listbox isSelected databinding in DataTemplate

Question

I try to simply databind IsSelected property with IsSelected field in my class. But after I change the value in code, it doesn't change the property, neither does clicking on ListBoxItem change the field value.

XAML:

<FlipView ItemsSource="{Binding Source={StaticResource itemsViewSource}}" ... >
    <FlipView.ItemTemplate>
        <DataTemplate>
            <UserControl Loaded="StartLayoutUpdates" 
                Unloaded="StopLayoutUpdates">
                <!-- other controls -->
                <ListBox Grid.Row="1" Grid.ColumnSpan="3"
                    SelectionMode="Multiple" VerticalAlignment="Center" 
                    ItemsSource="{Binding Answers}">
                    <ListBox.Resources>
                        <local:LogicToText x:Key="logToText" />
                    </ListBox.Resources>

                     <!-- bind IsSelected only in one way from 
                         code to content --> 
                     <ItemsControl.ItemTemplate>
                        <DataTemplate>
                            <ListBoxItem 
                              IsSelected="{Binding IsSelected, Mode=TwoWay, Converter={StaticResource logToText}}" 
                              Content="{Binding IsSelected, Mode=TwoWay, Converter={StaticResource logToText}}">

                            </ListBoxItem>

                        </DataTemplate>
                    </ItemsControl.ItemTemplate>


                    <!-- not working at all
                    <ListBox.Resources>
                        <Style TargetType="ListBoxItem">
                            <Setter Property="IsSelected" 
                                Value="{Binding IsSelected, Mode=TwoWay}"/>
                            <Setter Property="Content" 
                                Value="{Binding IsSelected, Mode=TwoWay}"/>
                        </Style>
                    </ListBox.Resources>-->

                </ListBox>
            </UserControl>
        </DataTemplate>
    </FlipView.ItemTemplate>
</FlipView>

Code:

Answers

private ObservableCollection<PrawoJazdyDataAnswer> _answers = 
    new ObservableCollection<PrawoJazdyDataAnswer>();
public ObservableCollection<PrawoJazdyDataAnswer> Answers 
{ 
    get 
    { 
       return this._answers; 
    }  
}    

Single item(Answer)

public class PrawoJazdyDataAnswer : NPCHelper// PrawoJazdy.Common.BindableBase
{
    public PrawoJazdyDataAnswer(String ans, bool ansb)
    {
        this._ans = ans;
        this._isSelected = ansb;
    }

    public override string ToString() 
    { 
        return _isSelected.ToString();  //Only For debug purposes 
                                        //normally return _ans 
    }
    private string _ans;
    public string Ans
    {
        get { return this._ans; }
        //set { this.SetProperty(ref this._ans, value); }
    }

    private bool _isSelected;
    public bool IsSelected
    {
        get { return this._isSelected; }
        set
        {
            _isSelected = value;
            FirePropertyChanged("IsSelected");
            //this.SetProperty(ref this._isSelected, value); 
        }
    }
}

FirePropertyChanged

public class NPCHelper : INotifyPropertyChanged
{
    public event PropertyChangedEventHandler PropertyChanged;
    public void FirePropertyChanged(string prop)
    {
        if (PropertyChanged != null)
            PropertyChanged(this, new PropertyChangedEventArgs(prop));
    }
}

Converter(which sometimes seems to be needed and others not..., I tried ~10 approaches from different tutorials/examples)

public class LogicToText : IValueConverter
{
    /// <summary>
    /// 
    /// </summary>
    public object Convert(object value, Type targetType, 
                          object parameter, string language)
    {
        //if (value == null || (bool)value == false)
          //  return "False";

        return value.ToString();
    }

    /// <summary>
    /// 
    /// </summary>
    public object ConvertBack(object value, Type targetType, 
                              object parameter, string language)
    {
        return value.ToString().Contains("True") ? true : false;
    }

Thanks in advance, and sorry for my English(still learning).

@edit Thanks for quick reply.

For test purposes I created a button and text block:

<Button Click="spr" >Sprawdź</Button>
<TextBlock Text="{Binding Answers[0].IsSelected, Mode=TwoWay}" > </TextBlock> 

It's in other controls part (above list box, but in FlipView) Click method

private void spr(object sender, RoutedEventArgs e)
    {
        var ans = ((PrawoJazdyDataQuestion)this.flipView.SelectedItem).Answers;
        foreach (var item in ans)
            item.IsSelected = item.IsSelected ? false : true;
    }

As I wrote, when i'm changing data from code side, it is changing content of element, but not appearance of ListBoxItem. And if I just select it on ListBox, it doesn't change the data in TextBlock neither in ListBox itself.

@edit2 fixing typos...

Answer 1

Do not bind to IsSelected on ListBoxItem. ListBox got SelectedItem or SelectedItems property, where You should pass item(s) to be selected, i.e. by binding. Setting IsSelected property in model is not good idea. Better make SelectedItem notify property in ViewModel.