The New York Times.

Background reading

Here’s a recap of the courtroom proceedings so far.

Mr. Trump’s trial enters its third day with seven jurors chosen.

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The Daily is made by Rachel Quester, Lynsea Garrison, Clare Toeniskoetter, Paige Cowett, Michael Simon Johnson, Brad Fisher, Chris Wood, Jessica Cheung, Stella Tan, Alexandra Leigh Young, Lisa Chow, Eric Krupke, Marc Georges, Luke Vander Ploeg, M.J. Davis Lin, Dan Powell, Sydney Harper, Mike Benoist, Liz O. Baylen, Asthaa Chaturvedi, Rachelle Bonja, Diana Nguyen, Marion Lozano, Corey Schreppel, Rob Szypko, Elisheba Ittoop, Mooj Zadie, Patricia Willens, Rowan Niemisto, Jody Becker, Rikki Novetsky, John Ketchum, Nina Feldman, Will Reid, Carlos Prieto, Ben Calhoun, Susan Lee, Lexie Diao, Mary Wilson, Alex Stern, Dan Farrell, Sophia Lanman, Shannon Lin, Diane Wong, Devon Taylor, Alyssa Moxley, Summer Thomad, Olivia Natt, Daniel Ramirez and Brendan Klinkenberg.

Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly. Special thanks to Sam Dolnick, Paula Szuchman, Lisa Tobin, Larissa Anderson, Julia Simon, Sofia Milan, Mahima Chablani, Elizabeth Davis-Moorer, Jeffrey Miranda, Renan Borelli, Maddy Masiello, Isabella Anderson and Nina Lassam.

Jonah E. Bromwich covers criminal justice in New York, with a focus on the Manhattan district attorney’s office and state criminal courts in Manhattan. More about Jonah E. Bromwich

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