How to add Data to a WPF datagrid programatically

.xaml:

<DataGrid x:Name="dataGrid" Margin="10">
    <DataGrid.Columns>
        <DataGridCheckBoxColumn Binding="{Binding Path=Column1}"/>
        <DataGridTextColumn Binding="{Binding Path=Column2}"/>
    </DataGrid.Columns>
</DataGrid>

.cs:

public class DataItem
{
    public bool Column1 { get; set; }
    public string Column2 { get; set; }
}

/// <summary>
/// Interaction logic for MainWindow.xaml
/// </summary>
public partial class MainWindow : Window
{
    public MainWindow()
    {
        InitializeComponent();
    }

    private void Window_Loaded(object sender, RoutedEventArgs e)
    {
        DataItem item = new DataItem();
        item.Column1 = true;
        item.Column2 = "test";
        dataGrid.Items.Add(item);
    }
}